A contribution to the modeling of metal plasticity and fracture: From continuum to discrete descriptions

NASA Astrophysics Data System (ADS)

Keralavarma, Shyam Mohan

The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill--Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified twodimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures.

Application of the Refined Zigzag Theory to the Modeling of Delaminations in Laminated Composites

NASA Technical Reports Server (NTRS)

Groh, Rainer M. J.; Weaver, Paul M.; Tessler, Alexander

2015-01-01

The Refined Zigzag Theory is applied to the modeling of delaminations in laminated composites. The commonly used cohesive zone approach is adapted for use within a continuum mechanics model, and then used to predict the onset and propagation of delamination in five cross-ply composite beams. The resin-rich area between individual composite plies is modeled explicitly using thin, discrete layers with isotropic material properties. A damage model is applied to these resin-rich layers to enable tracking of delamination propagation. The displacement jump across the damaged interfacial resin layer is captured using the zigzag function of the Refined Zigzag Theory. The overall model predicts the initiation of delamination to within 8% compared to experimental results and the load drop after propagation is represented accurately.

A homogenization-based quasi-discrete method for the fracture of heterogeneous materials

NASA Astrophysics Data System (ADS)

Berke, P. Z.; Peerlings, R. H. J.; Massart, T. J.; Geers, M. G. D.

2014-05-01

The understanding and the prediction of the failure behaviour of materials with pronounced microstructural effects is of crucial importance. This paper presents a novel computational methodology for the handling of fracture on the basis of the microscale behaviour. The basic principles presented here allow the incorporation of an adaptive discretization scheme of the structure as a function of the evolution of strain localization in the underlying microstructure. The proposed quasi-discrete methodology bridges two scales: the scale of the material microstructure, modelled with a continuum type description; and the structural scale, where a discrete description of the material is adopted. The damaging material at the structural scale is divided into unit volumes, called cells, which are represented as a discrete network of points. The scale transition is inspired by computational homogenization techniques; however it does not rely on classical averaging theorems. The structural discrete equilibrium problem is formulated in terms of the underlying fine scale computations. Particular boundary conditions are developed on the scale of the material microstructure to address damage localization problems. The performance of this quasi-discrete method with the enhanced boundary conditions is assessed using different computational test cases. The predictions of the quasi-discrete scheme agree well with reference solutions obtained through direct numerical simulations, both in terms of crack patterns and load versus displacement responses.

Continuum theory of fibrous tissue damage mechanics using bond kinetics: application to cartilage tissue engineering.

PubMed

Nims, Robert J; Durney, Krista M; Cigan, Alexander D; Dusséaux, Antoine; Hung, Clark T; Ateshian, Gerard A

2016-02-06

This study presents a damage mechanics framework that employs observable state variables to describe damage in isotropic or anisotropic fibrous tissues. In this mixture theory framework, damage is tracked by the mass fraction of bonds that have broken. Anisotropic damage is subsumed in the assumption that multiple bond species may coexist in a material, each having its own damage behaviour. This approach recovers the classical damage mechanics formulation for isotropic materials, but does not appeal to a tensorial damage measure for anisotropic materials. In contrast with the classical approach, the use of observable state variables for damage allows direct comparison of model predictions to experimental damage measures, such as biochemical assays or Raman spectroscopy. Investigations of damage in discrete fibre distributions demonstrate that the resilience to damage increases with the number of fibre bundles; idealizing fibrous tissues using continuous fibre distribution models precludes the modelling of damage. This damage framework was used to test and validate the hypothesis that growth of cartilage constructs can lead to damage of the synthesized collagen matrix due to excessive swelling caused by synthesized glycosaminoglycans. Therefore, alternative strategies must be implemented in tissue engineering studies to prevent collagen damage during the growth process.

Continuum theory of fibrous tissue damage mechanics using bond kinetics: application to cartilage tissue engineering

PubMed Central

Nims, Robert J.; Durney, Krista M.; Cigan, Alexander D.; Hung, Clark T.; Ateshian, Gerard A.

2016-01-01

This study presents a damage mechanics framework that employs observable state variables to describe damage in isotropic or anisotropic fibrous tissues. In this mixture theory framework, damage is tracked by the mass fraction of bonds that have broken. Anisotropic damage is subsumed in the assumption that multiple bond species may coexist in a material, each having its own damage behaviour. This approach recovers the classical damage mechanics formulation for isotropic materials, but does not appeal to a tensorial damage measure for anisotropic materials. In contrast with the classical approach, the use of observable state variables for damage allows direct comparison of model predictions to experimental damage measures, such as biochemical assays or Raman spectroscopy. Investigations of damage in discrete fibre distributions demonstrate that the resilience to damage increases with the number of fibre bundles; idealizing fibrous tissues using continuous fibre distribution models precludes the modelling of damage. This damage framework was used to test and validate the hypothesis that growth of cartilage constructs can lead to damage of the synthesized collagen matrix due to excessive swelling caused by synthesized glycosaminoglycans. Therefore, alternative strategies must be implemented in tissue engineering studies to prevent collagen damage during the growth process. PMID:26855751

Prediction of Size Effects in Notched Laminates Using Continuum Damage Mechanics

NASA Technical Reports Server (NTRS)

Camanho, D. P.; Maimi, P.; Davila, C. G.

2007-01-01

This paper examines the use of a continuum damage model to predict strength and size effects in notched carbon-epoxy laminates. The effects of size and the development of a fracture process zone before final failure are identified in an experimental program. The continuum damage model is described and the resulting predictions of size effects are compared with alternative approaches: the point stress and the inherent flaw models, the Linear-Elastic Fracture Mechanics approach, and the strength of materials approach. The results indicate that the continuum damage model is the most accurate technique to predict size effects in composites. Furthermore, the continuum damage model does not require any calibration and it is applicable to general geometries and boundary conditions.

Numerical modeling of fluid flow in a fault zone: a case of study from Majella Mountain (Italy).

NASA Astrophysics Data System (ADS)

Romano, Valentina; Battaglia, Maurizio; Bigi, Sabina; De'Haven Hyman, Jeffrey; Valocchi, Albert J.

2017-04-01

The study of fluid flow in fractured rocks plays a key role in reservoir management, including CO2 sequestration and waste isolation. We present a numerical model of fluid flow in a fault zone, based on field data acquired in Majella Mountain, in the Central Apennines (Italy). This fault zone is considered a good analogue for the massive presence of fluid migration in the form of tar. Faults are mechanical features and cause permeability heterogeneities in the upper crust, so they strongly influence fluid flow. The distribution of the main components (core, damage zone) can lead the fault zone to act as a conduit, a barrier, or a combined conduit-barrier system. We integrated existing information and our own structural surveys of the area to better identify the major fault features (e.g., type of fractures, statistical properties, geometrical and petro-physical characteristics). In our model the damage zones of the fault are described as discretely fractured medium, while the core of the fault as a porous one. Our model utilizes the dfnWorks code, a parallelized computational suite, developed at Los Alamos National Laboratory (LANL), that generates three dimensional Discrete Fracture Network (DFN) of the damage zones of the fault and characterizes its hydraulic parameters. The challenge of the study is the coupling between the discrete domain of the damage zones and the continuum one of the core. The field investigations and the basic computational workflow will be described, along with preliminary results of fluid flow simulation at the scale of the fault.

Landau-Zener transitions and Dykhne formula in a simple continuum model

NASA Astrophysics Data System (ADS)

Dunham, Yujin; Garmon, Savannah

The Landau-Zener model describing the interaction between two linearly driven discrete levels is useful in describing many simple dynamical systems; however, no system is completely isolated from the surrounding environment. Here we examine a generalizations of the original Landau-Zener model to study simple environmental influences. We consider a model in which one of the discrete levels is replaced with a energy continuum, in which we find that the survival probability for the initially occupied diabatic level is unaffected by the presence of the continuum. This result can be predicted by assuming that each step in the evolution for the diabatic state evolves independently according to the Landau-Zener formula, even in the continuum limit. We also show that, at least for the simplest model, this result can also be predicted with the natural generalization of the Dykhne formula for open systems. We also observe dissipation as the non-escape probability from the discrete levels is no longer equal to one.

Discrete structures in continuum descriptions of defective crystals

PubMed Central

2016-01-01

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of ‘plastic strain variables’, which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. PMID:27002070

Hybrid discrete/continuum algorithms for stochastic reaction networks

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; ...

2014-10-22

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less

Discrete structures in continuum descriptions of defective crystals.

PubMed

Parry, G P

2016-04-28

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of 'plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. © 2016 The Author(s).

Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models

NASA Technical Reports Server (NTRS)

Saether, Erik; Hochhalter, Jacob D.; Glaessgen, Edward H.

2012-01-01

A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.

A Micro-Mechanism-Based Continuum Corrosion Fatigue Damage Model for Steels

NASA Astrophysics Data System (ADS)

Sun, Bin; Li, Zhaoxia

2018-05-01

A micro-mechanism-based corrosion fatigue damage model is developed for studying the high-cycle corrosion fatigue of steel from multi-scale viewpoint. The developed physical corrosion fatigue damage model establishes micro-macro relationships between macroscopic continuum damage evolution and collective evolution behavior of microscopic pits and cracks, which can be used to describe the multi-scale corrosion fatigue process of steel. As a case study, the model is used to predict continuum damage evolution and number density of the corrosion pit and short crack of steel component in 5% NaCl water under constant stress amplitude at 20 kHz, and the numerical results are compared with experimental results. It shows that the model is effective and can be used to evaluate the continuum macroscopic corrosion fatigue damage and study microscopic corrosion fatigue mechanisms of steel.

A Micro-Mechanism-Based Continuum Corrosion Fatigue Damage Model for Steels

NASA Astrophysics Data System (ADS)

Sun, Bin; Li, Zhaoxia

2018-04-01

A micro-mechanism-based corrosion fatigue damage model is developed for studying the high-cycle corrosion fatigue of steel from multi-scale viewpoint. The developed physical corrosion fatigue damage model establishes micro-macro relationships between macroscopic continuum damage evolution and collective evolution behavior of microscopic pits and cracks, which can be used to describe the multi-scale corrosion fatigue process of steel. As a case study, the model is used to predict continuum damage evolution and number density of the corrosion pit and short crack of steel component in 5% NaCl water under constant stress amplitude at 20 kHz, and the numerical results are compared with experimental results. It shows that the model is effective and can be used to evaluate the continuum macroscopic corrosion fatigue damage and study microscopic corrosion fatigue mechanisms of steel.

On crack initiation in notched, cross-plied polymer matrix composites

NASA Astrophysics Data System (ADS)

Yang, Q. D.; Schesser, D.; Niess, M.; Wright, P.; Mavrogordato, M. N.; Sinclair, I.; Spearing, S. M.; Cox, B. N.

2015-05-01

The physics of crack initiation in a polymer matrix composite are investigated by varying the modeling choices made in simulations and comparing the resulting predictions with high-resolution in situ images of cracks. Experimental data were acquired using synchrotron-radiation computed tomography (SRCT) at a resolution on the order of 1 μm, which provides detailed measurement of the location, shape, and size of small cracks, as well as the crack opening and shear displacements. These data prove sufficient to discriminate among competing physical descriptions of crack initiation. Simulations are executed with a high-fidelity formulation, the augmented finite element method (A-FEM), which permits consideration of coupled damage mechanisms, including both discrete cracks and fine-scale continuum damage. The discrete cracks are assumed to be nonlinear fracture events, governed by reasonably general mixed-mode cohesive laws. Crack initiation is described in terms of strength parameters within the cohesive laws, so that the cohesive law provides a unified model for crack initiation and growth. Whereas the cracks investigated are typically 1 mm or less in length, the fine-scale continuum damage refers to irreversible matrix deformation occurring over gauge lengths extending down to the fiber diameter (0.007 mm). We find that the location and far-field stress for crack initiation are predicted accurately only if the variations of local stress within plies and in the presence of stress concentrators (notches, etc.) are explicitly computed and used in initiation criteria; stress redistribution due to matrix nonlinearity that occurs prior to crack initiation is accounted for; and a mixed-mode criterion is used for crack initiation. If these factors are not all considered, which is the case for commonly used failure criteria, predictions of the location and far-field stress for initiation are not accurate.

Experimental verification of a progressive damage model for composite laminates based on continuum damage mechanics. M.S. Thesis Final Report

NASA Technical Reports Server (NTRS)

Coats, Timothy William

1994-01-01

Progressive failure is a crucial concern when using laminated composites in structural design. Therefore the ability to model damage and predict the life of laminated composites is vital. The purpose of this research was to experimentally verify the application of the continuum damage model, a progressive failure theory utilizing continuum damage mechanics, to a toughened material system. Damage due to tension-tension fatigue was documented for the IM7/5260 composite laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables, respectively, to predict stiffness loss. A damage dependent finite element code qualitatively predicted trends in transverse matrix cracking, axial splits and local stress-strain distributions for notched quasi-isotropic laminates. The predictions were similar to the experimental data and it was concluded that the continuum damage model provided a good prediction of stiffness loss while qualitatively predicting damage growth in notched laminates.

An Off-Lattice Hybrid Discrete-Continuum Model of Tumor Growth and Invasion

PubMed Central

Jeon, Junhwan; Quaranta, Vito; Cummings, Peter T.

2010-01-01

Abstract We have developed an off-lattice hybrid discrete-continuum (OLHDC) model of tumor growth and invasion. The continuum part of the OLHDC model describes microenvironmental components such as matrix-degrading enzymes, nutrients or oxygen, and extracellular matrix (ECM) concentrations, whereas the discrete portion represents individual cell behavior such as cell cycle, cell-cell, and cell-ECM interactions and cell motility by the often-used persistent random walk, which can be depicted by the Langevin equation. Using this framework of the OLHDC model, we develop a phenomenologically realistic and bio/physically relevant model that encompasses the experimentally observed superdiffusive behavior (at short times) of mammalian cells. When systemic simulations based on the OLHDC model are performed, tumor growth and its morphology are found to be strongly affected by cell-cell adhesion and haptotaxis. There is a combination of the strength of cell-cell adhesion and haptotaxis in which fingerlike shapes, characteristic of invasive tumor, are observed. PMID:20074513

Discretization-dependent model for weakly connected excitable media

NASA Astrophysics Data System (ADS)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Continuum and discrete approach in modeling biofilm development and structure: a review.

PubMed

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Continuum modeling of the mechanical and thermal behavior of discrete large structures

NASA Technical Reports Server (NTRS)

Nayfeh, A. H.; Hefzy, M. S.

1980-01-01

In the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss-like repetitive structures. Once the actual structure is specified, the construction procedure can be outlined by the following three steps: (a) all sets of parallel members are identified, (b) unidirectional 'effective continuum' properties are derived for each of these sets and (c) orthogonal transformations are finally used to determine the contribution of each set to the 'overall effective continuum' properties of the structure. Here the properties includes mechanical (stiffnesses), thermal (coefficients of thermal expansions) and material densities. Once expanded descriptions of the steps (b) and (c) are done, the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods.

Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach.

PubMed

Rausch, M K; Karniadakis, G E; Humphrey, J D

2017-02-01

Biological soft tissues experience damage and failure as a result of injury, disease, or simply age; examples include torn ligaments and arterial dissections. Given the complexity of tissue geometry and material behavior, computational models are often essential for studying both damage and failure. Yet, because of the need to account for discontinuous phenomena such as crazing, tearing, and rupturing, continuum methods are limited. Therefore, we model soft tissue damage and failure using a particle/continuum approach. Specifically, we combine continuum damage theory with Smoothed Particle Hydrodynamics (SPH). Because SPH is a meshless particle method, and particle connectivity is determined solely through a neighbor list, discontinuities can be readily modeled by modifying this list. We show, for the first time, that an anisotropic hyperelastic constitutive model commonly employed for modeling soft tissue can be conveniently implemented within a SPH framework and that SPH results show excellent agreement with analytical solutions for uniaxial and biaxial extension as well as finite element solutions for clamped uniaxial extension in 2D and 3D. We further develop a simple algorithm that automatically detects damaged particles and disconnects the spatial domain along rupture lines in 2D and rupture surfaces in 3D. We demonstrate the utility of this approach by simulating damage and failure under clamped uniaxial extension and in a peeling experiment of virtual soft tissue samples. In conclusion, SPH in combination with continuum damage theory may provide an accurate and efficient framework for modeling damage and failure in soft tissues.

Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach

PubMed Central

Rausch, M. K.; Karniadakis, G. E.; Humphrey, J. D.

2016-01-01

Biological soft tissues experience damage and failure as a result of injury, disease, or simply age; examples include torn ligaments and arterial dissections. Given the complexity of tissue geometry and material behavior, computational models are often essential for studying both damage and failure. Yet, because of the need to account for discontinuous phenomena such as crazing, tearing, and rupturing, continuum methods are limited. Therefore, we model soft tissue damage and failure using a particle/continuum approach. Specifically, we combine continuum damage theory with Smoothed Particle Hydrodynamics (SPH). Because SPH is a meshless particle method, and particle connectivity is determined solely through a neighbor list, discontinuities can be readily modeled by modifying this list. We show, for the first time, that an anisotropic hyperelastic constitutive model commonly employed for modeling soft tissue can be conveniently implemented within a SPH framework and that SPH results show excellent agreement with analytical solutions for uniaxial and biaxial extension as well as finite element solutions for clamped uniaxial extension in 2D and 3D. We further develop a simple algorithm that automatically detects damaged particles and disconnects the spatial domain along rupture lines in 2D and rupture surfaces in 3D. We demonstrate the utility of this approach by simulating damage and failure under clamped uniaxial extension and in a peeling experiment of virtual soft tissue samples. In conclusion, SPH in combination with continuum damage theory may provide an accurate and efficient framework for modeling damage and failure in soft tissues. PMID:27538848

Dynamical discrete/continuum linear response shells theory of solvation: convergence test for NH4+ and OH- ions in water solution using DFT and DFTB methods.

PubMed

de Lima, Guilherme Ferreira; Duarte, Hélio Anderson; Pliego, Josefredo R

2010-12-09

A new dynamical discrete/continuum solvation model was tested for NH(4)(+) and OH(-) ions in water solvent. The method is similar to continuum solvation models in a sense that the linear response approximation is used. However, different from pure continuum models, explicit solvent molecules are included in the inner shell, which allows adequate treatment of specific solute-solvent interactions present in the first solvation shell, the main drawback of continuum models. Molecular dynamics calculations coupled with SCC-DFTB method are used to generate the configurations of the solute in a box with 64 water molecules, while the interaction energies are calculated at the DFT level. We have tested the convergence of the method using a variable number of explicit water molecules and it was found that even a small number of waters (as low as 14) are able to produce converged values. Our results also point out that the Born model, often used for long-range correction, is not reliable and our method should be applied for more accurate calculations.

Exact static solutions for discrete phi4 models free of the Peierls-Nabarro barrier: discretized first-integral approach.

PubMed

Dmitriev, S V; Kevrekidis, P G; Yoshikawa, N; Frantzeskakis, D J

2006-10-01

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested by Dmitriev [J. Phys. A 38, 7617 (2005)]. We then discuss some discrete phi4 models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently by Cooper [Phys. Rev. E 72, 036605 (2005)] but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schrödinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum phi4 equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

NASA Technical Reports Server (NTRS)

Campbell, Joel

2007-01-01

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

The SMM model as a boundary value problem using the discrete diffusion equation.

PubMed

Campbell, Joel

2007-12-01

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Quantum mechanical/molecular mechanical/continuum style solvation model: linear response theory, variational treatment, and nuclear gradients.

PubMed

Li, Hui

2009-11-14

Linear response and variational treatment are formulated for Hartree-Fock (HF) and Kohn-Sham density functional theory (DFT) methods and combined discrete-continuum solvation models that incorporate self-consistently induced dipoles and charges. Due to the variational treatment, analytic nuclear gradients can be evaluated efficiently for these discrete and continuum solvation models. The forces and torques on the induced point dipoles and point charges can be evaluated using simple electrostatic formulas as for permanent point dipoles and point charges, in accordance with the electrostatic nature of these methods. Implementation and tests using the effective fragment potential (EFP, a polarizable force field) method and the conductorlike polarizable continuum model (CPCM) show that the nuclear gradients are as accurate as those in the gas phase HF and DFT methods. Using B3LYP/EFP/CPCM and time-dependent-B3LYP/EFP/CPCM methods, acetone S(0)-->S(1) excitation in aqueous solution is studied. The results are close to those from full B3LYP/CPCM calculations.

A Geometrically Nonlinear Phase Field Theory of Brittle Fracture

DTIC Science & Technology

2014-10-01

of crack propagation. Philos Mag 91:75–95 Sun X, Khaleel M (2004) Modeling of glass fracture damage using continuum damage mechanics -static spherical...elastic fracture mechanics ). Engineering finite element (FE) simula- tions often invoke continuum damage mechanics the- ories, wherein the tangent...stiffness of a material ele- ment degrades as “damage” accumulates.Conventional continuum damage mechanics theories (Clayton and McDowell 2003, 2004; Sun and

Multiscale Simulations of Reactive Transport

NASA Astrophysics Data System (ADS)

Tartakovsky, D. M.; Bakarji, J.

2014-12-01

Discrete, particle-based simulations offer distinct advantages when modeling solute transport and chemical reactions. For example, Brownian motion is often used to model diffusion in complex pore networks, and Gillespie-type algorithms allow one to handle multicomponent chemical reactions with uncertain reaction pathways. Yet such models can be computationally more intensive than their continuum-scale counterparts, e.g., advection-dispersion-reaction equations. Combining the discrete and continuum models has a potential to resolve the quantity of interest with a required degree of physicochemical granularity at acceptable computational cost. We present computational examples of such "hybrid models" and discuss the challenges associated with coupling these two levels of description.

Numerical study of multi-point forming of thick sheet using remeshing procedure

NASA Astrophysics Data System (ADS)

Cherouat, A.; Ma, X.; Borouchaki, H.; Zhang, Q.

2018-05-01

Multi-point forming MPF is an innovative technology of manufacturing complex thick sheet metal products without the need for solid tools. The central component of this system is a pair of the desired discrete matrices of punches, and die surface constructed by changing the positions of the tools though CAD and a control system. Because reconfigurable discrete tools are used, part-manufacturing costs are reduced and manufacturing time is shorten substantially. Firstly, in this work we develop constitutive equations which couples isotropic ductile damage into various flow stress based on the Continuum Damage Mechanic theory. The modified Johnson-Cook flow model fully coupled with an isotropic ductile damage is established using the quasi-unilateral damage evolution for considering both the open and the close of micro-cracks. During the forming processes severe mesh distortion of elements occur after a few incremental forming steps. Secondly, we introduce 3D adaptive remeshing procedure based on linear tetrahedral element and geometrical/physical errors estimation to optimize the element quality, to refine the mesh size in the whole model and to adapt the deformed mesh to the tools geometry. Simulation of the MPF process (see Fig. 1) and the unloading spring-back are carried out using adaptive remeshing scheme using the commercial finite element package ABAQUS and OPTIFORM mesher. Subsequently, influencing factors of MPF spring-back are researched to investigate the MPF spring-back tendency with the proposed remeshing procedure.

Hotspot-Ridge Interaction: Shaping the Geometry of Mid-Ocean Ridges

NASA Astrophysics Data System (ADS)

Mittelstaedt, E.; Ito, G.

2004-12-01

Surface manifestations of hotspot-ridge interaction include geochemical anomalies, elevated ridge topography, negative gravity anomalies, off-axis volcanic lineaments, and ridge reorganization events. The last of these is expressed as either "captured" ridge segments due to asymmetric spreading, such as at the Galapagos, or as discrete jumps of the ridge axis toward the hotspot, such as at the Iceland, Tristan de Cuhna, Discovery, Shona, Louisville, Kerguelen, and Reunion hotspots. Mid-ocean ridge axis reorganizations through discrete jumps will cause variations in local volcanic patterns, lead to changes in overall plate shape and ridge axis morphology, and alter local mantle flow patterns. It has been proposed that discrete ridge jumps are a product of interaction between the lithosphere and a mantle plume. We examine this hypothesis using thin plate theory coupled with continuum damage mechanics to calculate the two-dimensional (plan-view) pattern of depth-integrated stresses in a plate of varying thickness with weakening due to volcanism at the ridge and above the plume center. Forces on the plate include plume shear, plate parallel gravitational forces due to buoyant uplift, and a prescribed velocity of plate motion along the edges of the model. We explore these forces and the effect of damage as mechanisms that may be required to predict ridge jumps.

Combined discrete particle and continuum model predicting solid-state fermentation in a drum fermentor.

PubMed

Schutyser, M A I; Briels, W J; Boom, R M; Rinzema, A

2004-05-20

The development of mathematical models facilitates industrial (large-scale) application of solid-state fermentation (SSF). In this study, a two-phase model of a drum fermentor is developed that consists of a discrete particle model (solid phase) and a continuum model (gas phase). The continuum model describes the distribution of air in the bed injected via an aeration pipe. The discrete particle model describes the solid phase. In previous work, mixing during SSF was predicted with the discrete particle model, although mixing simulations were not carried out in the current work. Heat and mass transfer between the two phases and biomass growth were implemented in the two-phase model. Validation experiments were conducted in a 28-dm3 drum fermentor. In this fermentor, sufficient aeration was provided to control the temperatures near the optimum value for growth during the first 45-50 hours. Several simulations were also conducted for different fermentor scales. Forced aeration via a single pipe in the drum fermentors did not provide homogeneous cooling in the substrate bed. Due to large temperature gradients, biomass yield decreased severely with increasing size of the fermentor. Improvement of air distribution would be required to avoid the need for frequent mixing events, during which growth is hampered. From these results, it was concluded that the two-phase model developed is a powerful tool to investigate design and scale-up of aerated (mixed) SSF fermentors. Copyright 2004 Wiley Periodicals, Inc.

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

A note on the discrete approach for generalized continuum models

NASA Astrophysics Data System (ADS)

Kalampakas, Antonios; Aifantis, Elias C.

2014-12-01

Generalized continuum theories for materials and processes have been introduced in order to account in a phenomenological manner for microstructural effects. Their drawback mainly rests in the determination of the extra phenomenological coefficients through experiments and simulations. It is shown here that a graphical representation of the local topology describing deformation models can be used to deduce restrictions on the phenomenological coefficients of the gradient elasticity continuum theories.

Development of a multiaxial viscoelastoplastic continuum damage model for asphalt mixtures.

DOT National Transportation Integrated Search

2009-09-01

This report highlights findings from the FHWA DTFH61-05-H-00019 project, which focused on the development of the multiaxial viscoelastoplastic continuum damage model for asphalt concrete in both compression and tension. Asphalt concrete pavement, one...

On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

DOE PAGES

Seleson, Pablo; Du, Qiang; Parks, Michael L.

2016-08-16

The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest-neighbor discretizations should be avoided in peridynamic simulations involving cracks, such discretizations are viable, for example for verification or validation purposes, in problems characterized by smooth deformations. Furthermore, we demonstrate that better quadrature rules in peridynamics can be obtained based on the functional form of solutions.« less

Discrete differential geometry: The nonplanar quadrilateral mesh

NASA Astrophysics Data System (ADS)

Twining, Carole J.; Marsland, Stephen

2012-06-01

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

Differential porosimetry and permeametry for random porous media.

PubMed

Hilfer, R; Lemmer, A

2015-07-01

Accurate determination of geometrical and physical properties of natural porous materials is notoriously difficult. Continuum multiscale modeling has provided carefully calibrated realistic microstructure models of reservoir rocks with floating point accuracy. Previous measurements using synthetic microcomputed tomography (μ-CT) were based on extrapolation of resolution-dependent properties for discrete digitized approximations of the continuum microstructure. This paper reports continuum measurements of volume and specific surface with full floating point precision. It also corrects an incomplete description of rotations in earlier publications. More importantly, the methods of differential permeametry and differential porosimetry are introduced as precision tools. The continuum microstructure chosen to exemplify the methods is a homogeneous, carefully calibrated and characterized model for Fontainebleau sandstone. The sample has been publicly available since 2010 on the worldwide web as a benchmark for methodical studies of correlated random media. High-precision porosimetry gives the volume and internal surface area of the sample with floating point accuracy. Continuum results with floating point precision are compared to discrete approximations. Differential porosities and differential surface area densities allow geometrical fluctuations to be discriminated from discretization effects and numerical noise. Differential porosimetry and Fourier analysis reveal subtle periodic correlations. The findings uncover small oscillatory correlations with a period of roughly 850μm, thus implying that the sample is not strictly stationary. The correlations are attributed to the deposition algorithm that was used to ensure the grain overlap constraint. Differential permeabilities are introduced and studied. Differential porosities and permeabilities provide scale-dependent information on geometry fluctuations, thereby allowing quantitative error estimates.

Bottom-up modeling of damage in heterogeneous quasi-brittle solids

NASA Astrophysics Data System (ADS)

Rinaldi, Antonio

2013-03-01

The theoretical modeling of multisite cracking in quasi-brittle materials is a complex damage problem, hard to model with traditional methods of fracture mechanics due to its multiscale nature and to strain localization induced by microcracks interaction. Macroscale "effective" elastic models can be conveniently applied if a suitable Helmholtz free energy function is identified for a given material scenario. Del Piero and Truskinovsky (Continuum Mech Thermodyn 21:141-171, 2009), among other authors, investigated macroscale continuum solutions capable of matching—in a top-down view—the phenomenology of the damage process for quasi-brittle materials regardless of the microstructure. On the contrary, this paper features a physically based solution method that starts from the direct consideration of the microscale properties and, in a bottom-up view, recovers a continuum elastic description. This procedure is illustrated for a simple one-dimensional problem of this type, a bar modeled stretched by an axial displacement, where the bar is modeled as a 2D random lattice of decohesive spring elements of finite strength. The (microscale) data from simulations are used to identify the "exact" (macro-) damage parameter and to build up the (macro-) Helmholtz function for the equivalent elastic model, bridging the macroscale approach by Del Piero and Truskinovsky. The elastic approach, coupled with microstructural knowledge, becomes a more powerful tool to reproduce a broad class of macroscopic material responses by changing the convexity-concavity of the Helmholtz energy. The analysis points out that mean-field statistics are appropriate prior to damage localization but max-field statistics are better suited in the softening regime up to failure, where microstrain fluctuation needs to be incorporated in the continuum model. This observation is of consequence to revise mean-field damage models from literature and to calibrate Nth gradient continuum models.

Equivalent-Continuum Modeling of Nano-Structured Materials

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Gates, Thomas S.; Nicholson, Lee M.; Wise, Kristopher E.

2001-01-01

A method has been developed for modeling structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalent-continuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.

Continuum simulation of the discharge of the granular silo: a validation test for the μ(I) visco-plastic flow law.

PubMed

Staron, L; Lagrée, P-Y; Popinet, S

2014-01-01

Using a continuum Navier-Stokes solver with the μ(I) flow law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt a quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement for the velocity is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement, while bulk deformations are found to be similar in both approaches. The influence of the parameters of the μ(I) flow law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. However, potential problems involving the systems size, the configuration and "non-local" effects, are suggested. Yet the general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.

PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils

NASA Technical Reports Server (NTRS)

Johnson, Scott; Walton, Otis; Settgast, Randolph

2013-01-01

PowderSim is a calculation tool that combines a discrete-element method (DEM) module, including calibrated interparticle-interaction relationships, with a mesh-free, continuum, SPH (smoothed-particle hydrodynamics) based module that utilizes enhanced, calibrated, constitutive models capable of mimicking both large deformations and the flow behavior of regolith simulants and lunar regolith under conditions anticipated during in situ resource utilization (ISRU) operations. The major innovation introduced in PowderSim is to use a mesh-free method (SPH-based) with a calibrated and slightly modified critical-state soil mechanics constitutive model to extend the ability of the simulation tool to also address full-scale engineering systems in the continuum sense. The PowderSim software maintains the ability to address particle-scale problems, like size segregation, in selected regions with a traditional DEM module, which has improved contact physics and electrostatic interaction models.

Setting up virgin stress conditions in discrete element models.

PubMed

Rojek, J; Karlis, G F; Malinowski, L J; Beer, G

2013-03-01

In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain.

Setting up virgin stress conditions in discrete element models

PubMed Central

Rojek, J.; Karlis, G.F.; Malinowski, L.J.; Beer, G.

2013-01-01

In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain. PMID:27087731

A finite deformation viscoelastic-viscoplastic constitutive model for self-healing materials

NASA Astrophysics Data System (ADS)

Shahsavari, H.; Naghdabadi, R.; Baghani, M.; Sohrabpour, S.

2016-12-01

In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing variables and employing the strain equivalence hypothesis, the strain tensor is determined in the effective configuration. Satisfying the Clausius-Duhem inequality, the evolution equations are introduced for the viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different prescribed functions. To employ the proposed model in different loading conditions, the model is discretized in the semi-implicit form. Material parameters of the model are identified employing experimental tests on asphalt mixes available in the literature. Finally, capability of the model is demonstrated comparing the model predictions in the creep-recovery and repeated creep-recovery with the experimental results available in the literature and a good agreement between predicted and test results is revealed.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Continuum damage model for ferroelectric materials and its application to multilayer actuators

NASA Astrophysics Data System (ADS)

Gellmann, Roman; Ricoeur, Andreas

2016-05-01

In this paper a micromechanical continuum damage model for ferroelectric materials is presented. As a constitutive law it is implemented into a finite element (FE) code. The model is based on micromechanical considerations of domain switching and its interaction with microcrack growth and coalescence. A FE analysis of a multilayer actuator is performed, showing the initiation of damage zones at the electrode tips during the poling process. Further, the influence of mechanical pre-stressing on damage evolution and actuating properties is investigated. The results provided in this work give useful information on the damage of advanced piezoelectric devices and their optimization.

System reliability approaches for advanced propulsion system structures

NASA Technical Reports Server (NTRS)

Cruse, T. A.; Mahadevan, S.

1991-01-01

This paper identifies significant issues that pertain to the estimation and use of system reliability in the design of advanced propulsion system structures. Linkages between the reliabilities of individual components and their effect on system design issues such as performance, cost, availability, and certification are examined. The need for system reliability computation to address the continuum nature of propulsion system structures and synergistic progressive damage modes has been highlighted. Available system reliability models are observed to apply only to discrete systems. Therefore a sequential structural reanalysis procedure is formulated to rigorously compute the conditional dependencies between various failure modes. The method is developed in a manner that supports both top-down and bottom-up analyses in system reliability.

Modeling damage in concrete pavements and bridges.

DOT National Transportation Integrated Search

2010-09-01

This project focused on micromechanical modeling of damage in concrete under general, multi-axial loading. A : continuum-level, three-dimensional constitutive model based on micromechanics was developed. The model : accounts for damage in concrete by...

Toward generalized continuum models of granular soil and granular soil-tire interaction: A combined discrete element and thermomicromechanical continuum analysis of densely packed assemblies

DTIC Science & Technology

2007-04-30

flow and deformation of soils in contact with metallic and/or rubber -like bodies” Proceedings, 13th International Conference of the ISTVS 1, pp 201-208...soil- tyre interaction problem”, Proceedings, First North American Workshop on Modeling the Mechanics of Off-Road Mobility. Paper GL-94-30 U.S

Basal friction evolution and crevasse distribution during the surge of Basin 3, Austfonna ice-cap - offline coupling between a continuum ice dynamic model and a discrete element model

NASA Astrophysics Data System (ADS)

Gong, Yongmei; Zwinger, Thomas; Åström, Jan; Gladstone, Rupert; Schellenberger, Thomas; Altena, Bas; Moore, John

2017-04-01

The outlet glacier at Basin 3, Austfonna ice-cap entered its active surge phase in autumn 2012. We assess the evolution of the basal friction during the surge through inverse modelling of basal friction coefficients using recent velocity observation from 2012 to 2014 in a continuum ice dynamic model Elmer/ice. The obtained basal friction coefficient distributions at different time instances are further used as a boundary condition in a discrete element model (HiDEM) that is capable of computing fracturing of ice. The inverted basal friction coefficient evolution shows a gradual 'unplugging' of the stagnant frontal area and northwards and inland expansion of the fast flowing region in the southern basin. The validation between the modeled crevasses distribution and the satellite observation in August 2013 shows a good agreement in shear zones inland and at the frontal area. Crevasse distributions of the summer before and after the glacier reached its maximum velocity in January 2013 (August 2012 and August 2014, respectively) are also evaluated. Previous studies suggest the triggering and development of the surge are linked to surface melt water penetrating through ice to form an efficient basal hydrology system thereby triggering a hydro- thermodynamic feedback. This preliminary offline coupling between a continuum ice dynamic model and a discrete element model will give a hint on future model development of linking supra-glacial to sub-glacial hydrology system.

A Behavioral Continuum: A Look at Personality Disorders.

ERIC Educational Resources Information Center

Harris, George; Kirk, Nancy A.

1985-01-01

Suggests that narcissistic, borderline, and antisocial personality disorders are not discrete diagnostic categories, but that they lie along a continuum and have in common the dimensions of degree of self-centeredness and degree of differentiation. Presents evidence supporting existence of continuum of behavior rather than discrete diagnostic…

Parameterisation of multi-scale continuum perfusion models from discrete vascular networks.

PubMed

Hyde, Eoin R; Michler, Christian; Lee, Jack; Cookson, Andrew N; Chabiniok, Radek; Nordsletten, David A; Smith, Nicolas P

2013-05-01

Experimental data and advanced imaging techniques are increasingly enabling the extraction of detailed vascular anatomy from biological tissues. Incorporation of anatomical data within perfusion models is non-trivial, due to heterogeneous vessel density and disparate radii scales. Furthermore, previous idealised networks have assumed a spatially repeating motif or periodic canonical cell, thereby allowing for a flow solution via homogenisation. However, such periodicity is not observed throughout anatomical networks. In this study, we apply various spatial averaging methods to discrete vascular geometries in order to parameterise a continuum model of perfusion. Specifically, a multi-compartment Darcy model was used to provide vascular scale separation for the fluid flow. Permeability tensor fields were derived from both synthetic and anatomically realistic networks using (1) porosity-scaled isotropic, (2) Huyghe and Van Campen, and (3) projected-PCA methods. The Darcy pressure fields were compared via a root-mean-square error metric to an averaged Poiseuille pressure solution over the same domain. The method of Huyghe and Van Campen performed better than the other two methods in all simulations, even for relatively coarse networks. Furthermore, inter-compartment volumetric flux fields, determined using the spatially averaged discrete flux per unit pressure difference, were shown to be accurate across a range of pressure boundary conditions. This work justifies the application of continuum flow models to characterise perfusion resulting from flow in an underlying vascular network.

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. Part II: impact modeling

NASA Astrophysics Data System (ADS)

Pigazzini, M. S.; Bazilevs, Y.; Ellison, A.; Kim, H.

2017-11-01

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on isogeometric analysis, where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum damage mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

A new multi-layer approach for progressive damage simulation in composite laminates based on isogeometric analysis and Kirchhoff-Love shells. Part I: basic theory and modeling of delamination and transverse shear

NASA Astrophysics Data System (ADS)

Bazilevs, Y.; Pigazzini, M. S.; Ellison, A.; Kim, H.

2017-11-01

In this two-part paper we introduce a new formulation for modeling progressive damage in laminated composite structures. We adopt a multi-layer modeling approach, based on Isogeometric Analysis (IGA), where each ply or lamina is represented by a spline surface, and modeled as a Kirchhoff-Love thin shell. Continuum Damage Mechanics is used to model intralaminar damage, and a new zero-thickness cohesive-interface formulation is introduced to model delamination as well as permitting laminate-level transverse shear compliance. In Part I of this series we focus on the presentation of the modeling framework, validation of the framework using standard Mode I and Mode II delamination tests, and assessment of its suitability for modeling thick laminates. In Part II of this series we focus on the application of the proposed framework to modeling and simulation of damage in composite laminates resulting from impact. The proposed approach has significant accuracy and efficiency advantages over existing methods for modeling impact damage. These stem from the use of IGA-based Kirchhoff-Love shells to represent the individual plies of the composite laminate, while the compliant cohesive interfaces enable transverse shear deformation of the laminate. Kirchhoff-Love shells give a faithful representation of the ply deformation behavior, and, unlike solids or traditional shear-deformable shells, do not suffer from transverse-shear locking in the limit of vanishing thickness. This, in combination with higher-order accurate and smooth representation of the shell midsurface displacement field, allows us to adopt relatively coarse in-plane discretizations without sacrificing solution accuracy. Furthermore, the thin-shell formulation employed does not use rotational degrees of freedom, which gives additional efficiency benefits relative to more standard shell formulations.

Multiscale Fiber Kinking: Computational Micromechanics and a Mesoscale Continuum Damage Mechanics Models

NASA Technical Reports Server (NTRS)

Herraez, Miguel; Bergan, Andrew C.; Gonzalez, Carlos; Lopes, Claudio S.

2017-01-01

In this work, the fiber kinking phenomenon, which is known as the failure mechanism that takes place when a fiber reinforced polymer is loaded under longitudinal compression, is studied. A computational micromechanics model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking based on the deformation gradient decomposition (DGD) and the LaRC04 failure criteria.

A dual-phase microstructural approach to damage and fracture of Ti3SiC2/SiC joints

NASA Astrophysics Data System (ADS)

Nguyen, Ba Nghiep; Henager, Charles H.; Kurtz, Richard J.

2018-02-01

The microcracking mechanisms responsible for Ti3SiC2/SiC joint damage observed at the macroscopic scale after neutron irradiation experiments are investigated in detail. A dual-phase microstructural approach to damage and fracture of Ti3SiC2/SiC joints is developed that uses a finely discretized two-phase domain based on a digital image of an actual microstructure involving embedded Ti3SiC2 and SiC phases. The behaviors of SiC and Ti3SiC2 in the domain are described by the continuum damage mechanics (CDM) model reported in Nguyen et al., J. Nucl. Mater., 2017, 495:504-515. This CDM model describes microcracking damage in brittle ceramics caused by thermomechanical loading and irradiation-induced swelling. The dual-phase microstructural model is applied to predict the microcracking mechanisms occurring in a typical Ti3SiC2/SiC joint subjected to heating to 800 °C followed by irradiation-induced swelling at this temperature and cooling to room temperature after the applied swelling has reached the maximum swelling levels observed in the experiments for SiC and Ti3SiC2. The model predicts minor damage of the joint after heating but significant microcracking in the SiC phase and along the boundaries between SiC and Ti3SiC2 as well as along the bonding joint during irradiation-induced swelling and cooling to room temperature. These predictions qualitatively agree with the limited experimental observations of joint damage at this irradiation temperature.

Discrete Calculus as a Bridge between Scales

NASA Astrophysics Data System (ADS)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

Computational modeling of brain tumors: discrete, continuum or hybrid?

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Deisboeck, Thomas S.

In spite of all efforts, patients diagnosed with highly malignant brain tumors (gliomas), continue to face a grim prognosis. Achieving significant therapeutic advances will also require a more detailed quantitative understanding of the dynamic interactions among tumor cells, and between these cells and their biological microenvironment. Data-driven computational brain tumor models have the potential to provide experimental tumor biologists with such quantitative and cost-efficient tools to generate and test hypotheses on tumor progression, and to infer fundamental operating principles governing bidirectional signal propagation in multicellular cancer systems. This review highlights the modeling objectives of and challenges with developing such in silico brain tumor models by outlining two distinct computational approaches: discrete and continuum, each with representative examples. Future directions of this integrative computational neuro-oncology field, such as hybrid multiscale multiresolution modeling are discussed.

Computational modeling of brain tumors: discrete, continuum or hybrid?

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Deisboeck, Thomas S.

2008-04-01

In spite of all efforts, patients diagnosed with highly malignant brain tumors (gliomas), continue to face a grim prognosis. Achieving significant therapeutic advances will also require a more detailed quantitative understanding of the dynamic interactions among tumor cells, and between these cells and their biological microenvironment. Data-driven computational brain tumor models have the potential to provide experimental tumor biologists with such quantitative and cost-efficient tools to generate and test hypotheses on tumor progression, and to infer fundamental operating principles governing bidirectional signal propagation in multicellular cancer systems. This review highlights the modeling objectives of and challenges with developing such in silicobrain tumor models by outlining two distinct computational approaches: discrete and continuum, each with representative examples. Future directions of this integrative computational neuro-oncology field, such as hybrid multiscale multiresolution modeling are discussed.

Level Density in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Myo, T.; Katō, K.

2005-06-01

It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of L(2) basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.

Diffusion of multiple species with excluded-volume effects.

PubMed

Bruna, Maria; Chapman, S Jonathan

2012-11-28

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

NASA Astrophysics Data System (ADS)

Petsev, Nikolai D.; Leal, L. Gary; Shell, M. Scott

2017-12-01

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely resolved (e.g., molecular dynamics) and coarse-grained (e.g., continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 084115 (2016)], simulated using a particle-based continuum method known as smoothed dissipative particle dynamics. An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.

Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS.

PubMed

Brackley, C A; Morozov, A N; Marenduzzo, D

2014-04-07

An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions relating to both bending and twisting of the rod are derived for both continuous and discrete cases, and results are compared with numerical simulations. Finally, two possible implementations of the discretised model in the multi-purpose molecular dynamics software package LAMMPS are described.

A coupled/uncoupled deformation and fatigue damage algorithm utilizing the finite element method

NASA Technical Reports Server (NTRS)

Wilt, Thomas E.; Arnold, Steven M.

1994-01-01

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum based fatigue damage model for unidirectional metal matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress which fully couples the fatigue damage calculations with the finite element deformation solution. An axisymmetric stress analysis was performed on a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. The composite core behavior was represented using Hill's anisotropic continuum based plasticity model, and similarly, the matrix cladding was represented by an isotropic plasticity model. Results are presented in the form of S-N curves and damage distribution plots.

Mesh Convergence Requirements for Composite Damage Models

NASA Technical Reports Server (NTRS)

Davila, Carlos G.

2016-01-01

The ability of the finite element method to accurately represent the response of objects with intricate geometry and loading renders the finite element method as an extremely versatile analysis technique for structural analysis. Finite element analysis is routinely used in industry to calculate deflections, stress concentrations, natural frequencies, buckling loads, and much more. The method works by discretizing complex problems into smaller, simpler approximations that are valid over small uniform domains. For common analyses, the maximum size of the elements that can be used is often be determined by experience. However, to verify the quality of a solution, analyses with several levels of mesh refinement should be performed to ensure that the solution has converged. In recent years, the finite element method has been used to calculate the resistance of structures, and in particular that of composite structures. A number of techniques such as cohesive zone modeling, the virtual crack closure technique, and continuum damage modeling have emerged that can be used to predict cracking, delaminations, fiber failure, and other composite damage modes that lead to structural collapse. However, damage models present mesh refinement requirements that are not well understood. In this presentation, we examine different mesh refinement issues related to the representation of damage in composite materials. Damage process zone sizes and their corresponding mesh requirements will be discussed. The difficulties of modeling discontinuities and the associated need for regularization techniques will be illustrated, and some unexpected element size constraints will be presented. Finally, some of the difficulties in constructing models of composite structures capable of predicting transverse matrix cracking will be discussed. It will be shown that to predict the initiation and propagation of transverse matrix cracks, their density, and their saturation may require models that are significantly more refined than those that have been contemplated in the past.

Comparison of algorithms for solving the sign problem in the O(3) model in 1 +1 dimensions at finite chemical potential

NASA Astrophysics Data System (ADS)

Katz, S. D.; Niedermayer, F.; Nógrádi, D.; Török, Cs.

2017-03-01

We study three possible ways to circumvent the sign problem in the O(3) nonlinear sigma model in 1 +1 dimensions. We compare the results of the worm algorithm to complex Langevin and multiparameter reweighting. Using the worm algorithm, the thermodynamics of the model is investigated, and continuum results are shown for the pressure at different μ /T values in the range 0-4. By performing T =0 simulations using the worm algorithm, the Silver Blaze phenomenon is reproduced. Regarding the complex Langevin, we test various implementations of discretizing the complex Langevin equation. We found that the exponentialized Euler discretization of the Langevin equation gives wrong results for the action and the density at low T /m . By performing a continuum extrapolation, we found that this discrepancy does not disappear and depends slightly on temperature. The discretization with spherical coordinates performs similarly at low μ /T but breaks down also at some higher temperatures at high μ /T . However, a third discretization that uses a constraining force to achieve the ϕ2=1 condition gives correct results for the action but wrong results for the density at low μ /T .

Equivalent-Continuum Modeling With Application to Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Odegard, Gregory M.; Gates, Thomas S.; Nicholson, Lee M.; Wise, Kristopher E.

2002-01-01

A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of single-walled carbon nanotubes and the design of nanotube-based devices, the modeling technique has been applied to determine the effective-continuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalent continuum models. As a result, an effective thickness of the continuum model has been determined. This effective thickness has been shown to be significantly larger than the interatomic spacing of graphite. The effective thickness has been shown to be significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the vibrational potential energy of the molecular model of a graphene sheet subjected to cylindrical bending with the strain energy of an equivalent continuum plate subjected to cylindrical bending.

Transport Phenomena of Water in Molecular Fluidic Channels

PubMed Central

Vo, Truong Quoc; Kim, BoHung

2016-01-01

In molecular-level fluidic transport, where the discrete characteristics of a molecular system are not negligible (in contrast to a continuum description), the response of the molecular water system might still be similar to the continuum description if the time and ensemble averages satisfy the ergodic hypothesis and the scale of the average is enough to recover the classical thermodynamic properties. However, even in such cases, the continuum description breaks down on the material interfaces. In short, molecular-level liquid flows exhibit substantially different physics from classical fluid transport theories because of (i) the interface/surface force field, (ii) thermal/velocity slip, (iii) the discreteness of fluid molecules at the interface and (iv) local viscosity. Therefore, in this study, we present the result of our investigations using molecular dynamics (MD) simulations with continuum-based energy equations and check the validity and limitations of the continuum hypothesis. Our study shows that when the continuum description is subjected to the proper treatment of the interface effects via modified boundary conditions, the so-called continuum-based modified-analytical solutions, they can adequately predict nanoscale fluid transport phenomena. The findings in this work have broad effects in overcoming current limitations in modeling/predicting the fluid behaviors of molecular fluidic devices. PMID:27650138

Experimental Verification of a Progressive Damage Model for IM7/5260 Laminates Subjected to Tension-Tension Fatigue

NASA Technical Reports Server (NTRS)

Coats, Timothy W.; Harris, Charles E.

1995-01-01

The durability and damage tolerance of laminated composites are critical design considerations for airframe composite structures. Therefore, the ability to model damage initiation and growth and predict the life of laminated composites is necessary to achieve structurally efficient and economical designs. The purpose of this research is to experimentally verify the application of a continuum damage model to predict progressive damage development in a toughened material system. Damage due to monotonic and tension-tension fatigue was documented for IM7/5260 graphite/bismaleimide laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables to predict stiffness loss in unnotched laminates. A damage dependent finite element code predicted the stiffness loss for notched laminates with good agreement to experimental data. It was concluded that the continuum damage model can adequately predict matrix damage progression in notched and unnotched laminates as a function of loading history and laminate stacking sequence.

Fracture-Based Mesh Size Requirements for Matrix Cracks in Continuum Damage Mechanics Models

NASA Technical Reports Server (NTRS)

Leone, Frank A.; Davila, Carlos G.; Mabson, Gerald E.; Ramnath, Madhavadas; Hyder, Imran

2017-01-01

This paper evaluates the ability of progressive damage analysis (PDA) finite element (FE) models to predict transverse matrix cracks in unidirectional composites. The results of the analyses are compared to closed-form linear elastic fracture mechanics (LEFM) solutions. Matrix cracks in fiber-reinforced composite materials subjected to mode I and mode II loading are studied using continuum damage mechanics and zero-thickness cohesive zone modeling approaches. The FE models used in this study are built parametrically so as to investigate several model input variables and the limits associated with matching the upper-bound LEFM solutions. Specifically, the sensitivity of the PDA FE model results to changes in strength and element size are investigated.

Three-dimensional analysis of a faulted CO 2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

DOE PAGES

Nguyen, Ba Nghiep; Hou, Zhangshuan; Last, George V.; ...

2016-09-29

This work develops a three-dimensional multiscale model to analyze a complex CO 2 faulted reservoir that includes some key geological features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO 2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, faultmore » damaged sandstone, fault damaged shale, and fault core. Rocks’ elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanka approach (EMTA). EMTA can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO 2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO 2 due to cracks that enhance the permeability of the fault damage zones. Here, the results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO 2 plume. Potential hydraulic fracture and the tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.« less

Three-dimensional analysis of a faulted CO 2 reservoir using an Eshelby-Mori-Tanaka approach to rock elastic properties and fault permeability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Hou, Zhangshuan; Last, George V.

This work develops a three-dimensional multiscale model to analyze a complex CO 2 faulted reservoir that includes some key geological features of the San Andreas and nearby faults southwest of the Kimberlina site. The model uses the STOMP-CO 2 code for flow modeling that is coupled to the ABAQUS® finite element package for geomechanical analysis. A 3D ABAQUS® finite element model is developed that contains a large number of 3D solid elements with two nearly parallel faults whose damage zones and cores are discretized using the same continuum elements. Five zones with different mineral compositions are considered: shale, sandstone, faultmore » damaged sandstone, fault damaged shale, and fault core. Rocks’ elastic properties that govern their poroelastic behavior are modeled by an Eshelby-Mori-Tanka approach (EMTA). EMTA can account for up to 15 mineral phases. The permeability of fault damage zones affected by crack density and orientations is also predicted by an EMTA formulation. A STOMP-CO 2 grid that exactly maps the ABAQUS® finite element model is built for coupled hydro-mechanical analyses. Simulations of the reservoir assuming three different crack pattern situations (including crack volume fraction and orientation) for the fault damage zones are performed to predict the potential leakage of CO 2 due to cracks that enhance the permeability of the fault damage zones. Here, the results illustrate the important effect of the crack orientation on fault permeability that can lead to substantial leakage along the fault attained by the expansion of the CO 2 plume. Potential hydraulic fracture and the tendency for the faults to slip are also examined and discussed in terms of stress distributions and geomechanical properties.« less

A continuum model for damage evolution in laminated composites

NASA Technical Reports Server (NTRS)

Lo, D. C.; Allen, D. H.; Harris, C. E.

1991-01-01

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

Micropolar continuum modelling of bi-dimensional tetrachiral lattices

PubMed Central

Chen, Y.; Liu, X. N.; Hu, G. K.; Sun, Q. P.; Zheng, Q. S.

2014-01-01

The in-plane behaviour of tetrachiral lattices should be characterized by bi-dimensional orthotropic material owing to the existence of two orthogonal axes of rotational symmetry. Moreover, the constitutive model must also represent the chirality inherent in the lattices. To this end, a bi-dimensional orthotropic chiral micropolar model is developed based on the theory of irreducible orthogonal tensor decomposition. The obtained constitutive tensors display a hierarchy structure depending on the symmetry of the underlying microstructure. Eight additional material constants, in addition to five for the hemitropic case, are introduced to characterize the anisotropy under Z2 invariance. The developed continuum model is then applied to a tetrachiral lattice, and the material constants of the continuum model are analytically derived by a homogenization process. By comparing with numerical simulations for the discrete lattice, it is found that the proposed continuum model can correctly characterize the static and wave properties of the tetrachiral lattice. PMID:24808754

Time dependent reliability model incorporating continuum damage mechanics for high-temperature ceramics

NASA Technical Reports Server (NTRS)

Duffy, Stephen F.; Gyekenyesi, John P.

1989-01-01

Presently there are many opportunities for the application of ceramic materials at elevated temperatures. In the near future ceramic materials are expected to supplant high temperature metal alloys in a number of applications. It thus becomes essential to develop a capability to predict the time-dependent response of these materials. The creep rupture phenomenon is discussed, and a time-dependent reliability model is outlined that integrates continuum damage mechanics principles and Weibull analysis. Several features of the model are presented in a qualitative fashion, including predictions of both reliability and hazard rate. In addition, a comparison of the continuum and the microstructural kinetic equations highlights a strong resemblance in the two approaches.

Multiaxial Fatigue Life Prediction Based on Nonlinear Continuum Damage Mechanics and Critical Plane Method

NASA Astrophysics Data System (ADS)

Wu, Z. R.; Li, X.; Fang, L.; Song, Y. D.

2018-04-01

A new multiaxial fatigue life prediction model has been proposed in this paper. The concepts of nonlinear continuum damage mechanics and critical plane criteria were incorporated in the proposed model. The shear strain-based damage control parameter was chosen to account for multiaxial fatigue damage under constant amplitude loading. Fatigue tests were conducted on nickel-based superalloy GH4169 tubular specimens at the temperature of 400 °C under proportional and nonproportional loading. The proposed method was checked against the multiaxial fatigue test data of GH4169. Most of prediction results are within a factor of two scatter band of the test results.

p-adic string theories provide lattice Discretization to the ordinary string worldsheet.

PubMed

Ghoshal, Debashis

2006-10-13

A class of models called p-adic strings is useful in understanding the tachyonic instability of string theory. These are found to be empirically related to the ordinary strings in the p-->1 limit. We propose that these models provide discretization for the string worldsheet and argue that the limit is naturally thought of as a continuum limit in the sense of the renormalization group.

p-adic String Theories Provide Lattice Discretization to the Ordinary String Worldsheet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghoshal, Debashis

2006-10-13

A class of models called p-adic strings is useful in understanding the tachyonic instability of string theory. These are found to be empirically related to the ordinary strings in the p{yields}1 limit. We propose that these models provide discretization for the string worldsheet and argue that the limit is naturally thought of as a continuum limit in the sense of the renormalization group.

A dual-phase microstructural approach to damage and fracture of Ti 3SiC 2/SiC joints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Henager, Charles H.; Kurtz, Richard J.

We investigate the microcracking mechanisms responsible for Ti 3SiC 2/SiC joint damage observed at the macroscopic scale after neutron irradiation experiments in detail. A dual-phase microstructural approach to damage and fracture of Ti 3SiC 2/SiC joints is developed that uses a finely discretized two-phase domain based on a digital image of an actual microstructure involving embedded Ti 3SiC 2 and SiC phases. The behaviors of SiC and Ti 3SiC 2 in the domain are described by the continuum damage mechanics (CDM) model reported in Nguyen et al., J. Nucl. Mater., 2017, 495:504–515. This CDM model describes microcracking damage in brittlemore » ceramics caused by thermomechanical loading and irradiation-induced swelling. The dual-phase microstructural model is applied to predict the microcracking mechanisms occurring in a typical Ti 3SiC 2/SiC joint subjected to heating to 800 °C followed by irradiation-induced swelling at this temperature and cooling to room temperature after the applied swelling has reached the maximum swelling levels observed in the experiments for SiC and Ti 3SiC 2. The model predicts minor damage of the joint after heating but significant microcracking in the SiC phase and along the boundaries between SiC and Ti 3SiC 2 as well as along the bonding joint during irradiation-induced swelling and cooling to room temperature. Our predictions qualitatively agree with the limited experimental observations of joint damage at this irradiation temperature.« less

A dual-phase microstructural approach to damage and fracture of Ti 3SiC 2/SiC joints

DOE PAGES

Nguyen, Ba Nghiep; Henager, Charles H.; Kurtz, Richard J.

2017-12-05

We investigate the microcracking mechanisms responsible for Ti 3SiC 2/SiC joint damage observed at the macroscopic scale after neutron irradiation experiments in detail. A dual-phase microstructural approach to damage and fracture of Ti 3SiC 2/SiC joints is developed that uses a finely discretized two-phase domain based on a digital image of an actual microstructure involving embedded Ti 3SiC 2 and SiC phases. The behaviors of SiC and Ti 3SiC 2 in the domain are described by the continuum damage mechanics (CDM) model reported in Nguyen et al., J. Nucl. Mater., 2017, 495:504–515. This CDM model describes microcracking damage in brittlemore » ceramics caused by thermomechanical loading and irradiation-induced swelling. The dual-phase microstructural model is applied to predict the microcracking mechanisms occurring in a typical Ti 3SiC 2/SiC joint subjected to heating to 800 °C followed by irradiation-induced swelling at this temperature and cooling to room temperature after the applied swelling has reached the maximum swelling levels observed in the experiments for SiC and Ti 3SiC 2. The model predicts minor damage of the joint after heating but significant microcracking in the SiC phase and along the boundaries between SiC and Ti 3SiC 2 as well as along the bonding joint during irradiation-induced swelling and cooling to room temperature. Our predictions qualitatively agree with the limited experimental observations of joint damage at this irradiation temperature.« less

Correction to the gas phase pressure term in the continuum model for partially saturated granular media presented by Pietruszczak and co-workers

NASA Astrophysics Data System (ADS)

Iveson, Simon M.

2003-06-01

Pietruszczak and coworkers (Internat. J. Numer. Anal. Methods Geomech. 1994; 18(2):93-105; Comput. Geotech. 1991; 12( ):55-71) have presented a continuum-based model for predicting the dynamic mechanical response of partially saturated granular media with viscous interstitial liquids. In their model they assume that the gas phase is distributed uniformly throughout the medium as discrete spherical air bubbles occupying the voids between the particles. However, their derivation of the air pressure inside these gas bubbles is inconsistent with their stated assumptions. In addition the resultant dependence of gas pressure on liquid saturation lies outside of the plausible range of possible values for discrete air bubbles. This results in an over-prediction of the average bulk modulus of the void phase. Corrected equations are presented.

Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions

NASA Astrophysics Data System (ADS)

Jin, Wang; Penington, Catherine J.; McCue, Scott W.; Simpson, Matthew J.

2016-10-01

Two-dimensional collective cell migration assays are used to study cancer and tissue repair. These assays involve combined cell migration and cell proliferation processes, both of which are modulated by cell-to-cell crowding. Previous discrete models of collective cell migration assays involve a nearest-neighbour proliferation mechanism where crowding effects are incorporated by aborting potential proliferation events if the randomly chosen target site is occupied. There are two limitations of this traditional approach: (i) it seems unreasonable to abort a potential proliferation event based on the occupancy of a single, randomly chosen target site; and, (ii) the continuum limit description of this mechanism leads to the standard logistic growth function, but some experimental evidence suggests that cells do not always proliferate logistically. Motivated by these observations, we introduce a generalised proliferation mechanism which allows non-nearest neighbour proliferation events to take place over a template of r≥slant 1 concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather than dealing with the occupancy of a single randomly chosen site. Analysing the continuum limit description of the stochastic model shows that the standard logistic source term, λ C(1-C), where λ is the proliferation rate, is generalised to a universal growth function, λ C f(C). Comparing the solution of the continuum description with averaged simulation data indicates that the continuum model performs well for many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.

Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions.

PubMed

Jin, Wang; Penington, Catherine J; McCue, Scott W; Simpson, Matthew J

2016-10-07

Two-dimensional collective cell migration assays are used to study cancer and tissue repair. These assays involve combined cell migration and cell proliferation processes, both of which are modulated by cell-to-cell crowding. Previous discrete models of collective cell migration assays involve a nearest-neighbour proliferation mechanism where crowding effects are incorporated by aborting potential proliferation events if the randomly chosen target site is occupied. There are two limitations of this traditional approach: (i) it seems unreasonable to abort a potential proliferation event based on the occupancy of a single, randomly chosen target site; and, (ii) the continuum limit description of this mechanism leads to the standard logistic growth function, but some experimental evidence suggests that cells do not always proliferate logistically. Motivated by these observations, we introduce a generalised proliferation mechanism which allows non-nearest neighbour proliferation events to take place over a template of [Formula: see text] concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f(C), which accounts for the density of agents within a group of sites rather than dealing with the occupancy of a single randomly chosen site. Analysing the continuum limit description of the stochastic model shows that the standard logistic source term, [Formula: see text], where λ is the proliferation rate, is generalised to a universal growth function, [Formula: see text]. Comparing the solution of the continuum description with averaged simulation data indicates that the continuum model performs well for many choices of f(C) and r. For nonlinear f(C), the quality of the continuum-discrete match increases with r.

Incorporating physically-based microstructures in materials modeling: Bridging phase field and crystal plasticity frameworks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, Hojun; Abdeljawad, Fadi; Owen, Steven J.

Here, the mechanical properties of materials systems are highly influenced by various features at the microstructural level. The ability to capture these heterogeneities and incorporate them into continuum-scale frameworks of the deformation behavior is considered a key step in the development of complex non-local models of failure. In this study, we present a modeling framework that incorporates physically-based realizations of polycrystalline aggregates from a phase field (PF) model into a crystal plasticity finite element (CP-FE) framework. Simulated annealing via the PF model yields ensembles of materials microstructures with various grain sizes and shapes. With the aid of a novel FEmore » meshing technique, FE discretizations of these microstructures are generated, where several key features, such as conformity to interfaces, and triple junction angles, are preserved. The discretizations are then used in the CP-FE framework to simulate the mechanical response of polycrystalline α-iron. It is shown that the conformal discretization across interfaces reduces artificial stress localization commonly observed in non-conformal FE discretizations. The work presented herein is a first step towards incorporating physically-based microstructures in lieu of the overly simplified representations that are commonly used. In broader terms, the proposed framework provides future avenues to explore bridging models of materials processes, e.g. additive manufacturing and microstructure evolution of multi-phase multi-component systems, into continuum-scale frameworks of the mechanical properties.« less

Incorporating physically-based microstructures in materials modeling: Bridging phase field and crystal plasticity frameworks

DOE PAGES

Lim, Hojun; Abdeljawad, Fadi; Owen, Steven J.; ...

2016-04-25

Here, the mechanical properties of materials systems are highly influenced by various features at the microstructural level. The ability to capture these heterogeneities and incorporate them into continuum-scale frameworks of the deformation behavior is considered a key step in the development of complex non-local models of failure. In this study, we present a modeling framework that incorporates physically-based realizations of polycrystalline aggregates from a phase field (PF) model into a crystal plasticity finite element (CP-FE) framework. Simulated annealing via the PF model yields ensembles of materials microstructures with various grain sizes and shapes. With the aid of a novel FEmore » meshing technique, FE discretizations of these microstructures are generated, where several key features, such as conformity to interfaces, and triple junction angles, are preserved. The discretizations are then used in the CP-FE framework to simulate the mechanical response of polycrystalline α-iron. It is shown that the conformal discretization across interfaces reduces artificial stress localization commonly observed in non-conformal FE discretizations. The work presented herein is a first step towards incorporating physically-based microstructures in lieu of the overly simplified representations that are commonly used. In broader terms, the proposed framework provides future avenues to explore bridging models of materials processes, e.g. additive manufacturing and microstructure evolution of multi-phase multi-component systems, into continuum-scale frameworks of the mechanical properties.« less

Possible role of interference, protein noise, and sink effects in nonphotochemical quenching in photosynthetic complexes.

PubMed

Berman, Gennady P; Nesterov, Alexander I; Gurvitz, Shmuel; Sayre, Richard T

2017-01-01

We analyze theoretically a simple and consistent quantum mechanical model that reveals the possible role of quantum interference, protein noise, and sink effects in the nonphotochemical quenching (NPQ) in light-harvesting complexes (LHCs). The model consists of a network of five interconnected sites (excitonic states of light-sensitive molecules) responsible for the NPQ mechanism. The model also includes the "damaging" and the dissipative channels. The damaging channel is responsible for production of singlet oxygen and other destructive outcomes. In our model, both damaging and "dissipative" charge transfer channels are described by discrete electron energy levels attached to their sinks, that mimic the continuum part of electron energy spectrum. All five excitonic sites interact with the protein environment that is modeled using a stochastic process. Our approach allowed us to derive the exact and closed system of linear ordinary differential equations for the reduced density matrix and its first momentums. These equations are solved numerically including for strong interactions between the light-sensitive molecules and protein environment. As an example, we apply our model to demonstrate possible contributions of quantum interference, protein noise, and sink effects in the NPQ mechanism in the CP29 minor LHC. The numerical simulations show that using proper combination of quantum interference effects, properties of noise, and sinks, one can significantly suppress the damaging channel. Our findings demonstrate the possible role of interference, protein noise, and sink effects for modeling, engineering, and optimizing the performance of the NPQ processes in both natural and artificial light-harvesting complexes.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

DOE PAGES

Petsev, Nikolai Dimitrov; Leal, L. Gary; Shell, M. Scott

2017-12-21

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely-resolved (e.g. molecular dynamics) and coarse-grained (e.g. continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 84115 (2016)], simulatedmore » using a particle-based continuum method known as smoothed dissipative particle dynamics (SDPD). An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.« less

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petsev, Nikolai Dimitrov; Leal, L. Gary; Shell, M. Scott

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely-resolved (e.g. molecular dynamics) and coarse-grained (e.g. continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 84115 (2016)], simulatedmore » using a particle-based continuum method known as smoothed dissipative particle dynamics (SDPD). An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.« less

A multiscale microstructural approach to ductile-phase toughened tungsten for plasma-facing materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Henager, Jr., Charles H.; Overman, Nicole R.

Increasing fracture toughness and modifying the ductile-brittle transition temperature of a tungsten-alloy relative to pure tungsten has been shown to be feasible by ductile-phase toughening (DPT) of tungsten for future plasma-facing materials for fusion energy. In DPT, a ductile phase is included in a brittle tungsten matrix to increase the overall work of fracture for the material. This research models the deformation behavior of DPT tungsten materials, such as tungsten-copper composites, using a multiscale modeling approach that involves a microstructural dual-phase (copper-tungsten) region of interest where the constituent phases are finely discretized and are described by a continuum damage mechanicsmore » model. Large deformation, damage, and fracture are allowed to occur and are modeled in a region that is connected to adjacent homogenized elastic regions to form a macroscopic structure, such as a test specimen. The present paper illustrates this multiscale modeling approach to analyze unnotched and single-edge notched (SENB) tungsten-copper composite specimens subjected to three-point bending. The predicted load-displacement responses and crack propagation patterns are compared to the corresponding experimental results to validate the model. Furthermore, such models may help design future DPT composite configurations for fusion materials, including volume fractions of ductile phase and microstructural optimization.« less

A multiscale microstructural approach to ductile-phase toughened tungsten for plasma-facing materials

DOE PAGES

Nguyen, Ba Nghiep; Henager, Jr., Charles H.; Overman, Nicole R.; ...

2018-05-23

Increasing fracture toughness and modifying the ductile-brittle transition temperature of a tungsten-alloy relative to pure tungsten has been shown to be feasible by ductile-phase toughening (DPT) of tungsten for future plasma-facing materials for fusion energy. In DPT, a ductile phase is included in a brittle tungsten matrix to increase the overall work of fracture for the material. This research models the deformation behavior of DPT tungsten materials, such as tungsten-copper composites, using a multiscale modeling approach that involves a microstructural dual-phase (copper-tungsten) region of interest where the constituent phases are finely discretized and are described by a continuum damage mechanicsmore » model. Large deformation, damage, and fracture are allowed to occur and are modeled in a region that is connected to adjacent homogenized elastic regions to form a macroscopic structure, such as a test specimen. The present paper illustrates this multiscale modeling approach to analyze unnotched and single-edge notched (SENB) tungsten-copper composite specimens subjected to three-point bending. The predicted load-displacement responses and crack propagation patterns are compared to the corresponding experimental results to validate the model. Furthermore, such models may help design future DPT composite configurations for fusion materials, including volume fractions of ductile phase and microstructural optimization.« less

Improvement of Progressive Damage Model to Predicting Crashworthy Composite Corrugated Plate

NASA Astrophysics Data System (ADS)

Ren, Yiru; Jiang, Hongyong; Ji, Wenyuan; Zhang, Hanyu; Xiang, Jinwu; Yuan, Fuh-Gwo

2018-02-01

To predict the crashworthy composite corrugated plate, different single and stacked shell models are evaluated and compared, and a stacked shell progressive damage model combined with continuum damage mechanics is proposed and investigated. To simulate and predict the failure behavior, both of the intra- and inter- laminar failure behavior are considered. The tiebreak contact method, 1D spot weld element and cohesive element are adopted in stacked shell model, and a surface-based cohesive behavior is used to capture delamination in the proposed model. The impact load and failure behavior of purposed and conventional progressive damage models are demonstrated. Results show that the single shell could simulate the impact load curve without the delamination simulation ability. The general stacked shell model could simulate the interlaminar failure behavior. The improved stacked shell model with continuum damage mechanics and cohesive element not only agree well with the impact load, but also capture the fiber, matrix debonding, and interlaminar failure of composite structure.

Progressive failure methodologies for predicting residual strength and life of laminated composites

NASA Technical Reports Server (NTRS)

Harris, Charles E.; Allen, David H.; Obrien, T. Kevin

1991-01-01

Two progressive failure methodologies currently under development by the Mechanics of Materials Branch at NASA Langley Research Center are discussed. The damage tolerance/fail safety methodology developed by O'Brien is an engineering approach to ensuring adequate durability and damage tolerance by treating only delamination onset and the subsequent delamination accumulation through the laminate thickness. The continuum damage model developed by Allen and Harris employs continuum damage laws to predict laminate strength and life. The philosophy, mechanics framework, and current implementation status of each methodology are presented.

A continuum damage model for delaminations in laminated composites

NASA Astrophysics Data System (ADS)

Zou, Z.; Reid, S. R.; Li, S.

2003-02-01

Delamination, a typical mode of interfacial damage in laminated composites, has been considered in the context of continuum damage mechanics in this paper. Interfaces where delaminations could occur are introduced between the constituent layers. A simple but appropriate continuum damage representation is proposed. A single scalar damage parameter is employed and the degradation of the interface stiffness is established. Use has been made of the concept of a damage surface to derive the damage evolution law. The damage surface is constructed so that it combines the conventional stress-based and fracture-mechanics-based failure criteria which take account of mode interaction in mixed-mode delamination problems. The damage surface shrinks as damage develops and leads to a softening interfacial constitutive law. By adjusting the shrinkage rate of the damage surface, various interfacial constitutive laws found in the literature can be reproduced. An incremental interfacial constitutive law is also derived for use in damage analysis of laminated composites, which is a non-linear problem in nature. Numerical predictions for problems involving a DCB specimen under pure mode I delamination and mixed-mode delamination in a split beam are in good agreement with available experimental data or analytical solutions. The model has also been applied to the prediction of the failure strength of overlap ply-blocking specimens. The results have been compared with available experimental and alternative theoretical ones and discussed fully.

Continuum Damage Mechanics Models for the Analysis of Progressive Failure in Open-Hole Tension Laminates

NASA Technical Reports Server (NTRS)

Song, Kyonchan; Li, Yingyong; Rose, Cheryl A.

2011-01-01

The performance of a state-of-the-art continuum damage mechanics model for interlaminar damage, coupled with a cohesive zone model for delamination is examined for failure prediction of quasi-isotropic open-hole tension laminates. Limitations of continuum representations of intra-ply damage and the effect of mesh orientation on the analysis predictions are discussed. It is shown that accurate prediction of matrix crack paths and stress redistribution after cracking requires a mesh aligned with the fiber orientation. Based on these results, an aligned mesh is proposed for analysis of the open-hole tension specimens consisting of different meshes within the individual plies, such that the element edges are aligned with the ply fiber direction. The modeling approach is assessed by comparison of analysis predictions to experimental data for specimen configurations in which failure is dominated by complex interactions between matrix cracks and delaminations. It is shown that the different failure mechanisms observed in the tests are well predicted. In addition, the modeling approach is demonstrated to predict proper trends in the effect of scaling on strength and failure mechanisms of quasi-isotropic open-hole tension laminates.

Improvements in continuum modeling for biomolecular systems

NASA Astrophysics Data System (ADS)

Yu, Qiao; Ben-Zhuo, Lu

2016-01-01

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann (PB)/Poisson-Nernst-Planck (PNP) equations has made great contributions towards simulation of these processes. However, the model has shortcomings in its commonly used form and cannot capture (or cannot accurately capture) some important physical properties of the biological systems. Considerable efforts have been made to improve the continuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecular systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress. Project supported by the National Natural Science Foundation of China (Grant No. 91230106) and the Chinese Academy of Sciences Program for Cross & Cooperative Team of the Science & Technology Innovation.

Differential continuum damage mechanics models for creep and fatigue of unidirectional metal matrix composites

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Kruch, S.

1991-01-01

Three multiaxial isothermal continuum damage mechanics models for creep, fatigue, and creep/fatigue interaction of a unidirectional metal matrix composite volume element are presented, only one of which will be discussed in depth. Each model is phenomenological and stress based, with varying degrees of complexity to accurately predict the initiation and propagation of intergranular and transgranular defects over a wide range of loading conditions. The development of these models is founded on the definition of an initially transversely isotropic fatigue limit surface, static fracture surface, normalized stress amplitude function and isochronous creep damage failure surface, from which both fatigue and creep damage evolutionary laws can be obtained. The anisotropy of each model is defined through physically meaningful invariants reflecting the local stress and material orientation. All three transversely isotropic models have been shown, when taken to their isotropic limit, to directly simplify to previously developed and validated creep and fatigue continuum damage theories. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation when attempting to characterize a large class of composite materials, and (2) its ability to predict anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Additionally, the potential for the inclusion of various micromechanical effects (e.g., fiber/matrix bond strength, fiber volume fraction, etc.), into the phenomenological anisotropic parameters is noted, as well as a detailed discussion regarding the necessary exploratory and characterization experiments needed to utilize the featured damage theories.

Modelling of Dynamic Rock Fracture Process with a Rate-Dependent Combined Continuum Damage-Embedded Discontinuity Model Incorporating Microstructure

NASA Astrophysics Data System (ADS)

Saksala, Timo

2016-10-01

This paper deals with numerical modelling of rock fracture under dynamic loading. For this end, a combined continuum damage-embedded discontinuity model is applied in finite element modelling of crack propagation in rock. In this model, the strong loading rate sensitivity of rock is captured by the rate-dependent continuum scalar damage model that controls the pre-peak nonlinear hardening part of rock behaviour. The post-peak exponential softening part of the rock behaviour is governed by the embedded displacement discontinuity model describing the mode I, mode II and mixed mode fracture of rock. Rock heterogeneity is incorporated in the present approach by random description of the rock mineral texture based on the Voronoi tessellation. The model performance is demonstrated in numerical examples where the uniaxial tension and compression tests on rock are simulated. Finally, the dynamic three-point bending test of a semicircular disc is simulated in order to show that the model correctly predicts the strain rate-dependent tensile strengths as well as the failure modes of rock in this test. Special emphasis is laid on modelling the loading rate sensitivity of tensile strength of Laurentian granite.

A Continuum Damage Mechanics Model for the Static and Cyclic Fatigue of Cellular Composites

PubMed Central

Huber, Otto

2017-01-01

The fatigue behavior of a cellular composite with an epoxy matrix and glass foam granules is analyzed and modeled by means of continuum damage mechanics. The investigated cellular composite is a particular type of composite foam, and is very similar to syntactic foams. In contrast to conventional syntactic foams constituted by hollow spherical particles (balloons), cellular glass, mineral, or metal place holders are combined with the matrix material (metal or polymer) in the case of cellular composites. A microstructural investigation of the damage behavior is performed using scanning electron microscopy. For the modeling of the fatigue behavior, the damage is separated into pure static and pure cyclic damage and described in terms of the stiffness loss of the material using damage models for cyclic and creep damage. Both models incorporate nonlinear accumulation and interaction of damage. A cycle jumping procedure is developed, which allows for a fast and accurate calculation of the damage evolution for constant load frequencies. The damage model is applied to examine the mean stress effect for cyclic fatigue and to investigate the frequency effect and the influence of the signal form in the case of static and cyclic damage interaction. The calculated lifetimes are in very good agreement with experimental results. PMID:28809806

Aqueous solvation of polyalanine α-helices with specific water molecules and with the CPCM and SM5.2 aqueous continuum models using density functional theory.

PubMed

Marianski, Mateusz; Dannenberg, J J

2012-02-02

We present density functional theory (DFT) calculations at the X3LYP/D95(d,p) level on the solvation of polyalanine α-helices in water. The study includes the effects of discrete water molecules and the CPCM and AMSOL SM5.2 solvent continuum model both separately and in combination. We find that individual water molecules cooperatively hydrogen-bond to both the C- and N-termini of the helix, which results in increases in the dipole moment of the helix/water complex to more than the vector sum of their individual dipole moments. These waters are found to be more stable than in bulk solvent. On the other hand, individual water molecules that interact with the backbone lower the dipole moment of the helix/water complex to below that of the helix itself. Small clusters of waters at the termini increase the dipole moments of the helix/water aggregates, but the effect diminishes as more waters are added. We discuss the somewhat complex behavior of the helix with the discrete waters in the continuum models.

Aqueous Solvation of Polyalanine α-Helices with Specific Water Molecules and with the CPCM and SM5.2 Aqueous Continuum Models using Density Functional Theory

PubMed Central

Marianski, Mateusz

2012-01-01

We present density functional theory (DFT) calculations at the X3LYP/D95(d,p) level on the solvation of polyalanine α-helices in water. The study includes the effects of discrete water molecules and the CPCM and AMSOL SM5.2 solvent continuum model both separately and in combination. We find that individual water molecules cooperatively hydrogen-bond to both the C- and N-termini of the helix, which results in increases in the dipole moment of the helix/water complex to more than the vector sum of their individual dipole moments. These waters are found to be more stable than in bulk solvent. On the other hand, individual water that interact with the backbone lower the dipole moment of the helix/water complex to below that of the helix, itself. Small clusters of waters at the termini increase the dipole moments of the helix/water aggregates, but the effect diminishes as more waters are added. We discuss the somewhat complex behavior of the helix with the discrete waters in the continuum models. PMID:22201227

A continuum membrane model for small deformations of a spider orb-web

NASA Astrophysics Data System (ADS)

Morassi, Antonino; Soler, Alejandro; Zaera, Ramón

2017-09-01

In this paper we propose a continuum membrane model for the infinitesimal deformation of a spider web. The model is derived in the simple context of axially-symmetric webs formed by radial threads connected with circumferential threads belonging to concentric circles. Under suitable assumption on the tensile pre-stress acting in the referential configuration, the out-of-plane static equilibrium and the free transverse and in-plane vibration of a supported circular orb-web are studied in detail. The accuracy of the model in describing a discrete spider web is numerically investigated.

A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices.

PubMed

Menon, Shakti N; Hall, Cameron L; McCue, Scott W; McElwain, D L Sean

2017-10-01

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.

Generation of Complex Karstic Conduit Networks with a Hydro-chemical Model

NASA Astrophysics Data System (ADS)

De Rooij, R.; Graham, W. D.

2016-12-01

The discrete-continuum approach is very well suited to simulate flow and solute transport within karst aquifers. Using this approach, discrete one-dimensional conduits are embedded within a three-dimensional continuum representative of the porous limestone matrix. Typically, however, little is known about the geometry of the karstic conduit network. As such the discrete-continuum approach is rarely used for practical applications. It may be argued, however, that the uncertainty associated with the geometry of the network could be handled by modeling an ensemble of possible karst conduit networks within a stochastic framework. We propose to generate stochastically realistic karst conduit networks by simulating the widening of conduits as caused by the dissolution of limestone over geological relevant timescales. We illustrate that advanced numerical techniques permit to solve the non-linear and coupled hydro-chemical processes efficiently, such that relatively large and complex networks can be generated in acceptable time frames. Instead of specifying flow boundary conditions on conduit cells to recharge the network as is typically done in classical speleogenesis models, we specify an effective rainfall rate over the land surface and let model physics determine the amount of water entering the network. This is advantageous since the amount of water entering the network is extremely difficult to reconstruct, whereas the effective rainfall rate may be quantified using paleoclimatic data. Furthermore, we show that poorly known flow conditions may be constrained by requiring a realistic flow field. Using our speleogenesis model we have investigated factors that influence the geometry of simulated conduit networks. We illustrate that our model generates typical branchwork, network and anastomotic conduit systems. Flow, solute transport and water ages in karst aquifers are simulated using a few illustrative networks.

Applications of Artificial Neural Networks in Structural Engineering with Emphasis on Continuum Models

NASA Technical Reports Server (NTRS)

Kapania, Rakesh K.; Liu, Youhua

1998-01-01

The use of continuum models for the analysis of discrete built-up complex aerospace structures is an attractive idea especially at the conceptual and preliminary design stages. But the diversity of available continuum models and hard-to-use qualities of these models have prevented them from finding wide applications. In this regard, Artificial Neural Networks (ANN or NN) may have a great potential as these networks are universal approximators that can realize any continuous mapping, and can provide general mechanisms for building models from data whose input-output relationship can be highly nonlinear. The ultimate aim of the present work is to be able to build high fidelity continuum models for complex aerospace structures using the ANN. As a first step, the concepts and features of ANN are familiarized through the MATLAB NN Toolbox by simulating some representative mapping examples, including some problems in structural engineering. Then some further aspects and lessons learned about the NN training are discussed, including the performances of Feed-Forward and Radial Basis Function NN when dealing with noise-polluted data and the technique of cross-validation. Finally, as an example of using NN in continuum models, a lattice structure with repeating cells is represented by a continuum beam whose properties are provided by neural networks.

On the derivation of approximations to cellular automata models and the assumption of independence.

PubMed

Davies, K J; Green, J E F; Bean, N G; Binder, B J; Ross, J V

2014-07-01

Cellular automata are discrete agent-based models, generally used in cell-based applications. There is much interest in obtaining continuum models that describe the mean behaviour of the agents in these models. Previously, continuum models have been derived for agents undergoing motility and proliferation processes, however, these models only hold under restricted conditions. In order to narrow down the reason for these restrictions, we explore three possible sources of error in deriving the model. These sources are the choice of limiting arguments, the use of a discrete-time model as opposed to a continuous-time model and the assumption of independence between the state of sites. We present a rigorous analysis in order to gain a greater understanding of the significance of these three issues. By finding a limiting regime that accurately approximates the conservation equation for the cellular automata, we are able to conclude that the inaccuracy between our approximation and the cellular automata is completely based on the assumption of independence. Copyright © 2014 Elsevier Inc. All rights reserved.

Simulation of Hydraulic and Natural Fracture Interaction Using a Coupled DFN-DEM Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, J.; Huang, H.; Deo, M.

2016-03-01

The presence of natural fractures will usually result in a complex fracture network due to the interactions between hydraulic and natural fracture. The reactivation of natural fractures can generally provide additional flow paths from formation to wellbore which play a crucial role in improving the hydrocarbon recovery in these ultra-low permeability reservoir. Thus, accurate description of the geometry of discrete fractures and bedding is highly desired for accurate flow and production predictions. Compared to conventional continuum models that implicitly represent the discrete feature, Discrete Fracture Network (DFN) models could realistically model the connectivity of discontinuities at both reservoir scale andmore » well scale. In this work, a new hybrid numerical model that couples Discrete Fracture Network (DFN) and Dual-Lattice Discrete Element Method (DL-DEM) is proposed to investigate the interaction between hydraulic fracture and natural fractures. Based on the proposed model, the effects of natural fracture orientation, density and injection properties on hydraulic-natural fractures interaction are investigated.« less

Simulation of Hydraulic and Natural Fracture Interaction Using a Coupled DFN-DEM Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

J. Zhou; H. Huang; M. Deo

The presence of natural fractures will usually result in a complex fracture network due to the interactions between hydraulic and natural fracture. The reactivation of natural fractures can generally provide additional flow paths from formation to wellbore which play a crucial role in improving the hydrocarbon recovery in these ultra-low permeability reservoir. Thus, accurate description of the geometry of discrete fractures and bedding is highly desired for accurate flow and production predictions. Compared to conventional continuum models that implicitly represent the discrete feature, Discrete Fracture Network (DFN) models could realistically model the connectivity of discontinuities at both reservoir scale andmore » well scale. In this work, a new hybrid numerical model that couples Discrete Fracture Network (DFN) and Dual-Lattice Discrete Element Method (DL-DEM) is proposed to investigate the interaction between hydraulic fracture and natural fractures. Based on the proposed model, the effects of natural fracture orientation, density and injection properties on hydraulic-natural fractures interaction are investigated.« less

Electrical characterization of plasma-grown oxides on gallium arsenide

NASA Technical Reports Server (NTRS)

Hshieh, F. I.; Bhat, K. N.; Ghandhi, S. K.; Borrego, J. M.

1985-01-01

Plasma-grown GaAs oxides and their interfaces have been characterized by measuring the electrical properties of metal-oxide-semiconductor capacitors and of Schottky junctions. The current transport mechanism in the oxide at high electrical field was found to be Frankel-Poole emission, with an electron trap center at 0.47 eV below the conduction band of the oxide. The interface-state density, evaluated from capacitance and conductance measurements, exhibits a U-shaped interface-state continuum extending over the entire band gap. Two discrete deep states with high concentration are superimposed on this continuum at 0.40 and 0.70 eV below the conduction band. The results obtained from measurements on Schottky junctions have excluded the possibility that these two deep states originate from plasma damage. Possible origins of these states are discussed in this paper.

Continuum damage modeling and simulation of hierarchical dental enamel

NASA Astrophysics Data System (ADS)

Ma, Songyun; Scheider, Ingo; Bargmann, Swantje

2016-05-01

Dental enamel exhibits high fracture toughness and stiffness due to a complex hierarchical and graded microstructure, optimally organized from nano- to macro-scale. In this study, a 3D representative volume element (RVE) model is adopted to study the deformation and damage behavior of the fibrous microstructure. A continuum damage mechanics model coupled to hyperelasticity is developed for modeling the initiation and evolution of damage in the mineral fibers as well as protein matrix. Moreover, debonding of the interface between mineral fiber and protein is captured by employing a cohesive zone model. The dependence of the failure mechanism on the aspect ratio of the mineral fibers is investigated. In addition, the effect of the interface strength on the damage behavior is studied with respect to geometric features of enamel. Further, the effect of an initial flaw on the overall mechanical properties is analyzed to understand the superior damage tolerance of dental enamel. The simulation results are validated by comparison to experimental data from micro-cantilever beam testing at two hierarchical levels. The transition of the failure mechanism at different hierarchical levels is also well reproduced in the simulations.

The continuum of monocyte phenotypes: Experimental evidence and prognostic utility in assessing cardiovascular risk.

PubMed

Cignarella, Andrea; Tedesco, Serena; Cappellari, Roberta; Fadini, Gian Paolo

2018-03-30

The monocyte-macrophage cell lineage represents a major player in innate immunity, and is involved in many physiologic and pathologic conditions. Particularly, monocyte-macrophages play a very important role in atherosclerosis and cardiovascular disease. Monocyte heterogeneity is well recognized but the biologic and clinical meaning of the various monocyte subtypes is not entirely understood. Traditionally, monocytes can be divided in classical, intermediate, and nonclassical based on expression of the surface antigens CD14 and CD16. While macrophage diversity is now well recognized to organize as a continuum, monocyte subsets have long been considered as separated entities. However, mounting evidence obtained by tracking the ontology of human monocytes help clarifying that monocytes mature from classical to nonclassical ones, through an intermediate phenotype. This concept is therefore best depicted as a continuum, whereas the subdivision into discrete CD14/CD16 subsets appears an oversimplification. In this review, we discuss the evidence supporting the existence of a monocyte continuum along with the technical challenges of monocyte characterization. In particular, we describe the advantage of considering monocytes along a continuous distribution for the evaluation of cardiovascular risk. We make the point that small transition along the monocyte continuum better reflects cardiovascular risk than a simplified analysis of discrete monocyte subsets. Recognizing the monocyte continuum can be helpful to model other pathophysiologic conditions where these cells are involved. ©2018 Society for Leukocyte Biology.

Mechanism of asymmetric lineshape broadening in GaAs1-xNx Raman spectra

NASA Astrophysics Data System (ADS)

Mialitsin, Aleksej; Fluegel, Brian; Ptak, Aaron; Mascarenhas, Angelo

2012-07-01

Resonance Raman spectroscopy is used to probe the asymmetric broadening of the LO phonon linewidth in a dilute GaAs1-xNx alloy (x=0.41%). Electronic Raman scattering from a broad continuum is observed that gets enhanced concurrently with the LO phonon linewidth under resonance. The Fano interaction between the LO phonon and the electronic continuum is used to develop a model that satisfactorily explains the origin of the asymmetric LO phonon linewidth broadening in this abnormal alloy as arising due to coupling between the discrete and the continuum configurations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Hong, E-mail: h-yu@seu.edu.cn; Chen, Hong-Bo

In this article, a new semi-continuum model is built to describe the fundamental vibration frequency of the silicon nanowires in <111> orientation. The Keating potential model and the discrete nature in the width and the thickness direction of the silicon nanowires in <111> orientation are applied in the new semi-continuum model. Based on the Keating model and the principle of conservation of energy, the vibration frequency of the silicon nanowires with the triangle, the rhombus, and the hexagon cross sections are derived. It is indicated that the calculation results based on this new model are accordant with the simulation resultsmore » of the software based on molecular dynamics (MD).« less

Hydro-mechanically coupled finite-element analysis of the stability of a fractured-rock slope using the equivalent continuum approach: a case study of planned reservoir banks in Blaubeuren, Germany

NASA Astrophysics Data System (ADS)

Song, Jie; Dong, Mei; Koltuk, Serdar; Hu, Hui; Zhang, Luqing; Azzam, Rafig

2018-05-01

Construction works associated with the building of reservoirs in mountain areas can damage the stability of adjacent valley slopes. Seepage processes caused by the filling and drawdown operations of reservoirs also affect the stability of the reservoir banks over time. The presented study investigates the stability of a fractured-rock slope subjected to seepage forces in the lower basin of a planned pumped-storage hydropower (PSH) plant in Blaubeuren, Germany. The investigation uses a hydro-mechanically coupled finite-element analyses. For this purpose, an equivalent continuum model is developed by using a representative elementary volume (REV) approach. To determine the minimum required REV size, a large number of discrete fracture networks are generated using Monte Carlo simulations. These analyses give a REV size of 28 × 28 m, which is sufficient to represent the equivalent hydraulic and mechanical properties of the investigated fractured-rock mass. The hydro-mechanically coupled analyses performed using this REV size show that the reservoir operations in the examined PSH plant have negligible effect on the adjacent valley slope.

LS-DYNA Simulation of Hemispherical-punch Stamping Process Using an Efficient Algorithm for Continuum Damage Based Elastoplastic Constitutive Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salajegheh, Nima; Abedrabbo, Nader; Pourboghrat, Farhang

An efficient integration algorithm for continuum damage based elastoplastic constitutive equations is implemented in LS-DYNA. The isotropic damage parameter is defined as the ratio of the damaged surface area over the total cross section area of the representative volume element. This parameter is incorporated into the integration algorithm as an internal variable. The developed damage model is then implemented in the FEM code LS-DYNA as user material subroutine (UMAT). Pure stretch experiments of a hemispherical punch are carried out for copper sheets and the results are compared against the predictions of the implemented damage model. Evaluation of damage parameters ismore » carried out and the optimized values that correctly predicted the failure in the sheet are reported. Prediction of failure in the numerical analysis is performed through element deletion using the critical damage value. The set of failure parameters which accurately predict the failure behavior in copper sheets compared to experimental data is reported as well.« less

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Two-dimensional Fano lineshapes: Excited-state absorption contributions

NASA Astrophysics Data System (ADS)

Finkelstein-Shapiro, Daniel; Pullerits, Tõnu; Hansen, Thorsten

2018-05-01

Fano interferences in nanostructures are influenced by dissipation effects as well as many-body interactions. Two-dimensional coherent spectroscopies have just begun to be applied to these systems where the spectroscopic signatures of a discrete-continuum structure are not known. In this article, we calculate the excited-state absorption contribution for different models of higher lying excited states. We find that the characteristic asymmetry of one-dimensional spectroscopies is recovered from the many-body contributions and that the higher lying excited manifolds have distorted lineshapes that are not anticipated from discrete-level Hamiltonians. We show that the Stimulated Emission cannot have contributions from a flat continuum of states. This work completes the Ground-State Bleach and Stimulated Emission signals that were calculated previously [D. Finkelstein-Shapiro et al., Phys. Rev. B 94, 205137 (2016)]. The model reproduces the observations reported for molecules on surfaces probed by 2DIR.

Two-dimensional Fano lineshapes: Excited-state absorption contributions.

PubMed

Finkelstein-Shapiro, Daniel; Pullerits, Tõnu; Hansen, Thorsten

2018-05-14

Fano interferences in nanostructures are influenced by dissipation effects as well as many-body interactions. Two-dimensional coherent spectroscopies have just begun to be applied to these systems where the spectroscopic signatures of a discrete-continuum structure are not known. In this article, we calculate the excited-state absorption contribution for different models of higher lying excited states. We find that the characteristic asymmetry of one-dimensional spectroscopies is recovered from the many-body contributions and that the higher lying excited manifolds have distorted lineshapes that are not anticipated from discrete-level Hamiltonians. We show that the Stimulated Emission cannot have contributions from a flat continuum of states. This work completes the Ground-State Bleach and Stimulated Emission signals that were calculated previously [D. Finkelstein-Shapiro et al., Phys. Rev. B 94, 205137 (2016)]. The model reproduces the observations reported for molecules on surfaces probed by 2DIR.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

Mesoscopic and continuum modelling of angiogenesis

PubMed Central

Spill, F.; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.

2016-01-01

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. PMID:24615007

From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

NASA Astrophysics Data System (ADS)

Finster, Felix

This survey article reviews recent results on fermion systems in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.

Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction

NASA Astrophysics Data System (ADS)

Kaewunruen, S.; Mirza, O.

2017-10-01

At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.

Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, M. P.; Centre for Quantum Technologies, National University of Singapore; QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft

2016-02-15

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.

Possible role of interference, protein noise, and sink effects in nonphotochemical quenching in photosynthetic complexes

DOE PAGES

Berman, Gennady P.; Nesterov, Alexander I.; Gurvitz, Shmuel; ...

2016-04-30

Here, we analyze theoretically a simple and consistent quantum mechanical model that reveals the possible role of quantum interference, protein noise, and sink effects in the nonphotochemical quenching (NPQ) in light-harvesting complexes (LHCs). The model consists of a network of five interconnected sites (excitonic states of light-sensitive molecules) responsible for the NPQ mechanism. The model also includes the “damaging” and the dissipative channels. The damaging channel is responsible for production of singlet oxygen and other destructive outcomes. In this model, both damaging and “dissipative” charge transfer channels are described by discrete electron energy levels attached to their sinks, that mimicmore » the continuum part of electron energy spectrum. All five excitonic sites interact with the protein environment that is modeled using a stochastic process. Our approach allowed us to derive the exact and closed system of linear ordinary differential equations for the reduced density matrix and its first momentums. Moreover, these equations are solved numerically including for strong interactions between the light-sensitive molecules and protein environment. As an example, we apply our model to demonstrate possible contributions of quantum interference, protein noise, and sink effects in the NPQ mechanism in the CP29 minor LHC. The numerical simulations show that using proper combination of quantum interference effects, properties of noise, and sinks, one can significantly suppress the damaging channel. Finally, our findings demonstrate the possible role of interference, protein noise, and sink effects for modeling, engineering, and optimizing the performance of the NPQ processes in both natural and artificial light-harvesting complexes.« less

Research on Damage Models for Continuous Fiber Composites

DTIC Science & Technology

1988-07-01

r ~.F (~ Mechanics and Materials Center TEXAS A&M UNIVERSITY College Station, Texas RESEARCH ON DAMAGE MODELS FOR CONTINUOUS FIBER COMPOSITES Final...Washington, DC 20332 11. TITLE (Include Security Clas=fication) Research on Damage Models for Continuous Fiber Composites - Final Technical Report 1...GROUP SUB-GROU ::=, COMPOsites ) continuum mechanics , ~ idamage, internal state variables V experimental mechanics, laminated composites o 19. ABSTRACT

Monolayers of hard rods on planar substrates. II. Growth

NASA Astrophysics Data System (ADS)

Klopotek, M.; Hansen-Goos, H.; Dixit, M.; Schilling, T.; Schreiber, F.; Oettel, M.

2017-02-01

Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing-up" transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion.

Computation and brain processes, with special reference to neuroendocrine systems.

PubMed

Toni, Roberto; Spaletta, Giulia; Casa, Claudia Della; Ravera, Simone; Sandri, Giorgio

2007-01-01

The development of neural networks and brain automata has made neuroscientists aware that the performance limits of these brain-like devices lies, at least in part, in their computational power. The computational basis of a. standard cybernetic design, in fact, refers to that of a discrete and finite state machine or Turing Machine (TM). In contrast, it has been suggested that a number of human cerebral activites, from feedback controls up to mental processes, rely on a mixing of both finitary, digital-like and infinitary, continuous-like procedures. Therefore, the central nervous system (CNS) of man would exploit a form of computation going beyond that of a TM. This "non conventional" computation has been called hybrid computation. Some basic structures for hybrid brain computation are believed to be the brain computational maps, in which both Turing-like (digital) computation and continuous (analog) forms of calculus might occur. The cerebral cortex and brain stem appears primary candidate for this processing. However, also neuroendocrine structures like the hypothalamus are believed to exhibit hybrid computional processes, and might give rise to computational maps. Current theories on neural activity, including wiring and volume transmission, neuronal group selection and dynamic evolving models of brain automata, bring fuel to the existence of natural hybrid computation, stressing a cooperation between discrete and continuous forms of communication in the CNS. In addition, the recent advent of neuromorphic chips, like those to restore activity in damaged retina and visual cortex, suggests that assumption of a discrete-continuum polarity in designing biocompatible neural circuitries is crucial for their ensuing performance. In these bionic structures, in fact, a correspondence exists between the original anatomical architecture and synthetic wiring of the chip, resulting in a correspondence between natural and cybernetic neural activity. Thus, chip "form" provides a continuum essential to chip "function". We conclude that it is reasonable to predict the existence of hybrid computational processes in the course of many human, brain integrating activities, urging development of cybernetic approaches based on this modelling for adequate reproduction of a variety of cerebral performances.

Kinetic Monte Carlo simulations of ion-induced ripple formation: Dependence on flux, temperature, and defect concentration in the linear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chason, E.; Chan, W. L.; Bharathi, M. S.

Low-energy ion bombardment produces spontaneous periodic structures (sputter ripples) on many surfaces. Continuum theories describe the pattern formation in terms of ion-surface interactions and surface relaxation kinetics, but many features of these models (such as defect concentration) are unknown or difficult to determine. In this work, we present results of kinetic Monte Carlo simulations that model surface evolution using discrete atomistic versions of the physical processes included in the continuum theories. From simulations over a range of parameters, we obtain the dependence of the ripple growth rate, wavelength, and velocity on the ion flux and temperature. The results are discussedmore » in terms of the thermally dependent concentration and diffusivity of ion-induced surface defects. We find that in the early stages of ripple formation the simulation results are surprisingly well described by the predictions of the continuum theory, in spite of simplifying approximations used in the continuum model.« less

Discrete rational and breather solution in the spatial discrete complex modified Korteweg-de Vries equation and continuous counterparts.

PubMed

Zhao, Hai-Qiong; Yu, Guo-Fu

2017-04-01

In this paper, a spatial discrete complex modified Korteweg-de Vries equation is investigated. The Lax pair, conservation laws, Darboux transformations, and breather and rational wave solutions to the semi-discrete system are presented. The distinguished feature of the model is that the discrete rational solution can possess new W-shape rational periodic-solitary waves that were not reported before. In addition, the first-order rogue waves reach peak amplitudes which are at least three times of the background amplitude, whereas their continuous counterparts are exactly three times the constant background. Finally, the integrability of the discrete system, including Lax pair, conservation laws, Darboux transformations, and explicit solutions, yields the counterparts of the continuous system in the continuum limit.

A CONTINUUM HARD-SPHERE MODEL OF PROTEIN ADSORPTION

PubMed Central

Finch, Craig; Clarke, Thomas; Hickman, James J.

2012-01-01

Protein adsorption plays a significant role in biological phenomena such as cell-surface interactions and the coagulation of blood. Two-dimensional random sequential adsorption (RSA) models are widely used to model the adsorption of proteins on solid surfaces. Continuum equations have been developed so that the results of RSA simulations can be used to predict the kinetics of adsorption. Recently, Brownian dynamics simulations have become popular for modeling protein adsorption. In this work a continuum model was developed to allow the results from a Brownian dynamics simulation to be used as the boundary condition in a computational fluid dynamics (CFD) simulation. Brownian dynamics simulations were used to model the diffusive transport of hard-sphere particles in a liquid and the adsorption of the particles onto a solid surface. The configuration of the adsorbed particles was analyzed to quantify the chemical potential near the surface, which was found to be a function of the distance from the surface and the fractional surface coverage. The near-surface chemical potential was used to derive a continuum model of adsorption that incorporates the results from the Brownian dynamics simulations. The equations of the continuum model were discretized and coupled to a CFD simulation of diffusive transport to the surface. The kinetics of adsorption predicted by the continuum model closely matched the results from the Brownian dynamics simulation. This new model allows the results from mesoscale simulations to be incorporated into micro- or macro-scale CFD transport simulations of protein adsorption in practical devices. PMID:23729843

Combined binary collision and continuum mechanics model applied to focused ion beam milling of a silicon membrane

NASA Astrophysics Data System (ADS)

Hobler, Gerhard

2015-06-01

Many experiments indicate the importance of stress and stress relaxation upon ion implantation. In this paper, a model is proposed that is capable of describing ballistic effects as well as stress relaxation by viscous flow. It combines atomistic binary collision simulation with continuum mechanics. The only parameters that enter the continuum model are the bulk modulus and the radiation-induced viscosity. The shear modulus can also be considered but shows only minor effects. A boundary-fitted grid is proposed that is usable both during the binary collision simulation and for the spatial discretization of the force balance equations. As an application, the milling of a slit into an amorphous silicon membrane with a 30 keV focused Ga beam is studied, which demonstrates the relevance of the new model compared to a more heuristic approach used in previous work.

Ensuring congruency in multiscale modeling: towards linking agent based and continuum biomechanical models of arterial adaptation.

PubMed

Hayenga, Heather N; Thorne, Bryan C; Peirce, Shayn M; Humphrey, Jay D

2011-11-01

There is a need to develop multiscale models of vascular adaptations to understand tissue-level manifestations of cellular level mechanisms. Continuum-based biomechanical models are well suited for relating blood pressures and flows to stress-mediated changes in geometry and properties, but less so for describing underlying mechanobiological processes. Discrete stochastic agent-based models are well suited for representing biological processes at a cellular level, but not for describing tissue-level mechanical changes. We present here a conceptually new approach to facilitate the coupling of continuum and agent-based models. Because of ubiquitous limitations in both the tissue- and cell-level data from which one derives constitutive relations for continuum models and rule-sets for agent-based models, we suggest that model verification should enforce congruency across scales. That is, multiscale model parameters initially determined from data sets representing different scales should be refined, when possible, to ensure that common outputs are consistent. Potential advantages of this approach are illustrated by comparing simulated aortic responses to a sustained increase in blood pressure predicted by continuum and agent-based models both before and after instituting a genetic algorithm to refine 16 objectively bounded model parameters. We show that congruency-based parameter refinement not only yielded increased consistency across scales, it also yielded predictions that are closer to in vivo observations.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

A lagrangian-eulerian description of debris transport by a tsunami in the Lisbon waterfront

NASA Astrophysics Data System (ADS)

Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.

2013-04-01

Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (eulerian) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (lagrangian) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the eulerian solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was thoroughly discretized with a mesh finer than street width so that the buildings would act as obstacles and the streets would bind the incoming flow. To simplify the plan-view geometry, it was assumed that buildings would retain its original shape after the earthquake. The results of the eulerian-continuum and of the lagrangian-discrete solutions are presented, compared and discussed. It was found that the patterns of deposition of the eulerian-continuum model can be considerably different to those obtained by the lagrangian-discrete solution if the latter assumes that vehicles have a small equivalent density and if momentum losses due to inter-particle collisions are neglected. Results become more similar if vehicles are considered much denser than water and that the mixture of water and solid bodies loses momentum due to particle collisions. Acknowledgements: Project PTDC/ECM/117660/2010, funded by the Portuguese Foundation for Science and Technology (FCT) has partially supported this work. References Canelas, R.; Murillo, J. & Ferreira, R.M.L. (2013) 2DH modelling of discontinuous flows over mobile beds. Accepted, Journal of Hydraulic Research, December 2012 Baptista M.A. Miranda, J.M. (2009). Revision of the Portuguese catalog of tsunamis. Nat. Hazards Earth Syst. Sci., 9, 25-42.

Induced seismicity in a salt mine environment evaluated by a coupled continuum-discrete modelling.

NASA Astrophysics Data System (ADS)

Mercerat, E.; Souley, M.; Driad, L.; Bernard, P.

2005-12-01

Within the framework of a research project launched to assess the feasibility of seismic monitoring of underground growing cavities, this specific work focus on two main complementary axis: the validation of seismic monitoring techniques in salt mine environments, and the numerical modelling of deformation and failure mechanisms with their associated acoustic emissions, the induced microseismicity. The underground cavity under monitoring is located at Cerville (Lorraine, France) within a salt layer 180 m deep and it presents a rather regular cylindrical shape of 100 m diameter. Typically, the overburden is characterized by the presence of two competent layers with elasto-brittle behaviour and located 50 m above the salt layer. When the salt exploitation restarts, the cavity will progressively grow causing irreversible damage of the upper layers until its final collapse at a time scale of the order of one year. Numerical modelling of such a complex process requires a large scale model which takes into account both the growing cavity within the salt layer and the mechanical behaviour of the overburden where high deformation and fracturing is expected. To keep the elasto-brittle behaviour of the competent layers where most seismic damage is expected, we use the PFC code (Itasca Cons). To approach the other layers (mainly composed of marls and salt) which present more ductile and/or viscoplastic behaviour, a continuum approach based on the FLAC code (Itasca Cons) is employed. Numerous calibration process were needed to estimate the microproperties used in PFC to reproduce the macroscopic behaviour from laboratory tests performed on samples extracted from the competent layers. As long as the size of the PFC inclusion representing the brittle material is much higher than the core sample sizes, the scale effect of microproperties is examined. The next stage is to perform calculations on the basis of previous macroscopic and microproperties calibration results, and compare them with the observed microseismicity in the rock mass.

Phase Field Model of Hydraulic Fracturing in Poroelastic Media: Fracture Propagation, Arrest, and Branching Under Fluid Injection and Extraction

NASA Astrophysics Data System (ADS)

Santillán, David; Juanes, Ruben; Cueto-Felgueroso, Luis

2018-03-01

The simulation of fluid-driven fracture propagation in a porous medium is a major computational challenge, with applications in geosciences and engineering. The two main families of modeling approaches are those models that represent fractures as explicit discontinuities and solve the moving boundary problem and those that represent fractures as thin damaged zones, solving a continuum problem throughout. The latter family includes the so-called phase field models. Continuum approaches to fracture face validation and verification challenges, in particular grid convergence, well posedness, and physical relevance in practical scenarios. Here we propose a new quasi-static phase field formulation. The approach fully couples fluid flow in the fracture with deformation and flow in the porous medium, discretizes flow in the fracture on a lower-dimension manifold, and employs the fluid flux between the fracture and the porous solid as coupling variable. We present a numerical assessment of the model by studying the propagation of a fracture in the quarter five-spot configuration. We study the interplay between injection flow rate and rock properties and elucidate fracture propagation patterns under the leak-off toughness dominated regime as a function of injection rate, initial fracture length, and poromechanical properties. For the considered injection scenario, we show that the final fracture length depends on the injection rate, and three distinct patterns are observed. We also rationalize the system response using dimensional analysis to collapse the model results. Finally, we propose some simplifications that alleviate the computational cost of the simulations without significant loss of accuracy.

Defects in Nematic Shells: A Γ-Convergence Discrete-to-Continuum Approach

NASA Astrophysics Data System (ADS)

Canevari, Giacomo; Segatti, Antonio

2018-07-01

In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment of the director field. To this end, we consider a discrete XY system on the shell M, described by a tangent vector field with unit norm sitting at the vertices of a triangulation of the shell. Defects emerge when we let the mesh size of the triangulation go to zero, namely in the discrete-to-continuum limit. In this paper we investigate the discrete-to-continuum limit in terms of Γ-convergence in two different asymptotic regimes. The first scaling promotes the appearance of a finite number of defects whose charges are in accordance with the topology of shell M, via the Poincaré-Hopf Theorem. The second scaling produces the so called Renormalized Energy that governs the equilibrium of the configurations with defects.

Continuum Level Density in Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Myo, T.; Katō, K.

2005-11-01

A new calculational method of continuum level density (CLD) at unbound energies is studied in the complex scaling method (CSM). It is shown that the CLD can be calculated by employing the discretization of continuum states in the CSM without any smoothing technique.

9Be scattering with microscopic wave functions and the continuum-discretized coupled-channel method

NASA Astrophysics Data System (ADS)

Descouvemont, P.; Itagaki, N.

2018-01-01

We use microscopic 9Be wave functions defined in a α +α +n multicluster model to compute 9Be+target scattering cross sections. The parameter sets describing 9Be are generated in the spirit of the stochastic variational method, and the optimal solution is obtained by superposing Slater determinants and by diagonalizing the Hamiltonian. The 9Be three-body continuum is approximated by square-integral wave functions. The 9Be microscopic wave functions are then used in a continuum-discretized coupled-channel (CDCC) calculation of 9Be+208Pb and of 9Be+27Al elastic scattering. Without any parameter fitting, we obtain a fair agreement with experiment. For a heavy target, the influence of 9Be breakup is important, while it is weaker for light targets. This result confirms previous nonmicroscopic CDCC calculations. One of the main advantages of the microscopic CDCC is that it is based on nucleon-target interactions only; there is no adjustable parameter. The present work represents a first step towards more ambitious calculations involving heavier Be isotopes.

Creep Tests and Modeling Based on Continuum Damage Mechanics for T91 and T92 Steels

NASA Astrophysics Data System (ADS)

Pan, J. P.; Tu, S. H.; Zhu, X. W.; Tan, L. J.; Hu, B.; Wang, Q.

2017-12-01

9-11%Cr ferritic steels play an important role in high-temperature and high-pressure boilers of advanced power plants. In this paper, a continuum damage mechanics (CDM)-based creep model was proposed to study the creep behavior of T91 and T92 steels at high temperatures. Long-time creep tests were performed for both steels under different conditions. The creep rupture data and creep curves obtained from creep tests were captured well by theoretical calculation based on the CDM model over a long creep time. It is shown that the developed model is able to predict creep data for the two ferritic steels accurately up to tens of thousands of hours.

Mathematical and Computational Aspects Related to Soil Modeling and Simulation

DTIC Science & Technology

2017-09-26

and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...applied math tools need to be established and used to figure out how to impose compatible boundary conditions, how to better approximate the gradient

DSSPcont: continuous secondary structure assignments for proteins

PubMed Central

Carter, Phil; Andersen, Claus A. F.; Rost, Burkhard

2003-01-01

The DSSP program automatically assigns the secondary structure for each residue from the three-dimensional co-ordinates of a protein structure to one of eight states. However, discrete assignments are incomplete in that they cannot capture the continuum of thermal fluctuations. Therefore, DSSPcont (http://cubic.bioc.columbia.edu/services/DSSPcont) introduces a continuous assignment of secondary structure that replaces ‘static’ by ‘dynamic’ states. Technically, the continuum results from calculating weighted averages over 10 discrete DSSP assignments with different hydrogen bond thresholds. A DSSPcont assignment for a particular residue is a percentage likelihood of eight secondary structure states, derived from a weighted average of the ten DSSP assignments. The continuous assignments have two important features: (i) they reflect the structural variations due to thermal fluctuations as detected by NMR spectroscopy; and (ii) they reproduce the structural variation between many NMR models from one single model. Therefore, functionally important variation can be extracted from a single X-ray structure using the continuous assignment procedure. PMID:12824310

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots.

PubMed

Hannan, Michael W; Walker, Ian D

2003-02-01

Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model. c2003 Wiley Periodicals, Inc.

Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots

NASA Technical Reports Server (NTRS)

Hannan, Michael W.; Walker, Ian D.

2003-01-01

Traditionally, robot manipulators have been a simple arrangement of a small number of serially connected links and actuated joints. Though these manipulators prove to be very effective for many tasks, they are not without their limitations, due mainly to their lack of maneuverability or total degrees of freedom. Continuum style (i.e., continuous "back-bone") robots, on the other hand, exhibit a wide range of maneuverability, and can have a large number of degrees of freedom. The motion of continuum style robots is generated through the bending of the robot over a given section; unlike traditional robots where the motion occurs in discrete locations, i.e., joints. The motion of continuum manipulators is often compared to that of biological manipulators such as trunks and tentacles. These continuum style robots can achieve motions that could only be obtainable by a conventionally designed robot with many more degrees of freedom. In this paper we present a detailed formulation and explanation of a novel kinematic model for continuum style robots. The design, construction, and implementation of our continuum style robot called the elephant trunk manipulator is presented. Experimental results are then provided to verify the legitimacy of our model when applied to our physical manipulator. We also provide a set of obstacle avoidance experiments that help to exhibit the practical implementation of both our manipulator and our kinematic model. c2003 Wiley Periodicals, Inc.

Literature Reviews on Modeling Internal Geometry of Textile Composites and Rate-Independent Continuum Damage

NASA Technical Reports Server (NTRS)

Su-Yuen, Hsu

2011-01-01

Textile composite materials have good potential for constructing composite structures where the effects of three-dimensional stresses are critical or geometric complexity is a manufacturing concern. There is a recent interest in advancing competence within Langley Research Center for modeling the degradation of mechanical properties of textile composites. In an initial effort, two critical areas are identified to pursue: (1) Construction of internal geometry of textile composites, and (2) Rate-independent continuum damage mechanics. This report documents reviews on the two subjects. Various reviewed approaches are categorized, their assumptions, methods, and progress are briefed, and then critiques are presented. Each review ends with recommended research.

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

NASA Technical Reports Server (NTRS)

Spear, Ashley D.; Priest, Amanda R.; Veilleux, Michael G.; Ingraffea, Anthony R.; Hochhalter, Jacob D.

2011-01-01

A surrogate model methodology is described for predicting in real time the residual strength of flight structures with discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. A residual strength test of a metallic, integrally-stiffened panel is simulated to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data would, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high-fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

NASA Technical Reports Server (NTRS)

Spear, Ashley D.; Priest, Amanda R.; Veilleux, Michael G.; Ingraffea, Anthony R.; Hochhalter, Jacob D.

2011-01-01

A surrogate model methodology is described for predicting, during flight, the residual strength of aircraft structures that sustain discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. Two ductile fracture simulations are presented to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data does, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Continuum-Kinetic Models and Numerical Methods for Multiphase Applications

NASA Astrophysics Data System (ADS)

Nault, Isaac Michael

This thesis presents a continuum-kinetic approach for modeling general problems in multiphase solid mechanics. In this context, a continuum model refers to any model, typically on the macro-scale, in which continuous state variables are used to capture the most important physics: conservation of mass, momentum, and energy. A kinetic model refers to any model, typically on the meso-scale, which captures the statistical motion and evolution of microscopic entitites. Multiphase phenomena usually involve non-negligible micro or meso-scopic effects at the interfaces between phases. The approach developed in the thesis attempts to combine the computational performance benefits of a continuum model with the physical accuracy of a kinetic model when applied to a multiphase problem. The approach is applied to modeling a single particle impact in Cold Spray, an engineering process that intimately involves the interaction of crystal grains with high-magnitude elastic waves. Such a situation could be classified a multiphase application due to the discrete nature of grains on the spatial scale of the problem. For this application, a hyper elasto-plastic model is solved by a finite volume method with approximate Riemann solver. The results of this model are compared for two types of plastic closure: a phenomenological macro-scale constitutive law, and a physics-based meso-scale Crystal Plasticity model.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation.

PubMed

Chen, Duan; Wei, Guo-Wei

2013-01-01

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Continuum kinetic modeling of the tokamak plasma edge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorf, M. A.; Dorr, M. R.; Hittinger, J. A.

2016-05-15

The first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalous radial transport.

Individual-based modelling of population growth and diffusion in discrete time.

PubMed

Tkachenko, Natalie; Weissmann, John D; Petersen, Wesley P; Lake, George; Zollikofer, Christoph P E; Callegari, Simone

2017-01-01

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers. We explore its emergent properties with analytical approximations and numerical simulations in parameter ranges relevant to human population dynamics and ecology, and reproduce continuous-time results in the limit of small transition probabilities. Our model prediction indicates that the population density and dispersal speed are affected by fluctuations in the number of individuals. The discrete-time model displays novel properties owing to the binomial character of the fluctuations: in certain regimes of the growth model, a decrease in time step size drives the system away from the continuum limit. These effects are especially important at local population sizes of <50 individuals, which largely correspond to group sizes of hunter-gatherers. As an application scenario, we model the late Pleistocene dispersal of Homo sapiens into the Americas, and discuss the agreement of model-based estimates of first-arrival dates with archaeological dates in dependence of IBM model parameter settings.

Bulbous head formation in bidisperse shallow granular flows over inclined planes

NASA Astrophysics Data System (ADS)

Denissen, I.; Thornton, A.; Weinhart, T.; Luding, S.

2017-12-01

Predicting the behaviour of hazardous natural granular flows (e.g. debris-flows and pyroclastic flows) is vital for an accurate assessment of the risks posed by such events. In these situations, an inversely graded vertical particle-size distribution develops, with larger particles on top of smaller particles. As the surface velocity of such flows is larger than the mean velocity, the larger material is then transported to the flow front. This creates a downstream size-segregation structure, resulting in a flow front composed purely of large particles, that are generally more frictional in geophysical flows. Thus, this segregation process reduces the mobility of the flow front, resulting in the formation of, a so-called, bulbous head. One of the main challenges of simulating these hazardous natural granular flows is the enormous number of particles they contain, which makes discrete particle simulations too computationally expensive to be practically useful. Continuum methods are able to simulate the bulk flow- and segregation behaviour of such flows, but have to make averaging approximations that reduce the huge number of degrees of freedom to a few continuum fields. Small-scale periodic discrete particle simulations can be used to determine the material parameters needed for the continuum model. In this presentation, we use a depth-averaged model to predict the flow profile for particulate chute flows, based on flow height, depth-averaged velocity and particle-size distribution [1], and show that the bulbous head structure naturally emerges from this model. The long-time behaviour of this solution of the depth-averaged continuum model converges to a novel travelling wave solution [2]. Furthermore, we validate this framework against computationally expensive 3D particle simulations, where we see surprisingly good agreement between both approaches, considering the approximations made in the continuum model. We conclude by showing that the travelling distance and height of a bidisperse granular avalanche can be well predicted by our continuum model. REFERENCES [1] M. J. Woodhouse, A. R. Thornton, C. G. Johnson, B. P. Kokelaar, J. M. N. T. Gray, J. Fluid Mech., 709, 543-580 (2012) [2] I.F.C. Denissen, T. Weinhart, A. Te Voortwis, S. Luding, J. M. N. T. Gray, A. R. Thornton, under review with J. Fluid Mech. (2017)

A differential CDM model for fatigue of unidirectional metal matrix composites

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Kruch, S.

1992-01-01

A multiaxial, isothermal, continuum damage mechanics (CDM) model for fatigue of a unidirectional metal matrix composite volume element is presented. The model is phenomenological, stress based, and assumes a single scalar internal damage variable, the evolution of which is anisotropic. The development of the fatigue damage model, (i.e., evolutionary law) is based on the definition of an initially transversely isotropic fatigue limit surface, a static fracture surface, and a normalized stress amplitude function. The anisotropy of these surfaces and function, and therefore the model, is defined through physically meaningful invariants reflecting the local stress and material orientation. This transversely isotropic model is shown, when taken to it's isotropic limit, to directly simplify to a previously developed and validated isotropic fatigue continuum damage model. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation in attempting to characterize a class of composite materials, and (2) the capability of the formulation in predicting anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Also, specific material parameters representing an initial characterization of the composite system SiC/Ti 15-3 and the matrix material (Ti 15-3) are reported.

An enhanced version of a bone-remodelling model based on the continuum damage mechanics theory.

PubMed

Mengoni, M; Ponthot, J P

2015-01-01

The purpose of this work was to propose an enhancement of Doblaré and García's internal bone remodelling model based on the continuum damage mechanics (CDM) theory. In their paper, they stated that the evolution of the internal variables of the bone microstructure, and its incidence on the modification of the elastic constitutive parameters, may be formulated following the principles of CDM, although no actual damage was considered. The resorption and apposition criteria (similar to the damage criterion) were expressed in terms of a mechanical stimulus. However, the resorption criterion is lacking a dimensional consistency with the remodelling rate. We propose here an enhancement to this resorption criterion, insuring the dimensional consistency while retaining the physical properties of the original remodelling model. We then analyse the change in the resorption criterion hypersurface in the stress space for a two-dimensional (2D) analysis. We finally apply the new formulation to analyse the structural evolution of a 2D femur. This analysis gives results consistent with the original model but with a faster and more stable convergence rate.

Discrete-element simulation of sea-ice mechanics: Contact mechanics and granular jamming

NASA Astrophysics Data System (ADS)

Damsgaard, A.; Adcroft, A.; Sergienko, O. V.; Stern, A. A.

2017-12-01

Lagrangian models of sea-ice dynamics offer several advantages to Eulerian continuum methods. Spatial discretization on the ice-floe scale is natural for Lagrangian models, which additionally offer the convenience of being able to handle arbitrary sea-ice concentrations. This is likely to improve model performance in ice-marginal zones with strong advection. Furthermore, phase transitions in granular rheology around the jamming limit, such as observed when sea ice moves through geometric confinements, includes sharp thresholds in effective viscosity which are typically ignored in Eulerian models. Granular jamming is a stochastic process dependent on having the right grains in the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. Difficult to parameterize in continuum formulations, jamming occurs naturally in dense granular systems simulated in a Lagrangian framework, and is a very relevant process controlling sea-ice transport through narrow straits. We construct a flexible discrete-element framework for simulating Lagrangian sea-ice dynamics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Using this framework, we demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to jam, and describe two different approaches based on friction and tensile strength which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model, with certain tensile strength values, can display jamming behavior which on the large scale is very similar to a more complex and realistic model with contact friction and ice-floe rotation.

Effects of Gas Rarefaction on Dynamic Characteristics of Micro Spiral-Grooved Thrust Bearing.

PubMed

Liu, Ren; Wang, Xiao-Li; Zhang, Xiao-Qing

2012-04-01

The effects of gas-rarefaction on dynamic characteristics of micro spiral-grooved-thrust-bearing are studied. The Reynolds equation is modified by the first order slip model, and the corresponding perturbation equations are then obtained on the basis of the linear small perturbation method. In the converted spiral-curve-coordinates system, the finite-volume-method (FVM) is employed to discrete the surface domain of micro bearing. The results show, compared with the continuum-flow model, that under the slip-flow regime, the decrease in the pressure and stiffness become obvious with the increasing of the compressibility number. Moreover, with the decrease of the relative gas-film-thickness, the deviations of dynamic coefficients between slip-flow-model and continuum-flow-model are increasing.

Continuum vs. spring network models of airway-parenchymal interdependence

PubMed Central

Ma, Baoshun

2012-01-01

The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought. PMID:22500006

Continuum limit of electrostatic gyrokinetic absolute equilibrium

NASA Astrophysics Data System (ADS)

Zhu, Jian-Zhou

2012-06-01

Electrostatic gyrokinetic absolute equilibria with continuum velocity field are obtained through the partition function and through the Green function of the functional integral. The new results justify and explain the prescription for quantization/discretization or taking the continuum limit of velocity. The mistakes in the Appendix D of our earlier work [J.-Z. Zhu and G. W. Hammett, Phys. Plasmas 17, 122307 (2010)] are explained and corrected. If the lattice spacing for discretizing velocity is big enough, all the invariants could concentrate at the lowest Fourier modes in a negative-temperature state, which might indicate a possible variation of the dual cascade picture in 2D plasma turbulence.

Nonlinear Multiscale Modeling of 3D Woven Fiber Composites under Ballistic Loading

DTIC Science & Technology

2013-07-11

contact parameters on the underlying damage processes is being studied and worked on. We further develop a material model suitable particularly for...of Material and Process Engineering. 2011/05/23 00:00:00, . : , TOTAL: 1 (d) Manuscripts Number of Peer-Reviewed Conference Proceeding publications...continuum damage mechanics suitable for polymer materials. The effect of contact parameters on the underlying damage processes is being studied and

Discrete shearlet transform: faithful digitization concept and its applications

NASA Astrophysics Data System (ADS)

Lim, Wang-Q.

2011-09-01

Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. Alongside the theoretical development of these systems, algorithmic realizations of the associated transforms were provided. However, one of the most common short-comings of these frameworks is the lack of providing a unified treatment of the continuum and digital world, i.e., allowing a digital theory to be a natural digitization of the continuum theory. Shearlets were introduced as means to sparsely encode anisotropic singularities of multivariate data while providing a unified treatment of the continuous and digital realm. In this paper, we introduce a discrete framework which allows a faithful digitization of the continuum domain shearlet transform based on compactly supported shearlets. Finally, we show numerical experiments demonstrating the potential of the discrete shearlet transform in several image processing applications.

Parallel multiscale simulations of a brain aneurysm

PubMed Central

Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em

2012-01-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκ αr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκ αr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work. PMID:23734066

Parallel multiscale simulations of a brain aneurysm.

PubMed

Grinberg, Leopold; Fedosov, Dmitry A; Karniadakis, George Em

2013-07-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκ αr . The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκ αr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.

Parallel multiscale simulations of a brain aneurysm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grinberg, Leopold; Fedosov, Dmitry A.; Karniadakis, George Em, E-mail: george_karniadakis@brown.edu

2013-07-01

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm.more » The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.« less

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome.

PubMed

Beard, D A; Schlick, T

2001-01-01

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels. Copyright 2000 John Wiley & Sons, Inc.

Perfect discretization of reparametrization invariant path integrals

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

2011-05-01

To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

NASA Technical Reports Server (NTRS)

Bergan, Andrew C.; Leone, Frank A., Jr.

2016-01-01

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

NASA Astrophysics Data System (ADS)

Karimi-Fard, M.; Durlofsky, L. J.

2016-10-01

A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.

Three-dimensional characterization of microporosity and permeability in fault zones hosted in heterolithic succession

NASA Astrophysics Data System (ADS)

Riegel, H. B.; Zambrano, M.; Jablonska, D.; Emanuele, T.; Agosta, F.; Mattioni, L.; Rustichelli, A.

2017-12-01

The hydraulic properties of fault zones depend upon the individual contributions of the damage zone and the fault core. In the case of the damage zone, it is generally characterized by means of fracture analysis and modelling implementing multiple approaches, for instance the discrete fracture network model, the continuum model, and the channel network model. Conversely, the fault core is more difficult to characterize because it is normally composed of fine grain material generated by friction and wear. If the dimensions of the fault core allows it, the porosity and permeability are normally studied by means of laboratory analysis or in the other case by two dimensional microporosity analysis and in situ measurements of permeability (e.g. micro-permeameter). In this study, a combined approach consisting of fracture modeling, three-dimensional microporosity analysis, and computational fluid dynamics was applied to characterize the hydraulic properties of fault zones. The studied fault zones crosscut a well-cemented heterolithic succession (sandstone and mudstones) and may vary in terms of fault core thickness and composition, fracture properties, kinematics (normal or strike-slip), and displacement. These characteristics produce various splay and fault core behavior. The alternation of sandstone and mudstone layers is responsible for the concurrent occurrence of brittle (fractures) and ductile (clay smearing) deformation. When these alternating layers are faulted, they produce corresponding fault cores which act as conduits or barriers for fluid migration. When analyzing damage zones, accurate field and data acquisition and stochastic modeling was used to determine the hydraulic properties of the rock volume, in relation to the surrounding, undamaged host rock. In the fault cores, the three-dimensional pore network quantitative analysis based on X-ray microtomography images includes porosity, pore connectivity, and specific surface area. In addition, images were used to perform computational fluid simulation (Lattice-Boltzmann multi relaxation time method) and estimate the permeability. These results will be useful for understanding the deformation process and hydraulic properties across meter-scale damage zones.

Modeling of Stone-impact Resistance of Monolithic Glass Ply Using Continuum Damage Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Xin; Khaleel, Mohammad A.; Davies, Richard W.

2005-04-01

We study the stone-impact resistance of a monolithic glass ply using a combined experimental and computational approach. Instrumented stone impact tests were first carried out in controlled environment. Explicit finite element analyses were then used to simulate the interactions of the indentor and the glass layer during the impact event, and a continuum damage mechanics (CDM) model was used to describe the constitutive behavior of glass. The experimentally measured strain histories for low velocity impact served as validation of the modeling procedures. Next, stair-stepping impact experiments were performed with two indentor sizes on two glass ply thickness, and the testmore » results were used to calibrate the critical stress parameters used in the CDM constitutive model. The purpose of this study is to establish the modeling procedures and the CDM critical stress parameters under impact loading conditions. The modeling procedures and the CDM model will be used in our future studies to predict through-thickness damage evolution patterns for different laminated windshield designs in automotive applications.« less

Continuum Damage Modeling for Dynamic Fracture Toughness of Metal Matrix Composites

NASA Astrophysics Data System (ADS)

Lee, Intaek; Ochi, Yasuo; Bae, Sungin; Song, Jungil

Short fiber reinforced metal-matrix composites (MMCs) have widely adopted as structural materials and many experimental researches have been performed to study fracture toughness of it. Fracture toughness is often referred as the plane strain(maximum constraint) fracture toughness KIc determined by the well-established standard test method, such as ASTM E399. But the application for dynamic fracture toughness KId has not been popular yet, because of reliance in capturing the crack propagating time. This paper deals with dynamic fracture toughness testing and simulation using finite element method to evaluate fracture behaviors of MMCs manufactured by squeeze casting process when material combination is varied with the type of reinforcement (appearance, size), volume fraction and combination of reinforcements, and the matrix alloy. The instrumented Charphy impact test was used for KId determination and continuum damage model embedded in commercial FE program is used to investigate the dynamic fracture toughness with the influence of elasto-visco-plastic constitutive relation of quasi-brittle fracture that is typical examples of ceramics and some fibre reinforced composites. With Compared results between experimental method and FE simulation, the determination process for KId is presented. FE simulation coupled with continuum damage model is emphasized single shot simulation can predict the dynamic fracture toughness, KId and real time evolution of that directly.

Low Activation Joining of SiC/SiC Composites for Fusion Applications: Thermomechanical Modeling of Dual-Phase Microstructures and Dissimilar Material Joints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Henager, Charles H.; Kurtz, Richard J.

2016-09-30

Finite element (FE) continuum damage mechanics (CDM) models have been developed to simulate and model dual-phase joints and cracked joints for improved analysis of SiC materials in nuclear environments. This report extends the analysis from the last reporting cycle by including preliminary thermomechanical analyses of cracked joints and implementation of dual-phase damage models.

PRELIMINARY PROGRESS IN THE DEVELOPMENT OF DUCTILE-PHASE TOUGHENED TUNGSTEN FOR PLASMA-FACING MATERIALS: DUAL-PHASE FINITE ELEMENT DAMAGE MODELS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henager, Charles H.; Nguyen, Ba Nghiep; Kurtz, Richard J.

The objective of this study is to develop a finite element continuum damage model suitable for modeling deformation, cracking, and crack bridging for W-Cu, W-Ni-Fe, and other ductile phase toughened W-composites, or more generally, any multi-phase composite structure where two or more phases undergo cooperative deformation in a composite system.

A Damage-Dependent Finite Element Analysis for Fiber-Reinforced Composite Laminates

NASA Technical Reports Server (NTRS)

Coats, Timothy W.; Harris, Charles E.

1998-01-01

A progressive damage methodology has been developed to predict damage growth and residual strength of fiber-reinforced composite structure with through penetrations such as a slit. The methodology consists of a damage-dependent constitutive relationship based on continuum damage mechanics. Damage is modeled using volume averaged strain-like quantities known as internal state variables and is represented in the equilibrium equations as damage induced force vectors instead of the usual degradation and modification of the global stiffness matrix.

Lagrangian approach to the Barrett-Crane spin foam model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonzom, Valentin; Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon; Livine, Etera R.

2009-03-15

We provide the Barrett-Crane spin foam model for quantum gravity with a discrete action principle, consisting in the usual BF term with discretized simplicity constraints which in the continuum turn topological BF theory into gravity. The setting is the same as usually considered in the literature: space-time is cut into 4-simplices, the connection describes how to glue these 4-simplices together and the action is a sum of terms depending on the holonomies around each triangle. We impose the discretized simplicity constraints on disjoint tetrahedra and we show how the Lagrange multipliers distort the parallel transport and the correlations between neighboringmore » simplices. We then construct the discretized BF action using a noncommutative * product between SU(2) plane waves. We show how this naturally leads to the Barrett-Crane model. This clears up the geometrical meaning of the model. We discuss the natural generalization of this action principle and the spin foam models it leads to. We show how the recently introduced spin foam fusion coefficients emerge with a nontrivial measure. In particular, we recover the Engle-Pereira-Rovelli spin foam model by weakening the discretized simplicity constraints. Finally, we identify the two sectors of Plebanski's theory and we give the analog of the Barrett-Crane model in the nongeometric sector.« less

Constraint algebra in Smolin's G →0 limit of 4D Euclidean gravity

NASA Astrophysics Data System (ADS)

Varadarajan, Madhavan

2018-05-01

Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.

Development of a 3D Soil-Plant-Atmosphere Continuum (SPAC) coupled to a Land Surface Model

NASA Astrophysics Data System (ADS)

Bisht, G.; Riley, W. J.; Lorenzetti, D.; Tang, J.

2015-12-01

Exchange of water between the atmosphere and biosphere via evapotranspiration (ET) influences global hydrological, energy, and biogeochemical cycles. Isotopic analysis has shown that evapotranspiration over the continents is largely dominated by transpiration. Water is taken up from soil by plant roots, transported through the plant's vascular system, and evaporated from the leaves. Yet current Land Surface Models (LSMs) integrated into Earth System Models (ESMs) treat plant roots as passive components. These models distribute the ET sink vertically over the soil column, neglect the vertical pressure distribution along the plant vascular system, and assume that leaves can directly access water from any soil layer within the root zone. Numerous studies have suggested that increased warming due to climate change will lead drought and heat-induced tree mortality. A more mechanistic treatment of water dynamics in the soil-plant-atmosphere continuum (SPAC) is essential for investigating the fate of ecosystems under a warmer climate. In this work, we describe a 3D SPAC model that can be coupled to a LSM. The SPAC model uses the variably saturated Richards equations to simulate water transport. The model uses individual governing equations and constitutive relationships for the various SPAC components (i.e., soil, root, and xylem). Finite volume spatial discretization and backward Euler temporal discretization is used to solve the SPAC model. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is used to numerically integrate the discretized system of equations. Furthermore, PETSc's multi-physics coupling capability (DMComposite) is used to solve the tightly coupled system of equations of the SPAC model. Numerical results are presented for multiple test problems.

Wave propagation in equivalent continuums representing truss lattice materials

DOE PAGES

Messner, Mark C.; Barham, Matthew I.; Kumar, Mukul; ...

2015-07-29

Stiffness scales linearly with density in stretch-dominated lattice meta-materials offering the possibility of very light yet very stiff structures. Current additive manufacturing techniques can assemble structures from lattice materials, but the design of such structures will require accurate, efficient simulation methods. Equivalent continuum models have several advantages over discrete truss models of stretch dominated lattices, including computational efficiency and ease of model construction. However, the development an equivalent model suitable for representing the dynamic response of a periodic truss in the small deformation regime is complicated by microinertial effects. This study derives a dynamic equivalent continuum model for periodic trussmore » structures suitable for representing long-wavelength wave propagation and verifies it against the full Bloch wave theory and detailed finite element simulations. The model must incorporate microinertial effects to accurately reproduce long wavelength characteristics of the response such as anisotropic elastic soundspeeds. Finally, the formulation presented here also improves upon previous work by preserving equilibrium at truss joints for simple lattices and by improving numerical stability by eliminating vertices in the effective yield surface.« less

76 FR 74655 - Damage Tolerance and Fatigue Evaluation of Composite Rotorcraft Structures

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-01

... and discrete flaws, and impact or other accidental damage (including the discrete source of the... discrete manufacturing defects or accidental damage, is avoided throughout the operational life or... and discrete flaws, and impact or other accidental damage (including the discrete source of the...

Molecular dynamics simulation of propagating cracks

NASA Technical Reports Server (NTRS)

Mullins, M.

1982-01-01

Steady state crack propagation is investigated numerically using a model consisting of 236 free atoms in two (010) planes of bcc alpha iron. The continuum region is modeled using the finite element method with 175 nodes and 288 elements. The model shows clear (010) plane fracture to the edge of the discrete region at moderate loads. Analysis of the results obtained indicates that models of this type can provide realistic simulation of steady state crack propagation.

Continuum kinetic modeling of the tokamak plasma edge

DOE PAGES

Dorf, M. A.; Dorr, M.; Rognlien, T.; ...

2016-03-10

In this study, the first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasmatransport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalousmore » radial transport.« less

Modeling Progressive Damage Using Local Displacement Discontinuities Within the FEAMAC Multiscale Modeling Framework

NASA Technical Reports Server (NTRS)

Ranatunga, Vipul; Bednarcyk, Brett A.; Arnold, Steven M.

2010-01-01

A method for performing progressive damage modeling in composite materials and structures based on continuum level interfacial displacement discontinuities is presented. The proposed method enables the exponential evolution of the interfacial compliance, resulting in unloading of the tractions at the interface after delamination or failure occurs. In this paper, the proposed continuum displacement discontinuity model has been used to simulate failure within both isotropic and orthotropic materials efficiently and to explore the possibility of predicting the crack path, therein. Simulation results obtained from Mode-I and Mode-II fracture compare the proposed approach with the cohesive element approach and Virtual Crack Closure Techniques (VCCT) available within the ABAQUS (ABAQUS, Inc.) finite element software. Furthermore, an eccentrically loaded 3-point bend test has been simulated with the displacement discontinuity model, and the resulting crack path prediction has been compared with a prediction based on the extended finite element model (XFEM) approach.

Mechanical and hydraulic properties of rocks related to induced seismicity

USGS Publications Warehouse

Witherspoon, P.A.; Gale, J.E.

1977-01-01

Witherspoon, P.A. and Gale, J.E., 1977. Mechanical and hydraulic properties of rocks related to induced seismicity. Eng. Geol., 11(1): 23-55. The mechanical and hydraulic properties of fractured rocks are considered with regard to the role they play in induced seismicity. In many cases, the mechanical properties of fractures determine the stability of a rock mass. The problems of sampling and testing these rock discontinuities and interpreting their non-linear behavior are reviewed. Stick slip has been proposed as the failure mechanism in earthquake events. Because of the complex interactions that are inherent in the mechanical behavior of fractured rocks, there seems to be no simple way to combine the deformation characteristics of several sets of fractures when there are significant perturbations of existing conditions. Thus, the more important fractures must be treated as individual components in the rock mass. In considering the hydraulic properties, it has been customary to treat a fracture as a parallel-plate conduit and a number of mathematical models of fracture systems have adopted this approach. Non-steady flow in fractured systems has usually been based on a two-porosity model, which assumes the primary (intergranular) porosity contributes only to storage and the secondary (fracture) porosity contributes only to the overall conductivity. Using such a model, it has been found that the time required to achieve quasi-steady state flow in a fractured reservoir is one or two orders of magnitude greater than it is in a homogeneous system. In essentially all of this work, the assumption has generally been made that the fractures are rigid. However, it is clear from a review of the mechanical and hydraulic properties that not only are fractures easily deformed but they constitute the main flow paths in many rock masses. This means that one must consider the interaction of mechanical and hydraulic effects. A considerable amount of laboratory and field data is now available that clearly demonstrates this stress-flow behavior. Two approaches have been used in attempting to numerically model such behavior: (1) continuum models, and (2) discrete models. The continuum approach only needs information as to average values of fracture spacing and material properties. But because of the inherent complexity of fractured rock masses and the corresponding decrease in symmetry, it is difficult to develop an equivalent continuum that will simulate the behavior of the entire system. The discrete approach, on the other hand, requires details of the fracture geometry and material properties of both fractures and rock matrix. The difficulty in obtaining such information has been considered a serious limitation of discrete models, but improved borehole techniques can enable one to obtain the necessary data, at least in shallow systems. The possibility of extending these methods to deeper fracture systems needs more investigation. Such data must be considered when deciding whether to use a continuum or discrete model to represent the interaction of rock and fluid forces in a fractured rock system, especially with regard to the problem of induced seismicity. When one is attempting to alter the pressure distribution in a fault zone by injection or withdrawal of fluids, the extent to which this can be achieved will be controlled in large measure by the behavior of the fractures that communicate with the borehole. Since this is essentially a point phenomenon, i.e., the changes will propagate from a relatively small region around the borehole, the use of a discrete model would appear to be preferable. ?? 1977.

Optimal Battery Charging for Damage Mitigation

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2003-01-01

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X Q

We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. Withmore » our 4D ({psi}, {theta}, {epsilon}, {mu}) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.« less

Continuum approach to the BF vacuum: The U(1) case

NASA Astrophysics Data System (ADS)

Drobiński, Patryk; Lewandowski, Jerzy

2017-12-01

A quantum representation of holonomies and exponentiated fluxes of a U(1) gauge theory that contains the Pullin-Dittrich-Geiller (DG) vacuum is presented and discussed. Our quantization is performed manifestly in a continuum theory, without any discretization. The discreteness emerges on the quantum level as a property of the spectrum of the quantum holonomy operators. The new type of a cylindrical consistency present in the DG approach now follows easily and naturally. A generalization to the non-Abelian case seems possible.

Comparing methods for modelling spreading cell fronts.

PubMed

Markham, Deborah C; Simpson, Matthew J; Maini, Philip K; Gaffney, Eamonn A; Baker, Ruth E

2014-07-21

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and the asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performance of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made. Copyright © 2014 Elsevier Ltd. All rights reserved.

3D ductile crack propagation within a polycrystalline microstructure using XFEM

NASA Astrophysics Data System (ADS)

Beese, Steffen; Loehnert, Stefan; Wriggers, Peter

2018-02-01

In this contribution we present a gradient enhanced damage based method to simulate discrete crack propagation in 3D polycrystalline microstructures. Discrete cracks are represented using the eXtended finite element method. The crack propagation criterion and the crack propagation direction for each point along the crack front line is based on the gradient enhanced damage variable. This approach requires the solution of a coupled problem for the balance of momentum and the additional global equation for the gradient enhanced damage field. To capture the discontinuity of the displacements as well as the gradient enhanced damage along the discrete crack, both fields are enriched using the XFEM in combination with level sets. Knowing the crack front velocity, level set methods are used to compute the updated crack geometry after each crack propagation step. The applied material model is a crystal plasticity model often used for polycrystalline microstructures of metals in combination with the gradient enhanced damage model. Due to the inelastic material behaviour after each discrete crack propagation step a projection of the internal variables from the old to the new crack configuration is required. Since for arbitrary crack geometries ill-conditioning of the equation system may occur due to (near) linear dependencies between standard and enriched degrees of freedom, an XFEM stabilisation technique based on a singular value decomposition of the element stiffness matrix is proposed. The performance of the presented methodology to capture crack propagation in polycrystalline microstructures is demonstrated with a number of numerical examples.

Micromechanical modelling of polyethylene

NASA Astrophysics Data System (ADS)

Alvarado Contreras, Jose Andres

2008-10-01

The increasing use of polyethylene in diverse applications motivates the need for understanding how its molecular properties relate to the overall behaviour of the material. Although microstructure and mechanical properties of polymers have been the subject of several studies, the irreversible microstructural rearrangements occurring at large deformations are not completely understood. The purpose of this thesis is to describe how the concepts of Continuum Damage Mechanics can be applied to modelling of polyethylene materials under different loading conditions. The first part of the thesis consists of the theoretical formulation and numerical implementation of a three-dimensional micromechanical model for crystalline polyethylene. Based on the theory of shear slip on crystallographic planes, the proposed model is expressed in the framework of viscoplasticity coupled with degradation at large deformations. Earlier models aid in the interpretation of the mechanical behaviour of crystalline polyethylene under different loading conditions; however, they cannot predict the microstructural damage caused by deformation. The model, originally due to Parks and Ahzi (199o), was further developed in the light of the concept of Continuum Damage Mechanics to consider the original microstructure, the particular irreversible rearrangements, and the deformation mechanisms. Damage mechanics has been a matter of intensive research by many authors, yet it has not been introduced to the micromodelling of semicrystalline polymeric materials such as polyethylene. Regarding the material representation, the microstructure is simplified as an aggregate of randomly oriented and perfectly bonded crystals. To simulate large deformations, the new constitutive model attempts to take into account existence of intracrystalline microcracks. The second part of the work presents the theoretical formulation and numerical implementation of a three-dimensional constitutive model for the mechanical behaviour of semicrystalline polyethylene. The model proposed herein attempts to describe the deformation and degradation process in semicrystalline polyethylene following the approach of damage mechanics. Structural degradation, an important phenomenon at large deformations, has not received sufficient attention in the literature. The modifications to the constitutive equations consist essentially of introducing the concept of Continuum Damage Mechanics to describe the rupture of the intermolecular (van der Waals) bonds that hold crystals as coherent structures. In order to model the mechanical behaviour, the material morphology is simplified as a collection of inclusions comprising the crystalline and amorphous phases with their characteristic average volume fractions. In the spatial arrangement, each inclusion consists of crystalline material lying in a thin lamella attached to an amorphous layer. To consider microstructural damage, two different approaches are analyzed. The first approach assumes damage occurs only in the crystalline phase, i.e., degradation of the amorphous phase is ignored. The second approach considers the effect of damage on the mechanical behaviour of both the amorphous and crystalline phases. To illustrate the proposed constitutive formulations, the models were used to predict the responses of crystalline and semicrystalline polyethylene under uniaxial tension and simple shear. The numerical simulations were compared with experimental data previously obtained by Bartczak et al. (1994), G'Sell and Jonas (1981), G'Sell et al. (1983), Hillmansen et al. (2000), and Li et al. (2001). Our model's predictions show a consistently good agreement with the experimental results and a significant improvement with respect to the ones obtained by Parks and Ahzi (1990), Schoenfeld et al. (1995), Yang and Chen (2001), Lee et al. (i993b), Lee et al. (1993a), and Nikolov et al. (2006). The newly proposed formulations demonstrate that these types of constitutive models based on Continuum Damage Mechanics are appropriate for predicting large deformations and failure in polyethylene materials.

A local PDE model of aggregation formation in bacterial colonies

NASA Astrophysics Data System (ADS)

Chavy-Waddy, Paul-Christopher; Kolokolnikov, Theodore

2016-10-01

We study pattern formation in a model of cyanobacteria motion recently proposed by Galante, Wisen, Bhaya and Levy. By taking a continuum limit of their model, we derive a novel fourth-order nonlinear parabolic PDE equation that governs the behaviour of the model. This PDE is {{u}t}=-{{u}xx}-{{u}xxxx}+α {{≤ft(\\frac{{{u}x}{{u}xx}}{u}\\right)}x} . We then derive the instability thresholds for the onset of pattern formation. We also compute analytically the spatial profiles of the steady state aggregation density. These profiles are shown to be of the form \\text{sec}{{\\text{h}}p} where the exponent p is related to the parameters of the model. Full numerical simulations give a favorable comparison between the continuum and the underlying discrete system, and show that the aggregation profiles are stable above the critical threshold.

A Ceramic Fracture Model for High Velocity Impact

DTIC Science & Technology

1993-05-01

employ damage concepts appear more relevant than crack growth models for this application . This research adopts existing fracture model concepts and...extends them through applications in an existing finite element continuum mechanics code (hydrocode) to the prediction of the damage and fracture processes...to be accurate in the lower velocity range of this work. Mescall and Tracy 15] investigated the selection of ceramic material for application in armors

Application of a Visco-Plastic Continuum Model to the Modeling of Near-Source Phenomenology and its Implications on Close-In Seismic Observables

NASA Astrophysics Data System (ADS)

Rougier, E.; Knight, E. E.

2015-12-01

The Source Physics Experiments (SPE) is a project funded by the U.S. Department of Energy at the National Nuclear Security Site. The project consists of a series of underground explosive tests designed to gain more insight on the generation and propagation of seismic energy from underground explosions in hard rock media, granite. Until now, four tests (SPE-1, SPE-2, SPE-3 and SPE-4Prime) with yields ranging from 87 kg to 1000 kg have been conducted in the same borehole. The generation and propagation of seismic waves is heavily influenced by the different damage mechanisms occurring at different ranges from the explosive source. These damage mechanisms include pore crushing, compressive (shear) damage, joint damage, spallation and fracture and fragmentation, etc. Understanding these mechanisms and how they interact with each other is essential to the interpretation of the characteristics of close-in seismic observables. Recent observations demonstrate that, for relatively small and shallow chemical explosions in granite, such as SPE-1, -2 and -3, the formation of a cavity around the working point is not the main mechanism responsible for the release of seismic moment. Shear dilatancy (bulking occurring as a consequence of compressive damage) of the medium around the source has been proposed as an alternative damage mechanism that explains the seismic moment release observed in the experiments. In this work, the interaction between cavity formation and bulking is investigated via a series of computer simulations for the SPE-2 event. The simulations are conducted using a newly developed material model, called AZ_Frac. AZ_Frac is a continuum-based-visco-plastic strain-rate-dependent material model. One of its key features is its ability to describe continuum fracture processes, while properly handling anisotropic material characteristics. The implications of the near source numerical results on the close-in seismic quantities, such as reduced displacement potentials and source spectra are presented.

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

NASA Astrophysics Data System (ADS)

Bacigalupo, Andrea; Gambarotta, Luigi

2017-05-01

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

Microdamage healing in asphalt and asphalt concrete, Volume 4 : a viscoelastic continuum damage fatigue model of asphalt concrete with microdamage healing

DOT National Transportation Integrated Search

2001-06-01

A mechanistic approach to fatigue characterization of asphalt-aggregate mixtures is presented in this volume. This approach is founded on a uniaxial viscoelastic correspondence principle is applied in order to evaluate damage growth and healing in cy...

Small-scale plasticity critically needs a new mechanics description

NASA Astrophysics Data System (ADS)

Ngan, Alfonso H. W.

2013-06-01

Continuum constitutive laws describe the plastic deformation of materials as a smooth, continuously differentiable process. However, provided that the measurement is done with a fine enough resolution, the plastic deformation of real materials is often found to comprise discrete events usually nanometric in size. For bulk-sized specimens, such nanoscale events are minute compared with the specimen size, and so their associated strain changes are negligibly small, and this is why the continuum laws work well. However, when the specimen size is in the micrometer scale or smaller, the strain changes due to the discrete events could be significant, and the continuum description would be highly unsatisfactory. Yet, because of the advent of microtechnology and nanotechnolgy, small-sized materials will be increasingly used, and so there is a strong need to develop suitable replacement descriptions for plasticity of small materials. As the occurrence of the discrete plastic events is also strongly stochastic, their satisfactory description should also be one of a probabilistic, rather than deterministic, nature.

3D Progressive Damage Modeling for Laminated Composite Based on Crack Band Theory and Continuum Damage Mechanics

NASA Technical Reports Server (NTRS)

Wang, John T.; Pineda, Evan J.; Ranatunga, Vipul; Smeltzer, Stanley S.

2015-01-01

A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.

A physically-based continuum damage mechanics model for numerical prediction of damage growth in laminated composite plates

NASA Astrophysics Data System (ADS)

Williams, Kevin Vaughan

Rapid growth in use of composite materials in structural applications drives the need for a more detailed understanding of damage tolerant and damage resistant design. Current analytical techniques provide sufficient understanding and predictive capabilities for application in preliminary design, but current numerical models applicable to composites are few and far between and their development into well tested, rigorous material models is currently one of the most challenging fields in composite materials. The present work focuses on the development, implementation, and verification of a plane-stress continuum damage mechanics based model for composite materials. A physical treatment of damage growth based on the extensive body of experimental literature on the subject is combined with the mathematical rigour of a continuum damage mechanics description to form the foundation of the model. The model has been implemented in the LS-DYNA3D commercial finite element hydrocode and the results of the application of the model are shown to be physically meaningful and accurate. Furthermore it is demonstrated that the material characterization parameters can be extracted from the results of standard test methodologies for which a large body of published data already exists for many materials. Two case studies are undertaken to verify the model by comparison with measured experimental data. The first series of analyses demonstrate the ability of the model to predict the extent and growth of damage in T800/3900-2 carbon fibre reinforced polymer (CFRP) plates subjected to normal impacts over a range of impact energy levels. The predicted force-time and force-displacement response of the panels compare well with experimental measurements. The damage growth and stiffness reduction properties of the T800/3900-2 CFRP are derived using published data from a variety of sources without the need for parametric studies. To further demonstrate the physical nature of the model, a IM6/937 CFRP with a more brittle matrix system than 3900-2 is also analysed. Results of analyses performed under the same impact conditions do not compare as well quantitatively with measurements but the results are still promising and qualitative differences between the T800/3900-2 and IM6/937 are accurately captured. Finally, to further demonstrate the capability of the model, the response of a notched CFRP plate under quasi-static tensile loading is simulated and compared to experimental measurements. Of particular significance is the fact that the experimental test modelled in this case is uniquely suited to the characterization of the strain softening phenomenon observed in FRP laminates. Results of this virtual experiment compare very favourably with the measured damage growth and force-displacement curves.

A Thermodynamically Consistent Damage Model for Advanced Composites

NASA Technical Reports Server (NTRS)

Maimi, Pere; Camanho, Pedro P.; Mayugo, Joan-Andreu; Davila, Carlos G.

2006-01-01

A continuum damage model for the prediction of damage onset and structural collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The principal damage mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a damage tensor that is fixed in space. Crack closure under load reversal effects are taken into account using damage variables established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different damage mechanisms occurring at the ply level. The constitutive damage model is implemented in a finite element code. The objectivity of the numerical model is assured by regularizing the dissipated energy at a material point using Bazant's Crack Band Model. To verify the accuracy of the approach, analyses of coupon specimens were performed, and the numerical predictions were compared with experimental data.

A study of material damping in large space structures

NASA Technical Reports Server (NTRS)

Highsmith, A. L.; Allen, D. H.

1989-01-01

A constitutive model was developed for predicting damping as a function of damage in continuous fiber reinforced laminated composites. The damage model is a continuum formulation, and uses internal state variables to quantify damage and its subsequent effect on material response. The model is sensitive to the stacking sequence of the laminate. Given appropriate baseline data from unidirectional material, and damping as a function of damage in one crossply laminate, damage can be predicted as a function of damage in other crossply laminates. Agreement between theory and experiment was quite good. A micromechanics model was also developed for examining the influence of damage on damping. This model explicitly includes crack surfaces. The model provides reasonable predictions of bending stiffness as a function of damage. Damping predictions are not in agreement with the experiment. This is thought to be a result of dissipation mechanisms such as friction, which are not presently included in the analysis.

Strong-field adiabatic passage in the continuum: Electromagnetically induced transparency and stimulated Raman adiabatic passage

NASA Astrophysics Data System (ADS)

Eilam, A.; Shapiro, M.

2012-01-01

We present a fully quantum-mechanical theory of the mutual light-matter effects when two laser pulses interact with three discrete states coupled to a (quasi)continuum. Our formulation uses a single set of equations to describe the time dependence of the discrete and continuum populations, as well as pulse propagation in electromagnetically induced transparency (EIT) and stimulated Raman adiabatic passage (STIRAP) situations, for both weak and strong laser pulses. The theory gives a mechanistic picture of the “slowing down of light” and the state of spontaneously emitted photons during this process. Surprising features regarding the time dependence of material and radiative transients as well as limitations on quantum light storage and retrieval are unraveled.

Topology and layout optimization of discrete and continuum structures

NASA Technical Reports Server (NTRS)

Bendsoe, Martin P.; Kikuchi, Noboru

1993-01-01

The basic features of the ground structure method for truss structure an continuum problems are described. Problems with a large number of potential structural elements are considered using the compliance of the structure as the objective function. The design problem is the minimization of compliance for a given structural weight, and the design variables for truss problems are the cross-sectional areas of the individual truss members, while for continuum problems they are the variable densities of material in each of the elements of the FEM discretization. It is shown how homogenization theory can be applied to provide a relation between material density and the effective material properties of a periodic medium with a known microstructure of material and voids.

Water solvent effects using continuum and discrete models: The nitromethane molecule, CH3NO2.

PubMed

Modesto-Costa, Lucas; Uhl, Elmar; Borges, Itamar

2015-11-15

The first three valence transitions of the two nitromethane conformers (CH3NO2) are two dark n → π* transitions and a very intense π → π* transition. In this work, these transitions in gas-phase and solvated in water of both conformers were investigated theoretically. The polarizable continuum model (PCM), two conductor-like screening (COSMO) models, and the discrete sequential quantum mechanics/molecular mechanics (S-QM/MM) method were used to describe the solvation effect on the electronic spectra. Time dependent density functional theory (TDDFT), configuration interaction including all single substitutions and perturbed double excitations (CIS(D)), the symmetry-adapted-cluster CI (SAC-CI), the multistate complete active space second order perturbation theory (CASPT2), and the algebraic-diagrammatic construction (ADC(2)) electronic structure methods were used. Gas-phase CASPT2, SAC-CI, and ADC(2) results are in very good agreement with published experimental and theoretical spectra. Among the continuum models, PCM combined either with CASPT2, SAC-CI, or B3LYP provided good agreement with available experimental data. COSMO combined with ADC(2) described the overall trends of the transition energy shifts. The effect of increasing the number of explicit water molecules in the S-QM/MM approach was discussed and the formation of hydrogen bonds was clearly established. By including explicitly 24 water molecules corresponding to the complete first solvation shell in the S-QM/MM approach, the ADC(2) method gives more accurate results as compared to the TDDFT approach and with similar computational demands. The ADC(2) with S-QM/MM model is, therefore, the best compromise for accurate solvent calculations in a polar environment. © 2015 Wiley Periodicals, Inc.

A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hadgu, Teklu; Karra, Satish; Kalinina, Elena

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. In this paper, we compare DFN and ECM in termsmore » of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km 3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. Finally, we identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.« less

A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock

DOE PAGES

Hadgu, Teklu; Karra, Satish; Kalinina, Elena; ...

2017-07-28

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. In this paper, we compare DFN and ECM in termsmore » of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km 3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. Finally, we identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.« less

A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock

NASA Astrophysics Data System (ADS)

Hadgu, Teklu; Karra, Satish; Kalinina, Elena; Makedonska, Nataliia; Hyman, Jeffrey D.; Klise, Katherine; Viswanathan, Hari S.; Wang, Yifeng

2017-10-01

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. We compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. We identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.

Effect of microstructural damage on ply stresses in laminated composites

NASA Technical Reports Server (NTRS)

Allen, D. H.; Nottorf, E. W.; Harris, C. E.

1988-01-01

The mechanisms involved in damage and failure of laminated orthotropic composites are investigated theoretically. The continuum model developed accounts for both matrix cracks and interply delamination using second-order tensor-valued internal-state variables based on the locally averaged microcrack dynamics. The derivation of the model is given in detail, and numerical results for sample problems are presented in extensive graphs and tables. The model is shown to be effective in predicting stresses at the ply level, and significant damage-induced decreases in laminate stress states are found.

Coupling of a continuum ice sheet model and a discrete element calving model using a scientific workflow system

NASA Astrophysics Data System (ADS)

Memon, Shahbaz; Vallot, Dorothée; Zwinger, Thomas; Neukirchen, Helmut

2017-04-01

Scientific communities generate complex simulations through orchestration of semi-structured analysis pipelines which involves execution of large workflows on multiple, distributed and heterogeneous computing and data resources. Modeling ice dynamics of glaciers requires workflows consisting of many non-trivial, computationally expensive processing tasks which are coupled to each other. From this domain, we present an e-Science use case, a workflow, which requires the execution of a continuum ice flow model and a discrete element based calving model in an iterative manner. Apart from the execution, this workflow also contains data format conversion tasks that support the execution of ice flow and calving by means of transition through sequential, nested and iterative steps. Thus, the management and monitoring of all the processing tasks including data management and transfer of the workflow model becomes more complex. From the implementation perspective, this workflow model was initially developed on a set of scripts using static data input and output references. In the course of application usage when more scripts or modifications introduced as per user requirements, the debugging and validation of results were more cumbersome to achieve. To address these problems, we identified a need to have a high-level scientific workflow tool through which all the above mentioned processes can be achieved in an efficient and usable manner. We decided to make use of the e-Science middleware UNICORE (Uniform Interface to Computing Resources) that allows seamless and automated access to different heterogenous and distributed resources which is supported by a scientific workflow engine. Based on this, we developed a high-level scientific workflow model for coupling of massively parallel High-Performance Computing (HPC) jobs: a continuum ice sheet model (Elmer/Ice) and a discrete element calving and crevassing model (HiDEM). In our talk we present how the use of a high-level scientific workflow middleware enables reproducibility of results more convenient and also provides a reusable and portable workflow template that can be deployed across different computing infrastructures. Acknowledgements This work was kindly supported by NordForsk as part of the Nordic Center of Excellence (NCoE) eSTICC (eScience Tools for Investigating Climate Change at High Northern Latitudes) and the Top-level Research Initiative NCoE SVALI (Stability and Variation of Arctic Land Ice).

Multiscale Modeling of Damage Processes in fcc Aluminum: From Atoms to Grains

NASA Technical Reports Server (NTRS)

Glaessgen, E. H.; Saether, E.; Yamakov, V.

2008-01-01

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, current analysis is limited to small domains and increasing the size of the MD domain quickly presents intractable computational demands. A preferred approach to surmount this computational limitation has been to combine continuum mechanics-based modeling procedures, such as the finite element method (FEM), with MD analyses thereby reducing the region of atomic scale refinement. Such multiscale modeling strategies can be divided into two broad classifications: concurrent multiscale methods that directly incorporate an atomistic domain within a continuum domain and sequential multiscale methods that extract an averaged response from the atomistic simulation for later use as a constitutive model in a continuum analysis.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Stress distribution retrieval in granular materials: A multi-scale model and digital image correlation measurements

NASA Astrophysics Data System (ADS)

Bruno, Luigi; Decuzzi, Paolo; Gentile, Francesco

2016-01-01

The promise of nanotechnology lies in the possibility of engineering matter on the nanoscale and creating technological interfaces that, because of their small scales, may directly interact with biological objects, creating new strategies for the treatment of pathologies that are otherwise beyond the reach of conventional medicine. Nanotechnology is inherently a multiscale, multiphenomena challenge. Fundamental understanding and highly accurate predictive methods are critical to successful manufacturing of nanostructured materials, bio/mechanical devices and systems. In biomedical engineering, and in the mechanical analysis of biological tissues, classical continuum approaches are routinely utilized, even if these disregard the discrete nature of tissues, that are an interpenetrating network of a matrix (the extra cellular matrix, ECM) and a generally large but finite number of cells with a size falling in the micrometer range. Here, we introduce a nano-mechanical theory that accounts for the-non continuum nature of bio systems and other discrete systems. This discrete field theory, doublet mechanics (DM), is a technique to model the mechanical behavior of materials over multiple scales, ranging from some millimeters down to few nanometers. In the paper, we use this theory to predict the response of a granular material to an external applied load. Such a representation is extremely attractive in modeling biological tissues which may be considered as a spatial set of a large number of particulate (cells) dispersed in an extracellular matrix. Possibly more important of this, using digital image correlation (DIC) optical methods, we provide an experimental verification of the model.

Modeling property evolution of container materials used in nuclear waste storage

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Garmestani, Hamid; Khaleel, Moe; Sun, Xin

2010-03-01

Container materials under irradiation for a long time will raise high energy in the structure to generate critical structural damage. This study investigated what kind of mesoscale microstructure will be more resistant to radiation damage. Mechanical properties evolution during irradiation was modeled using statistical continuum mechanics. Preliminary results also showed how to achieve the desired microstructure with higher resistance to radiation.

Modeling of damage driven fracture failure of fiber post-restored teeth.

PubMed

Xu, Binting; Wang, Yining; Li, Qing

2015-09-01

Mechanical failure of biomaterials, which can be initiated by either violent force, or progressive stress fatigue, is a serious issue. Great efforts have been made to improve the mechanical performances of dental restorations. Virtual simulation is a promising approach for biomechanical investigations, which presents significant advantages in improving efficiency than traditional in vivo/in vitro studies. Over the past few decades, a number of virtual studies have been conducted to investigate the biomechanical issues concerning dental biomaterials, but only with limited incorporation of brittle failure phenomena. Motivated by the contradictory findings between several finite element analyses and common clinical observations on the fracture resistance of post-restored teeth, this study aimed to provide an approach using numerical simulations for investigating the fracture failure process through a non-linear fracture mechanics model. The ability of this approach to predict fracture initiation and propagation in a complex biomechanical status based on the intrinsic material properties was investigated. Results of the virtual simulations matched the findings of experimental tests, in terms of the ultimate fracture failure strengths and predictive areas under risk of clinical failure. This study revealed that the failure of dental post-restored restorations is a typical damage-driven continuum-to-discrete process. This approach is anticipated to have ramifications not only for modeling fracture events, but also for the design and optimization of the mechanical properties of biomaterials for specific clinically determined requirements. Copyright © 2015 Elsevier Ltd. All rights reserved.

Navier-Stokes Dynamics by a Discrete Boltzmann Model

NASA Technical Reports Server (NTRS)

Rubinstein, Robet

2010-01-01

This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

Discrete and continuum simulations of near-field ground motion from Source Physics Experiments (SPE) (Invited)

NASA Astrophysics Data System (ADS)

Ezzedine, S. M.; Vorobiev, O.; Herbold, E. B.; Glenn, L. A.; Antoun, T.

2013-12-01

This work is focused on analysis of near-field measurements (up to 100 m from the source) recorded during Source Physics Experiments in a granitic formation. One of the main goals of these experiments is to investigate the possible mechanisms of shear wave generation in the nonlinear source region. SPE experiments revealed significant tangential motion (up to 30 % of the magnitude in the radial direction) at many locations. Furthermore, azimuthal variations in radial velocities were also observed which cannot be generated by a spherical source in isotropic materials. Understanding the nature of this non-radial motion is important for discriminating between the natural seismicity and underground explosions signatures. Possible mechanisms leading to such motion include, but not limited to, heterogeneities in the rock such as joints, faults and geologic layers as well as surface topography and vertical motion at the surface caused by material spall and gravity. We have performed a three dimensional computational studies considering all these effects. Both discrete and continuum methods have been employed to model heterogeneities. In the discrete method, the joints and faults were represented by cohesive contact elements. This enables us to examine various friction laws at the joints which include softening, dilatancy, water saturation and rate-dependent friction. Yet this approach requires the mesh to be aligned with joints, which may present technical difficulties in three dimensions when multiple non-persistent joints are present. In addition, the discrete method is more computationally expensive. The continuum approach assumes that the joints are stiff and the dilatancy and shear softening can be neglected. In this approach, the joints are modeled as weakness planes within the material, which are imbedded into and pass through many finite elements. The advantage of this approach is that it requires neither sophisticated meshing algorithms nor contact detection algorithm. It is also suitable for evaluating the bounds of possible shear motion due to uncertainties in the joints distribution. Details of this uncertainty quantification study are presented in a separate abstract (Vorobiev, et.al). In the present work using both the continuum and the discrete approaches we study the effects of the surface spall, in-situ stress and joint orientation on the observed near-field motion. Three dimensional numerical simulations are performed for different burial depths and yields to investigate scalability of both radial and shear motions. The motion calculated in the near-field is then propagated into a far field. Results of the far field study are presented in an accompanied work (Pitarka, et al). This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Simulation of Anisotropic Rock Damage for Geologic Fracturing

NASA Astrophysics Data System (ADS)

Busetti, S.; Xu, H.; Arson, C. F.

2014-12-01

A continuum damage model for differential stress-induced anisotropic crack formation and stiffness degradation is used to study geologic fracturing in rocks. The finite element-based model solves for deformation in the quasi-linear elastic domain and determines the six component damage tensor at each deformation increment. The model permits an isotropic or anisotropic intact or pre-damaged reference state, and the elasticity tensor evolves depending on the stress path. The damage variable, similar to Oda's fabric tensor, grows when the surface energy dissipated by three-dimensional opened cracks exceeds a threshold defined at the appropriate scale of the representative elementary volume (REV). At the laboratory or wellbore scale (<1m) brittle continuum damage reflects microcracking, grain boundary separation, grain crushing, or fine delamination, such as in shale. At outcrop (1m-100m), seismic (10m-1000m), and tectonic (>1000m) scales the damaged REV reflects early natural fracturing (background or tectonic fracturing) or shear strain localization (fault process zone, fault-tip damage, etc.). The numerical model was recently benchmarked against triaxial stress-strain data from laboratory rock mechanics tests. However, the utility of the model to predict geologic fabric such as natural fracturing in hydrocarbon reservoirs was not fully explored. To test the ability of the model to predict geological fracturing, finite element simulations (Abaqus) of common geologic scenarios with known fracture patterns (borehole pressurization, folding, faulting) are simulated and the modeled damage tensor is compared against physical fracture observations. Simulated damage anisotropy is similar to that derived using fractured rock-mass upscaling techniques for pre-determined fracture patterns. This suggests that if model parameters are constrained with local data (e.g., lab, wellbore, or reservoir domain), forward modeling could be used to predict mechanical fabric at the relevant REV scale. This reference fabric also can be used as the starting material property to pre-condition subsequent deformation or fluid flow. Continuing efforts are to expand the present damage model to couple damage evolution with plasticity and with permeability for more geologically realistic simulation.

Dissipation consistent fabric tensor definition from DEM to continuum for granular media

NASA Astrophysics Data System (ADS)

Li, X. S.; Dafalias, Y. F.

2015-05-01

In elastoplastic soil models aimed at capturing the impact of fabric anisotropy, a necessary ingredient is a measure of anisotropic fabric in the form of an evolving tensor. While it is possible to formulate such a fabric tensor based on indirect phenomenological observations at the continuum level, it is more effective and insightful to have the tensor defined first based on direct particle level microstructural observations and subsequently deduce a corresponding continuum definition. A practical means able to provide such observations, at least in the context of fabric evolution mechanisms, is the discrete element method (DEM). Some DEM defined fabric tensors such as the one based on the statistics of interparticle contact normals have already gained widespread acceptance as a quantitative measure of fabric anisotropy among researchers of granular material behavior. On the other hand, a fabric tensor in continuum elastoplastic modeling has been treated as a tensor-valued internal variable whose evolution must be properly linked to physical dissipation. Accordingly, the adaptation of a DEM fabric tensor definition to a continuum constitutive modeling theory must be thermodynamically consistent in regards to dissipation mechanisms. The present paper addresses this issue in detail, brings up possible pitfalls if such consistency is violated and proposes remedies and guidelines for such adaptation within a recently developed Anisotropic Critical State Theory (ACST) for granular materials.

Multiscale Analysis of Structurally-Graded Microstructures Using Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Crystal Plasticity

NASA Technical Reports Server (NTRS)

Saether, Erik; Hochhalter, Jacob D.; Glaessgen, Edward H.; Mishin, Yuri

2014-01-01

A multiscale modeling methodology is developed for structurally-graded material microstructures. Molecular dynamic (MD) simulations are performed at the nanoscale to determine fundamental failure mechanisms and quantify material constitutive parameters. These parameters are used to calibrate material processes at the mesoscale using discrete dislocation dynamics (DD). Different grain boundary interactions with dislocations are analyzed using DD to predict grain-size dependent stress-strain behavior. These relationships are mapped into crystal plasticity (CP) parameters to develop a computationally efficient finite element-based DD/CP model for continuum-level simulations and complete the multiscale analysis by predicting the behavior of macroscopic physical specimens. The present analysis is focused on simulating the behavior of a graded microstructure in which grain sizes are on the order of nanometers in the exterior region and transition to larger, multi-micron size in the interior domain. This microstructural configuration has been shown to offer improved mechanical properties over homogeneous coarse-grained materials by increasing yield stress while maintaining ductility. Various mesoscopic polycrystal models of structurally-graded microstructures are generated, analyzed and used as a benchmark for comparison between multiscale DD/CP model and DD predictions. A final series of simulations utilize the DD/CP analysis method exclusively to study macroscopic models that cannot be analyzed by MD or DD methods alone due to the model size.

The application of continuum damage mechanics to solve problems in geodynamics

NASA Astrophysics Data System (ADS)

Manaker, David Martin

Deformation within the Earth's lithosphere is largely controlled by the rheology of the rock. Ductile behavior in rocks is often associated with plasticity due to dislocation motion or diffusion under high pressures and temperatures. However, ductile behavior can also occur in brittle materials. An example would be cataclastic flow associated with folding at shallow crustal levels, steep subduction zones, and large-scale deformation at plate boundaries. Engineers utilize damage mechanics to model the continuum deformation of brittle materials. We utilize a modified form of damage mechanics where damage represents a reduction in frictional strength and includes a yield stress. We use this empirical approach to simulate the bending of the lithosphere. We use numerical simulations to obtain elastostatic solutions for plate bending and where the stress exceeds a yield stress, we apply damage to reduce the elastic moduli. Damage is calculated at each time step by a power-law relationship of the ratio of the yield stress to stress and the yield strain to the strain. To test our method, we apply our damage rheology to a plate deforming under applied shear, a constant bending moment, and a constant load. We simulate a wide range of behaviors from slow relaxation to instantaneous failure, over timescales that span six orders of magnitude. Stress relaxation produces elastic-perfectly plastic behavior in cases where failure does not occur. For cases of failure, we observe a rapid increase in damage leading to failure. The changes in the rate of damage accumulation in failure cases are similar to the changes in b-values of acoustic emissions observed in triaxial compression tests of fractured rock and b-value changes prior to some large earthquakes. Thus continuum damage mechanics can simulate ductile behavior due to brittle mechanisms as well as observations of laboratory experiments and seismicity.

A discrete mesoscopic particle model of the mechanics of a multi-constituent arterial wall.

PubMed

Witthoft, Alexandra; Yazdani, Alireza; Peng, Zhangli; Bellini, Chiara; Humphrey, Jay D; Karniadakis, George Em

2016-01-01

Blood vessels have unique properties that allow them to function together within a complex, self-regulating network. The contractile capacity of the wall combined with complex mechanical properties of the extracellular matrix enables vessels to adapt to changes in haemodynamic loading. Homogenized phenomenological and multi-constituent, structurally motivated continuum models have successfully captured these mechanical properties, but truly describing intricate microstructural details of the arterial wall may require a discrete framework. Such an approach would facilitate modelling interactions between or the separation of layers of the wall and would offer the advantage of seamless integration with discrete models of complex blood flow. We present a discrete particle model of a multi-constituent, nonlinearly elastic, anisotropic arterial wall, which we develop using the dissipative particle dynamics method. Mimicking basic features of the microstructure of the arterial wall, the model comprises an elastin matrix having isotropic nonlinear elastic properties plus anisotropic fibre reinforcement that represents the stiffer collagen fibres of the wall. These collagen fibres are distributed evenly and are oriented in four directions, symmetric to the vessel axis. Experimental results from biaxial mechanical tests of an artery are used for model validation, and a delamination test is simulated to demonstrate the new capabilities of the model. © 2016 The Author(s).

Comprehensive modeling of a liquid rocket combustion chamber

NASA Technical Reports Server (NTRS)

Liang, P.-Y.; Fisher, S.; Chang, Y. M.

1985-01-01

An analytical model for the simulation of detailed three-phase combustion flows inside a liquid rocket combustion chamber is presented. The three phases involved are: a multispecies gaseous phase, an incompressible liquid phase, and a particulate droplet phase. The gas and liquid phases are continuum described in an Eulerian fashion. A two-phase solution capability for these continuum media is obtained through a marriage of the Implicit Continuous Eulerian (ICE) technique and the fractional Volume of Fluid (VOF) free surface description method. On the other hand, the particulate phase is given a discrete treatment and described in a Lagrangian fashion. All three phases are hence treated rigorously. Semi-empirical physical models are used to describe all interphase coupling terms as well as the chemistry among gaseous components. Sample calculations using the model are given. The results show promising application to truly comprehensive modeling of complex liquid-fueled engine systems.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-03-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-07-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

Multiscale Modeling of Cell Interaction in Angiogenesis: From the Micro- to Macro-scale

NASA Astrophysics Data System (ADS)

Pillay, Samara; Maini, Philip; Byrne, Helen

Solid tumors require a supply of nutrients to grow in size. To this end, tumors induce the growth of new blood vessels from existing vasculature through the process of angiogenesis. In this work, we use a discrete agent-based approach to model the behavior of individual endothelial cells during angiogenesis. We incorporate crowding effects through volume exclusion, motility of cells through biased random walks, and include birth and death processes. We use the transition probabilities associated with the discrete models to determine collective cell behavior, in terms of partial differential equations, using a Markov chain and master equation framework. We find that the cell-level dynamics gives rise to a migrating cell front in the form of a traveling wave on the macro-scale. The behavior of this front depends on the cell interactions that are included and the extent to which volume exclusion is taken into account in the discrete micro-scale model. We also find that well-established continuum models of angiogenesis cannot distinguish between certain types of cell behavior on the micro-scale. This may impact drug development strategies based on these models.

Symposium on Continuum Models and Discrete Systems (6th) Held in Dijon, France on June 26 - 29, 1989

DTIC Science & Technology

1986-01-01

regard the I’ Burgers’ vector and the dislocation density tensor as measures of defectiveness. This practice can be given a systematic flavour . To begin...behaviour aims at describing the two main mechanisms of deformation, namely plastic slip of two granules over one another and changes of microstructure as

Dynamics of a Tapped Granular Column

NASA Astrophysics Data System (ADS)

Rosato, Anthony; Blackmore, Denis; Zuo, Luo; Hao, Wu; Horntrop, David

2015-11-01

We consider the behavior of a column of spheres subjected to a time-dependent vertical taps. Of interest are various dynamical properties, such as the motion of its mass center, its response to taps of different intensities and forms, and the effect of system size and material properties. The interplay between diverse time and length scales are the key contributors to the column's evolving dynamics. Soft sphere discrete element simulations were conducted over a very wide parameter space to obtain a portrait of column behavior as embodied by the collective dynamics of the mass center motion. Results compared favorably with a derived reduced-order paradigm of the mass center motion (surprisingly analogous to that for a single bouncing ball on an oscillating plate) with respect to dynamical regimes and their transitions. A continuum model obtained from a system of Newtonian equations, as a locally averaged limit in the transport mode along trajectories is described, and a numerical solution protocol for a one-dimensional system is outlined. Typical trajectories and density evolution profiles are shown. We conclude with a discussion of our investigations to relate predictions of the continuum and reduced dynamical systems models with discrete simulations.

Elastic scattering of ^4He by ^6Li at E(^4He) = 24, 25, and 26 MeV

NASA Astrophysics Data System (ADS)

Bartosz, E. E.; Cathers, P. D.; Kemper, K. W.; Maréchal, F.; Rusek, K.

1998-11-01

A previous optical model analysis of the elastic scattering of ^4He by ^6Li at E(^4He) = 18.5 MeV (P. V. Green, K. W. Kemper, P. L. Kerr, K. Mohajeri, E. G. Myers, D. Robson, K. Rusek and I. J. Thompson, Phys. Rev. C 53) 2862 (1996)., as well as a cluster-folded continuum- discretized coupled channels analysis (K. Rusek, P. V. Green, P. L. Kerr, and K. W. Kemper, Phys. Rev. C 56) 1895 (1997)., resulted in a good description of the data set, but the optical model analysis yielded a poor description of the 25 MeV elastic scattering data measured at the same time. New elastic and inelastic scattering angular distribution cross sections are reported for ^4He + ^6Li at E(^4He) = 24, 25 and 26 MeV. Three energies were used to rule out anomalous scattering at 25 MeV. The results of a cluster-folded continuum- discretized coupled channels analysis similar to that used with the 18.5 MeV data are presented for the three new data sets at 24, 25, and 26 MeV.

A Model for Predicting Grain Boundary Cracking in Polycrystalline Viscoplastic Materials Including Scale Effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allen, D.H.; Helms, K.L.E.; Hurtado, L.D.

1999-04-06

A model is developed herein for predicting the mechanical response of inelastic crystalline solids. Particular emphasis is given to the development of microstructural damage along grain boundaries, and the interaction of this damage with intragranular inelasticity caused by dislocation dissipation mechanisms. The model is developed within the concepts of continuum mechanics, with special emphasis on the development of internal boundaries in the continuum by utilizing a cohesive zone model based on fracture mechanics. In addition, the crystalline grains are assumed to be characterized by nonlinear viscoplastic mechanical material behavior in order to account for dislocation generation and migration. Due tomore » the nonlinearities introduced by the crack growth and viscoplastic constitution, a numerical algorithm is utilized to solve representative problems. Implementation of the model to a finite element computational algorithm is therefore briefly described. Finally, sample calculations are presented for a polycrystalline titanium alloy with particular focus on effects of scale on the predicted response.« less

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

A contact layer element for large deformations

NASA Astrophysics Data System (ADS)

Weißenfels, C.; Wriggers, P.

2015-05-01

In many contact situations the material behavior of one contact member strongly influences the force acting between the two bodies. Unfortunately standard friction models cannot reproduce all of these material effects at the contact layer and often continuum interface elements are used instead. These elements are intrinsically tied to the fixed grid and hence cannot be used in large sliding simulations. Due to the shortcomings of the standard contact formulations and of the interface elements a new type of a contact layer element is developed in this work. The advantages of this element are the direct implementation of continuum models into the contact formulation and the application to arbitrary large deformations. Showing a relation between continuum and contact kinematics based on the solid-shell concept the new contact element is at the end a natural extension of the standard contact formulations into 3D. Two examples show that the continuum behavior can be exactly reproduced at the contact surface even in large sliding situations using this contact layer element. For the discretization of the new contact element the Mortar method is chosen exemplary, but it can be combined with all kinds of contact formulations.

Dynamic simulations of geologic materials using combined FEM/DEM/SPH analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morris, J P; Johnson, S M

2008-03-26

An overview of the Lawrence Discrete Element Code (LDEC) is presented, and results from a study investigating the effect of explosive and impact loading on geologic materials using the Livermore Distinct Element Code (LDEC) are detailed. LDEC was initially developed to simulate tunnels and other structures in jointed rock masses using large numbers of polyhedral blocks. Many geophysical applications, such as projectile penetration into rock, concrete targets, and boulder fields, require a combination of continuum and discrete methods in order to predict the formation and interaction of the fragments produced. In an effort to model this class of problems, LDECmore » now includes implementations of Cosserat point theory and cohesive elements. This approach directly simulates the transition from continuum to discontinuum behavior, thereby allowing for dynamic fracture within a combined finite element/discrete element framework. In addition, there are many application involving geologic materials where fluid-structure interaction is important. To facilitate solution of this class of problems a Smooth Particle Hydrodynamics (SPH) capability has been incorporated into LDEC to simulate fully coupled systems involving geologic materials and a saturating fluid. We will present results from a study of a broad range of geomechanical problems that exercise the various components of LDEC in isolation and in tandem.« less

Fractional-order difference equations for physical lattices and some applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Continuum-kinetic approach to sheath simulations

NASA Astrophysics Data System (ADS)

Cagas, Petr; Hakim, Ammar; Srinivasan, Bhuvana

2016-10-01

Simulations of sheaths are performed using a novel continuum-kinetic model with collisions including ionization/recombination. A discontinuous Galerkin method is used to directly solve the Boltzmann-Poisson system to obtain a particle distribution function. Direct discretization of the distribution function has advantages of being noise-free compared to particle-in-cell methods. The distribution function, which is available at each node of the configuration space, can be readily used to calculate the collision integrals in order to get ionization and recombination operators. Analytical models are used to obtain the cross-sections as a function of energy. Results will be presented incorporating surface physics with a classical sheath in Hall thruster-relevant geometry. This work was sponsored by the Air Force Office of Scientific Research under Grant Number FA9550-15-1-0193.

Comment on "Route from discreteness to the continuum for the Tsallis q -entropy"

NASA Astrophysics Data System (ADS)

Ou, Congjie; Abe, Sumiyoshi

2018-06-01

Several years ago, it had been discussed that nonlogarithmic entropies, such as the Tsallis q -entropy cannot be applied to systems with continuous variables. Now, in their recent paper [Phys. Rev. E 97, 012104 (2018), 10.1103/PhysRevE.97.012104], Oikonomou and Bagci have modified the form of the q -entropy for discrete variables in such a way that its continuum limit exists. Here, it is shown that this modification violates the expandability property of entropy, and their work is actually supporting evidence for the absence of the q -entropy for systems with continuous variables.

Variable Weight Fractional Collisions for Multiple Species Mixtures

DTIC Science & Technology

2017-08-28

DISTRIBUTION A: APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED; PA #17517 6 / 21 VARIABLE WEIGHTS FOR DYNAMIC RANGE Continuum to Discrete ...Representation: Many Particles →̃ Continuous Distribution Discretized VDF Yields Vlasov But Collision Integral Still a Problem Particle Methods VDF to Delta...Function Set Collisions between Discrete Velocities But Poorly Resolved Tail (Tail Critical to Inelastic Collisions) Variable Weights Permit Extra DOF in

Finite Elements Analysis of a Composite Semi-Span Test Article With and Without Discrete Damage

NASA Technical Reports Server (NTRS)

Lovejoy, Andrew E.; Jegley, Dawn C. (Technical Monitor)

2000-01-01

AS&M Inc. performed finite element analysis, with and without discrete damage, of a composite semi-span test article that represents the Boeing 220-passenger transport aircraft composite semi-span test article. A NASTRAN bulk data file and drawings of the test mount fixtures and semi-span components were utilized to generate the baseline finite element model. In this model, the stringer blades are represented by shell elements, and the stringer flanges are combined with the skin. Numerous modeling modifications and discrete source damage scenarios were applied to the test article model throughout the course of the study. This report details the analysis method and results obtained from the composite semi-span study. Analyses were carried out for three load cases: Braked Roll, LOG Down-Bending and 2.5G Up-Bending. These analyses included linear and nonlinear static response, as well as linear and nonlinear buckling response. Results are presented in the form of stress and strain plots. factors of safety for failed elements, buckling loads and modes, deflection prediction tables and plots, and strainage prediction tables and plots. The collected results are presented within this report for comparison to test results.

Does Geophysics Need "A new kind of Science"?

NASA Astrophysics Data System (ADS)

Turcotte, D. L.; Rundle, J. B.

2002-12-01

Stephen Wolfram's book "A New Kind of Science" has received a great deal of attention in the last six months, both positive and negative. The theme of the book is that "cellular automata", which arise from spatial and temporal coarse-graining of equations of motion, provide the foundations for a new nonlinear science of "complexity". The old science is the science of partial differential equations. Some of the major contributions of this old science have been in geophysics, i.e. gravity, magnetics, seismic waves, heat flow. The basis of the new science is the use of massive computing and numerical simulations. The new science is motivated by the observations that many physical systems display a vast multiplicity of space and time scales, and have hidden dynamics that in many cases are impossible to directly observe. An example would be molecular dynamics. Statistical physics derives continuum equations from the discrete interactions between atoms and molecules, in the modern world the continuum equations are then discretized using finite differences, finite elements, etc. in order to obtain numerical solutions. Examples of widely used cellular automata models include diffusion limited aggregation and site percolation. Also the class of models that are said to exhibit self-organized criticality, the sand-pile model, the slider-block model, the forest-fire model. Applications of these models include drainage networks, seismicity, distributions of minerals,and the evolution of landforms and coastlines. Simple cellular automata models generate deterministic chaos, i.e. the logistic map.

Modelling CO2 flow in naturally fractured geological media using MINC and multiple subregion upscaling procedure

NASA Astrophysics Data System (ADS)

Tatomir, Alexandru Bogdan A. C.; Flemisch, Bernd; Class, Holger; Helmig, Rainer; Sauter, Martin

2017-04-01

Geological storage of CO2 represents one viable solution to reduce greenhouse gas emission in the atmosphere. Potential leakage of CO2 storage can occur through networks of interconnected fractures. The geometrical complexity of these networks is often very high involving fractures occurring at various scales and having hierarchical structures. Such multiphase flow systems are usually hard to solve with a discrete fracture modelling (DFM) approach. Therefore, continuum fracture models assuming average properties are usually preferred. The multiple interacting continua (MINC) model is an extension of the classic double porosity model (Warren and Root, 1963) which accounts for the non-linear behaviour of the matrix-fracture interactions. For CO2 storage applications the transient representation of the inter-porosity two phase flow plays an important role. This study tests the accuracy and computational efficiency of the MINC method complemented with the multiple sub-region (MSR) upscaling procedure versus the DFM. The two phase flow MINC simulator is implemented in the free-open source numerical toolbox DuMux (www.dumux.org). The MSR (Gong et al., 2009) determines the inter-porosity terms by solving simplified local single-phase flow problems. The DFM is considered as the reference solution. The numerical examples consider a quasi-1D reservoir with a quadratic fracture system , a five-spot radial symmetric reservoir, and a completely random generated fracture system. Keywords: MINC, upscaling, two-phase flow, fractured porous media, discrete fracture model, continuum fracture model

Discrete spacetime, quantum walks, and relativistic wave equations

NASA Astrophysics Data System (ADS)

Mlodinow, Leonard; Brun, Todd A.

2018-04-01

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper, we define the three-dimensional discrete-time walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space; each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis—that is, that the walk be symmetric under parity transformations and steps along different axes of the cubic lattice be uncorrelated—leads, in the case of the simplest solution, to the requirement that the continuum limit of the walk is fully Lorentz-invariant. We show further that, in the case of a massive particle, this symmetry requirement necessitates the use of a four-dimensional internal space (as in the Dirac equation). The "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated with each dimension must all anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.

Hyper-elastoplastic/damage modeling of rock with application to porous limestone

DOE PAGES

Bennett, Kane C.; Borja, Ronaldo I.

2018-03-13

Relations between porosity, damage, and bulk plasticity are examined in the context of continuum damage and hyper-elastoplasticity of porous rocks. Attention is given to a thermodynamically consistent derivation of the damage evolution equations and their role in the constitutive equations, for which the Eshelby stress is found to be important. The provided phenomenological framework allows for volumetric damage associated with pore growth to be distinguished from the isochoric damage associated with distributed microcracks, and a novel Drucker-Prager/cap type material model that includes damage evolution is presented. The model is shown to capture well the hardening/softening behavior and pressure dependence ofmore » the so-called brittle-ductile transition by comparison with confined triaxial compression measurements from the literature. Non-linear finite element simulations are also provided of the prediction of damage within porous limestone around a horizontal borehole wall.« less

Hyper-elastoplastic/damage modeling of rock with application to porous limestone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bennett, Kane C.; Borja, Ronaldo I.

Relations between porosity, damage, and bulk plasticity are examined in the context of continuum damage and hyper-elastoplasticity of porous rocks. Attention is given to a thermodynamically consistent derivation of the damage evolution equations and their role in the constitutive equations, for which the Eshelby stress is found to be important. The provided phenomenological framework allows for volumetric damage associated with pore growth to be distinguished from the isochoric damage associated with distributed microcracks, and a novel Drucker-Prager/cap type material model that includes damage evolution is presented. The model is shown to capture well the hardening/softening behavior and pressure dependence ofmore » the so-called brittle-ductile transition by comparison with confined triaxial compression measurements from the literature. Non-linear finite element simulations are also provided of the prediction of damage within porous limestone around a horizontal borehole wall.« less

Hydraulic tomography of discrete networks of conduits and fractures in a karstic aquifer by using a deterministic inversion algorithm

NASA Astrophysics Data System (ADS)

Fischer, P.; Jardani, A.; Lecoq, N.

2018-02-01

In this paper, we present a novel inverse modeling method called Discrete Network Deterministic Inversion (DNDI) for mapping the geometry and property of the discrete network of conduits and fractures in the karstified aquifers. The DNDI algorithm is based on a coupled discrete-continuum concept to simulate numerically water flows in a model and a deterministic optimization algorithm to invert a set of observed piezometric data recorded during multiple pumping tests. In this method, the model is partioned in subspaces piloted by a set of parameters (matrix transmissivity, and geometry and equivalent transmissivity of the conduits) that are considered as unknown. In this way, the deterministic optimization process can iteratively correct the geometry of the network and the values of the properties, until it converges to a global network geometry in a solution model able to reproduce the set of data. An uncertainty analysis of this result can be performed from the maps of posterior uncertainties on the network geometry or on the property values. This method has been successfully tested for three different theoretical and simplified study cases with hydraulic responses data generated from hypothetical karstic models with an increasing complexity of the network geometry, and of the matrix heterogeneity.

Effects of Composite Pions on the Chiral Condensate within the PNJL Model at Finite Temperature

NASA Astrophysics Data System (ADS)

Blaschke, D.; Dubinin, A.; Ebert, D.; Friesen, A. V.

2018-05-01

We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth-Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. This in turn also entails a modification of the Polyakov-loop so that the SU(3) center symmetry gets broken at finite temperature and dynamical quarks (and gluons) appear in the system, taking over the role of the dominant degrees of freedom from the pions. At low temperatures our model reproduces the chiral perturbation theory result for the chiral condensate while at high temperatures the PNJL model result is recovered. The new aspect of the current work is a consistent treatment of the chiral restoration transition region within the Beth-Uhlenbeck approach on the basis of mesonic phase shifts for the treatment of the correlations.

Computational mechanics of viral capsids.

PubMed

Gibbons, Melissa M; Perotti, Luigi E; Klug, William S

2015-01-01

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.

Wavelet-based surrogate time series for multiscale simulation of heterogeneous catalysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Savara, Aditya Ashi; Daw, C. Stuart; Xiong, Qingang

We propose a wavelet-based scheme that encodes the essential dynamics of discrete microscale surface reactions in a form that can be coupled with continuum macroscale flow simulations with high computational efficiency. This makes it possible to simulate the dynamic behavior of reactor-scale heterogeneous catalysis without requiring detailed concurrent simulations at both the surface and continuum scales using different models. Our scheme is based on the application of wavelet-based surrogate time series that encodes the essential temporal and/or spatial fine-scale dynamics at the catalyst surface. The encoded dynamics are then used to generate statistically equivalent, randomized surrogate time series, which canmore » be linked to the continuum scale simulation. As a result, we illustrate an application of this approach using two different kinetic Monte Carlo simulations with different characteristic behaviors typical for heterogeneous chemical reactions.« less

Wavelet-based surrogate time series for multiscale simulation of heterogeneous catalysis

DOE PAGES

Savara, Aditya Ashi; Daw, C. Stuart; Xiong, Qingang; ...

2016-01-28

We propose a wavelet-based scheme that encodes the essential dynamics of discrete microscale surface reactions in a form that can be coupled with continuum macroscale flow simulations with high computational efficiency. This makes it possible to simulate the dynamic behavior of reactor-scale heterogeneous catalysis without requiring detailed concurrent simulations at both the surface and continuum scales using different models. Our scheme is based on the application of wavelet-based surrogate time series that encodes the essential temporal and/or spatial fine-scale dynamics at the catalyst surface. The encoded dynamics are then used to generate statistically equivalent, randomized surrogate time series, which canmore » be linked to the continuum scale simulation. As a result, we illustrate an application of this approach using two different kinetic Monte Carlo simulations with different characteristic behaviors typical for heterogeneous chemical reactions.« less

Microscopic description of elastic and direct inelastic nucleon scattering off spherical nuclei

NASA Astrophysics Data System (ADS)

Dupuis, M.

2017-05-01

The purpose of this study is to improve the modeling of nucleon direct inelastic scattering to the continuum using a microscopic and parameter-free approach. For the first time, direct elastic scattering, inelastic scattering to discrete excitations and to the continuum are described within a microscopic approach without adjustable parameters. Proton scattering off 90Zr and 208Pb are the reactions used as test case examples of the calculations. The model uses the Melbourne g-matrix and the Random Phase Approximation description of nuclear states, implemented with the Gogny D1S interaction. The relevant optical and transition potentials in a finite nucleus are calculated within a local density approximation. As we use the nuclear matter approach we limit our study to incident energies above 40 MeV. We first checked that this model provides an accurate account of measured cross sections for elastic scattering and inelastic scattering to discrete states. It is then applied to the direct inelastic scattering to the continuum considering all one-phonon excitations predicted within the RPA approach. This accounts for a part of the direct pre-equilibrium emission, often labeled as the one-step direct process in quantum-based approaches. Our approach provides a very accurate description of angular distributions where the one-step process dominates. The impact of collective excitations is shown to be non negligible for energy transfer to the target up to 20 MeV, decreasing as the incident energy increases. For incident energies above 80 MeV, our modeling provides a good account of direct proton emission for an energy transfer to the target up to 30 MeV. However, the proton emission we predict underestimates the measured cross sections for incident energies below 80 MeV. We compare our prediction to those of the phenomenological exciton model to help interpret this result. Directions that may improve our modeling are discussed.

A nonlinear CDM based damage growth law for ductile materials

NASA Astrophysics Data System (ADS)

Gautam, Abhinav; Priya Ajit, K.; Sarkar, Prabir Kumar

2018-02-01

A nonlinear ductile damage growth criterion is proposed based on continuum damage mechanics (CDM) approach. The model is derived in the framework of thermodynamically consistent CDM assuming damage to be isotropic. In this study, the damage dissipation potential is also derived to be a function of varying strain hardening exponent in addition to damage strain energy release rate density. Uniaxial tensile tests and load-unload-cyclic tensile tests for AISI 1020 steel, AISI 1030 steel and Al 2024 aluminum alloy are considered for the determination of their respective damage variable D and other parameters required for the model(s). The experimental results are very closely predicted, with a deviation of 0%-3%, by the proposed model for each of the materials. The model is also tested with predictabilities of damage growth by other models in the literature. Present model detects the state of damage quantitatively at any level of plastic strain and uses simpler material tests to find the parameters of the model. So, it should be useful in metal forming industries to assess the damage growth for the desired deformation level a priori. The superiority of the new model is clarified by the deviations in the predictability of test results by other models.

Predictions of Poisson's ratio in cross-ply laminates containing matrix cracks and delaminations

NASA Technical Reports Server (NTRS)

Harris, Charles E.; Allen, David H.; Nottorf, Eric W.

1989-01-01

A damage-dependent constitutive model for laminated composites has been developed for the combined damage modes of matrix cracks and delaminations. The model is based on the concept of continuum damage mechanics and uses second-order tensor valued internal state variables to represent each mode of damage. The internal state variables are defined as the local volume average of the relative crack face displacements. Since the local volume for delaminations is specified at the laminate level, the constitutive model takes the form of laminate analysis equations modified by the internal state variables. Model implementation is demonstrated for the laminate engineering modulus E(x) and Poisson's ratio nu(xy) of quasi-isotropic and cross-ply laminates. The model predictions are in close agreement to experimental results obtained for graphite/epoxy laminates.

Discrete, continuous, and stochastic models of protein sorting in the Golgi apparatus

PubMed Central

Gong, Haijun; Guo, Yusong; Linstedt, Adam

2017-01-01

The Golgi apparatus plays a central role in processing and sorting proteins and lipids in eukaryotic cells. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development, and osmotic stress. We have developed three minimal models of membrane and protein exchange in the Golgi—a discrete, stochastic model, a continuous ordinary differential equation model, and a continuous stochastic differential equation model—each based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of cargoes and soluble N-ethylmaleimide-sensitive factor attachment protein receptor SNARE proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. By exploring where the models differ, we hope to discover whether the discrete, stochastic nature of vesicle-mediated transport is likely to have appreciable functional consequences for the Golgi. All three models show similar ability to restore and maintain distinct identities over broad parameter ranges. They diverge, however, in conditions corresponding to collapse and reassembly of the Golgi. The results suggest that a continuum model provides a good description of Golgi maintenance but that considering the discrete nature of vesicle-based traffic is important to understanding assembly and disassembly of the Golgi. Experimental analysis validates a prediction of the models that altering guanine nucleotide exchange factor expression levels will modulate Golgi size. PMID:20365406

DAMAGE MODELING OF INJECTION-MOLDED SHORT- AND LONG-FIBER THERMOPLASTICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, Ba Nghiep; Kunc, Vlastimil; Bapanapalli, Satish K.

2009-10-30

This article applies the recent anisotropic rotary diffusion – reduced strain closure (ARD-RSC) model for predicting fiber orientation and a new damage model for injection-molded long-fiber thermoplastics (LFTs) to analyze progressive damage leading to total failure of injection-molded long-glass-fiber/polypropylene (PP) specimens. The ARD-RSC model was implemented in a research version of the Autodesk Moldflow Plastics Insight (MPI) processing code, and it has been used to simulate injection-molding of a long-glass-fiber/PP plaque. The damage model combines micromechanical modeling with a continuum damage mechanics description to predict the nonlinear behavior due to plasticity coupled with damage in LFTs. This model has beenmore » implemented in the ABAQUS finite element code via user-subroutines and has been used in the damage analyses of tensile specimens removed from the injection-molded long-glass-fiber/PP plaques. Experimental characterization and mechanical testing were performed to provide input data to support and validate both process modeling and damage analyses. The predictions are in agreement with the experimental results.« less

A new thermo-mechanical coupled DEM model with non-spherical grains for thermally induced damage of rocks

NASA Astrophysics Data System (ADS)

Chen, Zhiqiang; Jin, Xu; Wang, Moran

2018-07-01

Thermally induced damage often occurs in rocks in geophysical systems. Discrete element method (DEM) is a useful tool to model this thermo-mechanical coupled process owing to its explicit representation of fracture initiation and propagation. However, the previous DEM models for this are mostly based on spherical discrete elements, which are not able to capture all consequences (e.g. high ratio of compressive to tensile strength) of real rocks (e.g. granite) composed of complex-geometry grains. In order to overcome this intrinsic limitation, we present a new model allowing to mimick thermally induced damage of brittle rock with non-spherical grains. After validations, the new model is used to study thermal gradient cracking with a special emphasis on the effects from rock heterogeneity. The obtained fracture initiation and propagation are consistent with experimental observations, which demonstrates the ability of current model to reproduce the thermally induced damage of rocks. Meanwhile, the results show that rock heterogeneity influences thermal gradient cracking significantly, and more micro cracks uniformly scattering around the borehole are induced in the heterogeneous sample, which is not good for applications such as nuclear waste disposal. The present model provides a promising approach at micro-scale to explore mechanisms of thermally induced damage of rocks in geological engineering.

Multiscale Modeling of Angiogenesis and Predictive Capacity

NASA Astrophysics Data System (ADS)

Pillay, Samara; Byrne, Helen; Maini, Philip

Tumors induce the growth of new blood vessels from existing vasculature through angiogenesis. Using an agent-based approach, we model the behavior of individual endothelial cells during angiogenesis. We incorporate crowding effects through volume exclusion, motility of cells through biased random walks, and include birth and death-like processes. We use the transition probabilities associated with the discrete model and a discrete conservation equation for cell occupancy to determine collective cell behavior, in terms of partial differential equations (PDEs). We derive three PDE models incorporating single, multi-species and no volume exclusion. By fitting the parameters in our PDE models and other well-established continuum models to agent-based simulations during a specific time period, and then comparing the outputs from the PDE models and agent-based model at later times, we aim to determine how well the PDE models predict the future behavior of the agent-based model. We also determine whether predictions differ across PDE models and the significance of those differences. This may impact drug development strategies based on PDE models.

Modelling tidewater glacier calving: from detailed process models to simple calving laws

NASA Astrophysics Data System (ADS)

Benn, Doug; Åström, Jan; Zwinger, Thomas; Todd, Joe; Nick, Faezeh

2017-04-01

The simple calving laws currently used in ice sheet models do not adequately reflect the complexity and diversity of calving processes. To be effective, calving laws must be grounded in a sound understanding of how calving actually works. We have developed a new approach to formulating calving laws, using a) the Helsinki Discrete Element Model (HiDEM) to explicitly model fracture and calving processes, and b) the full-Stokes continuum model Elmer/Ice to identify critical stress states associated with HiDEM calving events. A range of observed calving processes emerges spontaneously from HiDEM in response to variations in ice-front buoyancy and the size of subaqueous undercuts, and we show that HiDEM calving events are associated with characteristic stress patterns simulated in Elmer/Ice. Our results open the way to developing calving laws that properly reflect the diversity of calving processes, and provide a framework for a unified theory of the calving process continuum.

Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization

PubMed Central

Teichtmeister, S.; Aldakheel, F.

2016-01-01

This work outlines a novel variational-based theory for the phase-field modelling of ductile fracture in elastic–plastic solids undergoing large strains. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modelling. It is linked to a formulation of gradient plasticity at finite strains. The framework includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges. PMID:27002069

Precision measurement of the electromagnetic dipole strengths in Be11

NASA Astrophysics Data System (ADS)

Kwan, E.; Wu, C. Y.; Summers, N. C.; Hackman, G.; Drake, T. E.; Andreoiu, C.; Ashley, R.; Ball, G. C.; Bender, P. C.; Boston, A. J.; Boston, H. C.; Chester, A.; Close, A.; Cline, D.; Cross, D. S.; Dunlop, R.; Finlay, A.; Garnsworthy, A. B.; Hayes, A. B.; Laffoley, A. T.; Nano, T.; Navrátil, P.; Pearson, C. J.; Pore, J.; Quaglioni, S.; Svensson, C. E.; Starosta, K.; Thompson, I. J.; Voss, P.; Williams, S. J.; Wang, Z. M.

2014-05-01

The electromagnetic dipole strength in Be11 between the bound states has been measured using low-energy projectile Coulomb excitation at bombarding energies of 1.73 and 2.09 MeV/nucleon on a Pt196 target. An electric dipole transition probability B(E1;1/2-→1/2+)=0.102(2) e2fm was determined using the semi-classical code Gosia, and a value of 0.098(4) e2fm was determined using the Extended Continuum Discretized Coupled Channels method with the quantum mechanical code FRESCO. These extracted B(E1) values are consistent with the average value determined by a model-dependent analysis of intermediate energy Coulomb excitation measurements and are approximately 14% lower than that determined by a lifetime measurement. The much-improved precisions of 2% and 4% in the measured B(E1) values between the bound states deduced using Gosia and the Extended Continuum Discretized Coupled Channels method, respectively, compared to the previous accuracy of ˜10% will help in our understanding of and better improve the realistic inter-nucleon interactions.

Discrete Analysis of Damage and Shear Banding in Argillaceous Rocks

NASA Astrophysics Data System (ADS)

Dinç, Özge; Scholtès, Luc

2018-05-01

A discrete approach is proposed to study damage and failure processes taking place in argillaceous rocks which present a transversely isotropic behavior. More precisely, a dedicated discrete element method is utilized to provide a micromechanical description of the mechanisms involved. The purpose of the study is twofold: (1) presenting a three-dimensional discrete element model able to simulate the anisotropic macro-mechanical behavior of the Callovo-Oxfordian claystone as a particular case of argillaceous rocks; (2) studying how progressive failure develops in such material. Material anisotropy is explicitly taken into account in the numerical model through the introduction of weakness planes distributed at the interparticle scale following predefined orientation and intensity. Simulations of compression tests under plane-strain and triaxial conditions are performed to clarify the development of damage and the appearance of shear bands through micromechanical analyses. The overall mechanical behavior and shear banding patterns predicted by the numerical model are in good agreement with respect to experimental observations. Both tensile and shear microcracks emerging from the modeling also present characteristics compatible with microstructural observations. The numerical results confirm that the global failure of argillaceous rocks is well correlated with the mechanisms taking place at the local scale. Specifically, strain localization is shown to directly result from shear microcracking developing with a preferential orientation distribution related to the orientation of the shear band. In addition, localization events presenting characteristics similar to shear bands are observed from the early stages of the loading and might thus be considered as precursors of strain localization.

A Continuum of Learning: From Rote Memorization to Meaningful Learning in Organic Chemistry

ERIC Educational Resources Information Center

Grove, Nathaniel P.; Bretz, Stacey Lowery

2012-01-01

The Assimilation Theory of Ausubel and Novak has typically been used in the research literature to describe two extremes to learning chemistry: meaningful learning "versus" rote memorization. It is unlikely, however, that such discrete categories of learning exist. Rote and meaningful learning, rather, are endpoints along a continuum of…

Used Fuel Disposal in Crystalline Rocks. FY15 Progress Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yifeng

2015-08-20

The objective of the Crystalline Disposal R&D Work Package is to advance our understanding of long-term disposal of used fuel in crystalline rocks and to develop necessary experimental and computational capabilities to evaluate various disposal concepts in such media. Chapter headings are as follows: Fuel matrix degradation model and its integration with performance assessments, Investigation of thermal effects on the chemical behavior of clays, Investigation of uranium diffusion and retardation in bentonite, Long-term diffusion of U(VI) in bentonite: dependence on density, Sorption and desorption of plutonium by bentonite, Dissolution of plutonium intrinsic colloids in the presence of clay and asmore » a function of temperature, Laboratory investigation of colloid-facilitated transport of cesium by bentonite colloids in a crystalline rock system, Development and demonstration of discrete fracture network model, Fracture continuum model and its comparison with discrete fracture network model.« less

Continuum Damage Mechanics Used to Predict the Creep Life of Monolithic Ceramics

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Jadaan, Osama M.

1998-01-01

Significant improvements in propulsion and power generation for the next century will require revolutionary advances in high-temperature materials and structural design. Advanced ceramics are candidate materials for these elevated temperature applications. High-temperature and long-duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. An analytical methodology in the form of the integrated design program-Ceramics Analysis and Reliability Evaluation of Structures/Creep (CARES/Creep) has been developed by the NASA Lewis Research Center to predict the life of ceramic structural components subjected to creep rupture conditions. This program utilizes commercially available finite element packages and takes into account the transient state of stress and creep strain distributions (stress relaxation as well as the asymmetric response to tension and compression). The creep life of a component is discretized into short time steps, during which the stress distribution is assumed constant. Then, the damage is calculated for each time step on the basis of a modified Monkman-Grant (MMG) creep rupture criterion. The cumulative damage is subsequently calculated as time elapses in a manner similar to Miner's rule for cyclic fatigue loading. Failure is assumed to occur when the normalized cumulative damage at any point in the component reaches unity. The corresponding time is the creep rupture life for that component.

Extended optical model for fission

DOE PAGES

Sin, M.; Capote, R.; Herman, M. W.; ...

2016-03-07

A comprehensive formalism to calculate fission cross sections based on the extension of the optical model for fission is presented. It can be used for description of nuclear reactions on actinides featuring multi-humped fission barriers with partial absorption in the wells and direct transmission through discrete and continuum fission channels. The formalism describes the gross fluctuations observed in the fission probability due to vibrational resonances, and can be easily implemented in existing statistical reaction model codes. The extended optical model for fission is applied for neutron induced fission cross-section calculations on 234,235,238U and 239Pu targets. A triple-humped fission barrier ismore » used for 234,235U(n,f), while a double-humped fission barrier is used for 238U(n,f) and 239Pu(n,f) reactions as predicted by theoretical barrier calculations. The impact of partial damping of class-II/III states, and of direct transmission through discrete and continuum fission channels, is shown to be critical for a proper description of the measured fission cross sections for 234,235,238U(n,f) reactions. The 239Pu(n,f) reaction can be calculated in the complete damping approximation. Calculated cross sections for 235,238U(n,f) and 239Pu(n,f) reactions agree within 3% with the corresponding cross sections derived within the Neutron Standards least-squares fit of available experimental data. Lastly, the extended optical model for fission can be used for both theoretical fission studies and nuclear data evaluation.« less

A continuum thermo-inelastic model for damage and healing in self-healing glass materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Wei; Sun, Xin; Koeppel, Brian J.

Self-healing glass, a recent advancement in the class of smart sealing materials, has attracted great attention from both research and industrial communities because of its unique capability of repairing itself at elevated temperatures. However, further development and optimization of this material rely on a more fundamental and thorough understanding of its essential thermo-mechanical response characteristics, which is also pivotal in predicting the coupling and interactions between the nonlinear stress and temperature dependent damage and healing behaviors. In the current study, a continuum three-dimensional thermo-inelastic damage-healing constitutive framework has been developed for the compliant self-healing glass material. The important feature ofmore » the present model is that various phenomena governing the mechanical degradation and recovery process, i.e. the nucleation, growth, and healing of the cracks and pores, are described with distinct mechanism-driven kinetics, where the healing constitutive relations are propagated from lower-length scale simulations. The proposed formulations are implemented into finite element analyses and the effects of various loading conditions and material properties on the material’s mechanical resistance are investigated.« less

A trans-phase granular continuum relation and its use in simulation

NASA Astrophysics Data System (ADS)

Kamrin, Ken; Dunatunga, Sachith; Askari, Hesam

The ability to model a large granular system as a continuum would offer tremendous benefits in computation time compared to discrete particle methods. However, two infamous problems arise in the pursuit of this vision: (i) the constitutive relation for granular materials is still unclear and hotly debated, and (ii) a model and corresponding numerical method must wear ``many hats'' as, in general circumstances, it must be able to capture and accurately represent the material as it crosses through its collisional, dense-flowing, and solid-like states. Here we present a minimal trans-phase model, merging an elastic response beneath a fictional yield criterion, a mu(I) rheology for liquid-like flow above the static yield criterion, and a disconnection rule to model separation of the grains into a low-temperature gas. We simulate our model with a meshless method (in high strain/mixing cases) and the finite-element method. It is able to match experimental data in many geometries, including collapsing columns, impact on granular beds, draining silos, and granular drag problems.

Simulating Fragmentation and Fluid-Induced Fracture in Disordered Media Using Random Finite-Element Meshes

DOE PAGES

Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania

2016-11-08

Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipatedmore » during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.« less

Simulating Fragmentation and Fluid-Induced Fracture in Disordered Media Using Random Finite-Element Meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania

Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipatedmore » during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.« less

Multiscale Analysis of Delamination of Carbon Fiber-Epoxy Laminates with Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Riddick, Jaret C.; Frankland, SJV; Gates, TS

2006-01-01

A multi-scale analysis is presented to parametrically describe the Mode I delamination of a carbon fiber/epoxy laminate. In the midplane of the laminate, carbon nanotubes are included for the purposes of selectively enhancing the fracture toughness of the laminate. To analyze carbon fiber epoxy carbon nanotube laminate, the multi-scale methodology presented here links a series of parameterizations taken at various length scales ranging from the atomistic through the micromechanical to the structural level. At the atomistic scale molecular dynamics simulations are performed in conjunction with an equivalent continuum approach to develop constitutive properties for representative volume elements of the molecular structure of components of the laminate. The molecular-level constitutive results are then used in the Mori-Tanaka micromechanics to develop bulk properties for the epoxy-carbon nanotube matrix system. In order to demonstrate a possible application of this multi-scale methodology, a double cantilever beam specimen is modeled. An existing analysis is employed which uses discrete springs to model the fiber bridging affect during delamination propagation. In the absence of empirical data or a damage mechanics model describing the effect of CNTs on fracture toughness, several tractions laws are postulated, linking CNT volume fraction to fiber bridging in a DCB specimen. Results from this demonstration are presented in terms of DCB specimen load-displacement responses.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Continuum modeling of neuronal cell under blast loading

PubMed Central

Jérusalem, Antoine; Dao, Ming

2012-01-01

Traumatic brain injuries have recently been put under the spotlight as one of the most important causes of accidental brain dysfunctions. Significant experimental and modeling efforts are thus ongoing to study the associated biological, mechanical and physical mechanisms. In the field of cell mechanics, progresses are also being made at the experimental and modeling levels to better characterize many of the cell functions such as differentiation, growth, migration and death, among others. The work presented here aims at bridging both efforts by proposing a continuum model of neuronal cell submitted to blast loading. In this approach, cytoplasm, nucleus and membrane (plus cortex) are differentiated in a representative cell geometry, and different material constitutive models are adequately chosen for each one. The material parameters are calibrated against published experimental work of cell nanoindentation at multiple rates. The final cell model is ultimately subjected to blast loading within a complete fluid-structure interaction computational framework. The results are compared to the nanoindentation simulation and the specific effects of the blast wave on the pressure and shear levels at the interfaces are identified. As a conclusion, the presented model successfully captures some of the intrinsic intracellular phenomena occurring during its deformation under blast loading and potentially leading to cell damage. It suggests more particularly the localization of damage at the nucleus membrane similarly to what has already been observed at the overall cell membrane. This degree of damage is additionally predicted to be worsened by a longer blast positive phase duration. As a conclusion, the proposed model ultimately provides a new three dimensional computational tool to evaluate intracellular damage during blast loading. PMID:22562014

Adhesive Characterization and Progressive Damage Analysis of Bonded Composite Joints

NASA Technical Reports Server (NTRS)

Girolamo, Donato; Davila, Carlos G.; Leone, Frank A.; Lin, Shih-Yung

2014-01-01

The results of an experimental/numerical campaign aimed to develop progressive damage analysis (PDA) tools for predicting the strength of a composite bonded joint under tensile loads are presented. The PDA is based on continuum damage mechanics (CDM) to account for intralaminar damage, and cohesive laws to account for interlaminar and adhesive damage. The adhesive response is characterized using standard fracture specimens and digital image correlation (DIC). The displacement fields measured by DIC are used to calculate the J-integrals, from which the associated cohesive laws of the structural adhesive can be derived. A finite element model of a sandwich conventional splice joint (CSJ) under tensile loads was developed. The simulations indicate that the model is capable of predicting the interactions of damage modes that lead to the failure of the joint.

Pore-scale and Continuum Simulations of Solute Transport Micromodel Benchmark Experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oostrom, Martinus; Mehmani, Yashar; Romero Gomez, Pedro DJ

Four sets of micromodel nonreactive solute transport experiments were conducted with flow velocity, grain diameter, pore-aspect ratio, and flow focusing heterogeneity as the variables. The data sets were offered to pore-scale modeling groups to test their simulators. Each set consisted of two learning experiments, for which all results was made available, and a challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing, and considerably enhanced mixing due to flow focusing.more » Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice-Boltzmann (LB) approach, and one employed a computational fluid dynamics (CFD) technique. The learning experiments were used by the PN models to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used these experiments to appropriately discretize the grid representations. The continuum model use published non-linear relations between transverse dispersion coefficients and Peclet numbers to compute the required dispersivity input values. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values and, resulting in less dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models needed up to several days on supercomputers to resolve the more complex problems.« less

Interaction Among Inhomogeneities.

DTIC Science & Technology

1980-12-01

imposed to eigenstrain distribu- tions throughout the inclusion and to the anisotropy of elastic media for matrices. -2- When eigenstrains are of a...introduce any stress field. It is called an impotent inclusion. Such an inclusion exists when an eigenstrain is a gradient of a function which vanishes...Appl. Mech. 44, 591-594 (1977). T. Mura, " Eigenstrains in Lattice Theory," Continuum Models in Discrete Systems, Proc. 2nd Int. Conf., Mont Gabriel

Continuous modeling of a grain boundary in MgO and its disclination induced grain-boundary migration mechanism

NASA Astrophysics Data System (ADS)

Cordier, P.; Sun, X.; Taupin, V.; Fressengeas, C.

2016-12-01

Grain boundaries (GBs) are thin material layers where the lattice rotates from one orientation to the next one within a few nanometers. Because they treat these layers as infinitely thin interfaces, large-scale polycrystalline representations fail to describe their structure. Conversely, atomistic representations provide a detailed description of the GBs, but their character remains discrete and not prone to coarse-graining procedures. Continuum descriptions based on kinematic and crystal defect fields defined at interatomic scale are appealing because they can provide smooth and thorough descriptions of GBs, recovering in some sense the atomistic description and potentially serving as a basis for coarse-grained polycrystalline representations. In this work, a crossover between atomistic description and continuous representation of a MgO tilt boundary in polycrystals is set-up to model the periodic arrays of structural units by using dislocation and disclination dipole arrays along GBs. The strain, rotation, curvature, disclination and dislocation density fields are determined in the boundary area by using the discrete atomic positions generated by molecular dynamics simulations. Then, this continuous disclination/dislocation model is used as part of the initial conditions in elasto-plastic continuum mechanics simulations to investigate the shear-coupled boundary migration of tilt boundaries. The present study leads to better understanding of the structure and mechanical architecture of grain boundaries.

Four-body extension of the continuum-discretized coupled-channels method

NASA Astrophysics Data System (ADS)

Descouvemont, P.

2018-06-01

I develop an extension of the continuum-discretized coupled-channels (CDCC) method to reactions where both nuclei present a low breakup threshold. This leads to a four-body model, where the only inputs are the interactions describing the colliding nuclei, and the four optical potentials between the fragments. Once these potentials are chosen, the model does not contain any additional parameter. First I briefly discuss the general formalism, and emphasize the need for dealing with large coupled-channel systems. The method is tested with existing benchmarks on 4 α bound states with the Ali-Bodmer potential. Then I apply the four-body CDCC to the 11Be+d system, where I consider the 10Be(0+,2+)+n configuration for 11Be. I show that breakup channels are crucial to reproduce the elastic cross section, but that core excitation plays a weak role. The 7Li+d system is investigated with an α +t cluster model for 7Li. I show that breakup channels significantly improve the agreement with the experimental cross section, but an additional imaginary term, simulating missing transfer channels, is necessary. The full CDCC results can be interpreted by equivalent potentials. For both systems, the real part is weakly affected by breakup channels, but the imaginary part is strongly modified. I suggest that the present wave functions could be used in future DWBA calculations.

The effect of spatial discretization upon traveling wave body forcing of a turbulent wall-bounded flow

NASA Astrophysics Data System (ADS)

You, Soyoung; Goldstein, David

2015-11-01

DNS is employed to simulate turbulent channel flow subject to a traveling wave body force field near the wall. The regions in which forces are applied are made progressively more discrete in a sequence of simulations to explore the boundaries between the effects of discrete flow actuators and spatially continuum actuation. The continuum body force field is designed to correspond to the ``optimal'' resolvent mode of McKeon and Sharma (2010), which has the L2 norm of σ1. That is, the normalized harmonic forcing that gives the largest disturbance energy is the first singular mode with the gain of σ1. 2D and 3D resolvent modes are examined at a modest Reτ of 180. For code validation, nominal flow simulations without discretized forcing are compared to previous work by Sharma and Goldstein (2014) in which we find that as we increase the forcing amplitude there is a decrease in the mean velocity and an increase in turbulent kinetic energy. The same force field is then sampled into isolated sub-domains to emulate the effect of discrete physical actuators. Several cases will be presented to explore the dependencies between the level of discretization and the turbulent flow behavior.

LOW ACTIVATION JOINING OF SIC/SIC COMPOSITES FOR FUSION APPLICATIONS: MODELING DUAL-PHASE MICROSTRUCTURES AND DISSIMILAR MATERIAL JOINTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henager, Charles H.; Nguyen, Ba Nghiep; Kurtz, Richard J.

2016-03-31

Finite element continuum damage models (FE-CDM) have been developed to simulate and model dual-phase joints and cracked joints for improved analysis of SiC materials in nuclear environments. This report extends the analysis from the last reporting cycle by including results from dual-phase models and from cracked joint models.

Soil compaction: Evaluation of stress transmission and resulting soil structure

NASA Astrophysics Data System (ADS)

Naveed, Muhammad; Schjønning, Per; Keller, Thomas; Lamande, Mathieu

2016-04-01

Accurate estimation of stress transmission and resultant deformation in soil profiles is a prerequisite for the development of predictive models and decision support tools for preventing soil compaction. Numerous studies have been carried out on the effects of soil compaction, whilst relatively few studies have focused on the cause (mode of stress transmission in the soil). We have coupled both cause and effects together in the present study by carrying out partially confined compression tests on (1) wet aggregates, (2) air dry aggregates, and (3) intact soils to quantify stress transmission and compaction-resulted soil structure at the same time. Stress transmission was quantified using both X-ray CT and Tactilus sensor mat, and soil-pore structure was quantified using X-ray CT. Our results imply that stress transmission through soil highly depends on the magnitude of applied load and aggregate strength. As soon as the applied load is lower than the aggregate strength, the mode of stress transmission is discrete as stresses were mainly transmitted through chain of aggregates. With increasing applied load soil aggregates start deforming that transformed heterogeneous soil into homogenous, as a result stress transmission mode was shifted from discrete towards more like a continuum. Continuum-like stress transmission mode was better simulated with Boussinesq (1885) model based on theory of elasticity compared to discrete. The soil-pore structure was greatly affected by increasing applied stresses. Total porosity was reduced 5-16% and macroporosity 50-85% at 620 kPa applied stress for the intact soils. Similarly, significant changes in the morphological indices of the macropore space were also observed with increasing applied stresses.

On the path to 2025: understanding the Alzheimer's disease continuum.

PubMed

Aisen, Paul S; Cummings, Jeffrey; Jack, Clifford R; Morris, John C; Sperling, Reisa; Frölich, Lutz; Jones, Roy W; Dowsett, Sherie A; Matthews, Brandy R; Raskin, Joel; Scheltens, Philip; Dubois, Bruno

2017-08-09

Basic research advances in recent years have furthered our understanding of the natural history of Alzheimer's disease (AD). It is now recognized that pathophysiological changes begin many years prior to clinical manifestations of disease and the spectrum of AD spans from clinically asymptomatic to severely impaired. Defining AD purely by its clinical presentation is thus artificial and efforts have been made to recognize the disease based on both clinical and biomarker findings. Advances with biomarkers have also prompted a shift in how the disease is considered as a clinico-pathophysiological entity, with an increasing appreciation that AD should not only be viewed with discrete and defined clinical stages, but as a multifaceted process moving along a seamless continuum. Acknowledging this concept is critical to understanding the development process for disease-modifying therapies, and for initiating effective diagnostic and disease management options. In this article, we discuss the concept of a disease continuum from pathophysiological, biomarker, and clinical perspectives, and highlight the importance of considering AD as a continuum rather than discrete stages. While the pathophysiology of AD has still not been elucidated completely, there is ample evidence to support researchers and clinicians embracing the view of a disease continuum in their study, diagnosis, and management of the disease.

Lagrangian continuum dynamics in ALEGRA.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Michael K. W.; Love, Edward

Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow

NASA Astrophysics Data System (ADS)

Alexandrou, Constantia; Athenodorou, Andreas; Cichy, Krzysztof; Constantinou, Martha; Horkel, Derek P.; Jansen, Karl; Koutsou, Giannis; Larkin, Conor

2018-04-01

We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral-projector method. We use ensembles with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cutoff effects. This finally yields a much smaller total error in the spectral-projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility.

General phase spaces: from discrete variables to rotor and continuum limits

NASA Astrophysics Data System (ADS)

Albert, Victor V.; Pascazio, Saverio; Devoret, Michel H.

2017-12-01

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.

In Praise of Numerical Computation

NASA Astrophysics Data System (ADS)

Yap, Chee K.

Theoretical Computer Science has developed an almost exclusively discrete/algebraic persona. We have effectively shut ourselves off from half of the world of computing: a host of problems in Computational Science & Engineering (CS&E) are defined on the continuum, and, for them, the discrete viewpoint is inadequate. The computational techniques in such problems are well-known to numerical analysis and applied mathematics, but are rarely discussed in theoretical algorithms: iteration, subdivision and approximation. By various case studies, I will indicate how our discrete/algebraic view of computing has many shortcomings in CS&E. We want embrace the continuous/analytic view, but in a new synthesis with the discrete/algebraic view. I will suggest a pathway, by way of an exact numerical model of computation, that allows us to incorporate iteration and approximation into our algorithms’ design. Some recent results give a peek into how this view of algorithmic development might look like, and its distinctive form suggests the name “numerical computational geometry” for such activities.

Discrete and continuum links to a nonlinear coupled transport problem of interacting populations

NASA Astrophysics Data System (ADS)

Duong, M. H.; Muntean, A.; Richardson, O. M.

2017-07-01

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

Application of Discrete Fracture Modeling and Upscaling Techniques to Complex Fractured Reservoirs

NASA Astrophysics Data System (ADS)

Karimi-Fard, M.; Lapene, A.; Pauget, L.

2012-12-01

During the last decade, an important effort has been made to improve data acquisition (seismic and borehole imaging) and workflow for reservoir characterization which has greatly benefited the description of fractured reservoirs. However, the geological models resulting from the interpretations need to be validated or calibrated against dynamic data. Flow modeling in fractured reservoirs remains a challenge due to the difficulty of representing mass transfers at different heterogeneity scales. The majority of the existing approaches are based on dual continuum representation where the fracture network and the matrix are represented separately and their interactions are modeled using transfer functions. These models are usually based on idealized representation of the fracture distribution which makes the integration of real data difficult. In recent years, due to increases in computer power, discrete fracture modeling techniques (DFM) are becoming popular. In these techniques the fractures are represented explicitly allowing the direct use of data. In this work we consider the DFM technique developed by Karimi-Fard et al. [1] which is based on an unstructured finite-volume discretization. The mass flux between two adjacent control-volumes is evaluated using an optimized two-point flux approximation. The result of the discretization is a list of control-volumes with the associated pore-volumes and positions, and a list of connections with the associated transmissibilities. Fracture intersections are simplified using a connectivity transformation which contributes considerably to the efficiency of the methodology. In addition, the method is designed for general purpose simulators and any connectivity based simulator can be used for flow simulations. The DFM technique is either used standalone or as part of an upscaling technique. The upscaling techniques are required for large reservoirs where the explicit representation of all fractures and faults is not possible. Karimi-Fard et al. [2] have developed an upscaling technique based on DFM representation. The original version of this technique was developed to construct a dual-porosity model from a discrete fracture description. This technique has been extended and generalized so it can be applied to a wide range of problems from reservoirs with a few or no fracture to highly fractured reservoirs. In this work, we present the application of these techniques to two three-dimensional fractured reservoirs constructed using real data. The first model contains more than 600 medium and large scale fractures. The fractures are not always connected which requires a general modeling technique. The reservoir has 50 wells (injectors and producers) and water flooding simulations are performed. The second test case is a larger reservoir with sparsely distributed faults. Single-phase simulations are performed with 5 producing wells. [1] Karimi-Fard M., Durlofsky L.J., and Aziz K. 2004. An efficient discrete-fracture model applicable for general-purpose reservoir simulators. SPE Journal, 9(2): 227-236. [2] Karimi-Fard M., Gong B., and Durlofsky L.J. 2006. Generation of coarse-scale continuum flow models from detailed fracture characterizations. Water Resources Research, 42(10): W10423.

Demographic inference under the coalescent in a spatial continuum.

PubMed

Guindon, Stéphane; Guo, Hongbin; Welch, David

2016-10-01

Understanding population dynamics from the analysis of molecular and spatial data requires sound statistical modeling. Current approaches assume that populations are naturally partitioned into discrete demes, thereby failing to be relevant in cases where individuals are scattered on a spatial continuum. Other models predict the formation of increasingly tight clusters of individuals in space, which, again, conflicts with biological evidence. Building on recent theoretical work, we introduce a new genealogy-based inference framework that alleviates these issues. This approach effectively implements a stochastic model in which the distribution of individuals is homogeneous and stationary, thereby providing a relevant null model for the fluctuation of genetic diversity in time and space. Importantly, the spatial density of individuals in a population and their range of dispersal during the course of evolution are two parameters that can be inferred separately with this method. The validity of the new inference framework is confirmed with extensive simulations and the analysis of influenza sequences collected over five seasons in the USA. Copyright © 2016 Elsevier Inc. All rights reserved.

Implementation and Validation of the Viscoelastic Continuum Damage Theory for Asphalt Mixture and Pavement Analysis in Brazil

NASA Astrophysics Data System (ADS)

Nascimento, Luis Alberto Herrmann do

This dissertation presents the implementation and validation of the viscoelastic continuum damage (VECD) model for asphalt mixture and pavement analysis in Brazil. It proposes a simulated damage-to-fatigue cracked area transfer function for the layered viscoelastic continuum damage (LVECD) program framework and defines the model framework's fatigue cracking prediction error for asphalt pavement reliability-based design solutions in Brazil. The research is divided into three main steps: (i) implementation of the simplified viscoelastic continuum damage (S-VECD) model in Brazil (Petrobras) for asphalt mixture characterization, (ii) validation of the LVECD model approach for pavement analysis based on field performance observations, and defining a local simulated damage-to-cracked area transfer function for the Fundao Project's pavement test sections in Rio de Janeiro, RJ, and (iii) validation of the Fundao project local transfer function to be used throughout Brazil for asphalt pavement fatigue cracking predictions, based on field performance observations of the National MEPDG Project's pavement test sections, thereby validating the proposed framework's prediction capability. For the first step, the S-VECD test protocol, which uses controlled-on-specimen strain mode-of-loading, was successfully implemented at the Petrobras and used to characterize Brazilian asphalt mixtures that are composed of a wide range of asphalt binders. This research verified that the S-VECD model coupled with the GR failure criterion is accurate for fatigue life predictions of Brazilian asphalt mixtures, even when very different asphalt binders are used. Also, the applicability of the load amplitude sweep (LAS) test for the fatigue characterization of the asphalt binders was checked, and the effects of different asphalt binders on the fatigue damage properties of the asphalt mixtures was investigated. The LAS test results, modeled according to VECD theory, presented a strong correlation with the asphalt mixtures' fatigue performance. In the second step, the S-VECD test protocol was used to characterize the asphalt mixtures used in the 27 selected Fundao project test sections and subjected to real traffic loading. Thus, the asphalt mixture properties, pavement structure data, traffic loading, and climate were input into the LVECD program for pavement fatigue cracking performance simulations. The simulation results showed good agreement with the field-observed distresses. Then, a damage shift approach, based on the initial simulated damage growth rate, was introduced in order to obtain a unique relationship between the LVECD-simulated shifted damage and the pavement-observed fatigue cracked areas. This correlation was fitted to a power form function and defined as the averaged reduced damage-to-cracked area transfer function. The last step consisted of using the averaged reduced damage-to-cracked area transfer function that was developed in the Fundao project to predict pavement fatigue cracking in 17 National MEPDG project test sections. The procedures for the material characterization and pavement data gathering adopted in this step are similar to those used for the Fundao project simulations. This research verified that the transfer function defined for the Fundao project sections can be used for the fatigue performance predictions of a wide range of pavements all over Brazil, as the predicted and observed cracked areas for the National MEPDG pavements presented good agreement, following the same trends found for the Fundao project pavement sites. Based on the prediction errors determined for all 44 pavement test sections (Fundao and National MEPDG test sections), the proposed framework's prediction capability was determined so that reliability-based solutions can be applied for flexible pavement design. It was concluded that the proposed LVECD program framework has very good fatigue cracking prediction capability.

Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization.

PubMed

Miehe, C; Teichtmeister, S; Aldakheel, F

2016-04-28

This work outlines a novel variational-based theory for the phase-field modelling of ductile fracture in elastic-plastic solids undergoing large strains. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modelling. It is linked to a formulation of gradient plasticity at finite strains. The framework includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges. © 2016 The Author(s).

Analysis of Discrete-Source Damage Progression in a Tensile Stiffened Composite Panel

NASA Technical Reports Server (NTRS)

Wang, John T.; Lotts, Christine G.; Sleight, David W.

1999-01-01

This paper demonstrates the progressive failure analysis capability in NASA Langley s COMET-AR finite element analysis code on a large-scale built-up composite structure. A large-scale five stringer composite panel with a 7-in. long discrete source damage was analyzed from initial loading to final failure including the geometric and material nonlinearities. Predictions using different mesh sizes, different saw cut modeling approaches, and different failure criteria were performed and assessed. All failure predictions have a reasonably good correlation with the test result.

Linking asphalt binder fatigue to asphalt mixture fatigue performance using viscoelastic continuum damage modeling

NASA Astrophysics Data System (ADS)

Safaei, Farinaz; Castorena, Cassie; Kim, Y. Richard

2016-08-01

Fatigue cracking is a major form of distress in asphalt pavements. Asphalt binder is the weakest asphalt concrete constituent and, thus, plays a critical role in determining the fatigue resistance of pavements. Therefore, the ability to characterize and model the inherent fatigue performance of an asphalt binder is a necessary first step to design mixtures and pavements that are not susceptible to premature fatigue failure. The simplified viscoelastic continuum damage (S-VECD) model has been used successfully by researchers to predict the damage evolution in asphalt mixtures for various traffic and climatic conditions using limited uniaxial test data. In this study, the S-VECD model, developed for asphalt mixtures, is adapted for asphalt binders tested under cyclic torsion in a dynamic shear rheometer. Derivation of the model framework is presented. The model is verified by producing damage characteristic curves that are both temperature- and loading history-independent based on time sweep tests, given that the effects of plasticity and adhesion loss on the material behavior are minimal. The applicability of the S-VECD model to the accelerated loading that is inherent of the linear amplitude sweep test is demonstrated, which reveals reasonable performance predictions, but with some loss in accuracy compared to time sweep tests due to the confounding effects of nonlinearity imposed by the high strain amplitudes included in the test. The asphalt binder S-VECD model is validated through comparisons to asphalt mixture S-VECD model results derived from cyclic direct tension tests and Accelerated Loading Facility performance tests. The results demonstrate good agreement between the asphalt binder and mixture test results and pavement performance, indicating that the developed model framework is able to capture the asphalt binder's contribution to mixture fatigue and pavement fatigue cracking performance.

Hybrid multiscale modeling and prediction of cancer cell behavior

PubMed Central

Habibi, Jafar

2017-01-01

Background Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems. Methods In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters. Results Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable. Conclusion Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset. PMID:28846712

Nonlinear modelling of cancer: bridging the gap between cells and tumours

PubMed Central

Lowengrub, J S; Frieboes, H B; Jin, F; Chuang, Y-L; Li, X; Macklin, P; Wise, S M; Cristini, V

2010-01-01

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis. PMID:20808719

Nonlinear modelling of cancer: bridging the gap between cells and tumours

NASA Astrophysics Data System (ADS)

Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y.-L.; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V.

2010-01-01

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

Hybrid multiscale modeling and prediction of cancer cell behavior.

PubMed

Zangooei, Mohammad Hossein; Habibi, Jafar

2017-01-01

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems. In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters. Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable. Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

Chaos and Localization in Dieterich-Ruina Friction

NASA Astrophysics Data System (ADS)

Erickson, B. A.; Birnir, B.; Lavallee, D.

2009-12-01

We consider two models derived from a 1-D Burridge-Knopoff chain of spring connected blocks subject to the Dieterich-Ruina (D-R) friction law. We analyze both the discrete ordinary differential equations, as well as the continuum model. Preliminary investigation into the ODEs shows evidence of the Dieterich-Ruina law exhibiting chaos, dependent on the size of the system. Periodic behavior occurs when considering chains of 3 or 5 blocks, while a chain of 10 blocks with the same parameter values results in chaotic motion. The continuum model (PDE) undergoes a transition to chaos when a specific parameter is increased and the chaotic regime is reached for smaller critical values than in the case of a single block (see Erickson et. al. 2008). This parameter, epsilon is the ratio of the stress parameters (B-A) and A in the D-R friction law. The parameter A is a measure of the direct velocity dependence (sometimes called the "direct effect") while (A-B) is a measure of the steady-state velocity dependence. When compared to the slip weakening friction law, the parameter (B-A) plays a role of a stress drop while A corresponds to the strength excess. In the case of a single block, transitions to chaos occur when epsilon = 11, a value too high for applications in seismology. For the continuum model however, the chaotic regime is reached for epsilon = 1. That the transition to chaos ensues for smaller parameter values than in the case of a single block may also be an indication that a careful rescaling of the friction law is necessary, similar to the conclusions made by Schmittbuhl et. al. (1996) who studied a "hierarchical array of blocks" and found that velocity weakening friction was scale dependent. We also observe solutions to both the discrete and the continuous model where the slip remains localized in space, suggesting the presence of solitonic behavior. Initial data in the form of a gaussian pulse tends to remain localized under certain parameter values and we explore the space of values for which this occurs. These solitonic or localized solutions can be understood as proxy for the propagation of the rupture across the fault during an earthquake. Under the Dieterich-Ruina law we may have discovered only a small subset of solutions to both the discrete and the continuous model, but there is no question that even in one spatial dimension, a rich phenomenology of dynamics exists.

Edge-relevant plasma simulations with the continuum code COGENT

NASA Astrophysics Data System (ADS)

Dorf, M.; Dorr, M.; Ghosh, D.; Hittinger, J.; Rognlien, T.; Cohen, R.; Lee, W.; Schwartz, P.

2016-10-01

We describe recent advances in cross-separatrix and other edge-relevant plasma simulations with COGENT, a continuum gyro-kinetic code being developed by the Edge Simulation Laboratory (ESL) collaboration. The distinguishing feature of the COGENT code is its high-order finite-volume discretization methods, which employ arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. This paper discusses the 4D (axisymmetric) electrostatic version of the code, and the presented topics include: (a) initial simulations with kinetic electrons and development of reduced fluid models; (b) development and application of implicit-explicit (IMEX) time integration schemes; and (c) conservative modeling of drift-waves and the universal instability. Work performed for USDOE, at LLNL under contract DE-AC52-07NA27344 and at LBNL under contract DE-AC02-05CH11231.

Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2013-01-25

The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy.more » Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.« less

Photon Strength Function at Low Energies in 95Mo

DOE PAGES

Wiedeking, M.; Bernstein, L. A.; Allmond, J. M.; ...

2014-05-01

A new and model-independent experimental method has been developed to determine the energy dependence of the photon strength function. It is designed to study statistical feeding from the quasi continuum to individual low-lying discrete levels. This new technique is presented and results for 95Mo are compared to data from the University of Oslo. In particular, questions regarding the existence of the low-energy enhancement in the photon strength function are addressed.

Slip Continuity in Explicit Crystal Plasticity Simulations Using Nonlocal Continuum and Semi-discrete Approaches

DTIC Science & Technology

2013-01-01

Based Micropolar Single Crystal Plasticity: Comparison of Multi - and Single Criterion Theories. J. Mech. Phys. Solids 2011, 59, 398–422. ALE3D ...element boundaries in a multi -step constitutive evaluation (Becker, 2011). The results showed the desired effects of smoothing the deformation field...Implementation The model was implemented in the large-scale parallel, explicit finite element code ALE3D (2012). The crystal plasticity

Flexible Automatic Discretization for Finite Differences: Eliminating the Human Factor

NASA Astrophysics Data System (ADS)

Pranger, Casper

2017-04-01

In the geophysical numerical modelling community, finite differences are (in part due to their small footprint) a popular spatial discretization method for PDEs in the regular-shaped continuum that is the earth. However, they rapidly become prone to programming mistakes when physics increase in complexity. To eliminate opportunities for human error, we have designed an automatic discretization algorithm using Wolfram Mathematica, in which the user supplies symbolic PDEs, the number of spatial dimensions, and a choice of symbolic boundary conditions, and the script transforms this information into matrix- and right-hand-side rules ready for use in a C++ code that will accept them. The symbolic PDEs are further used to automatically develop and perform manufactured solution benchmarks, ensuring at all stages physical fidelity while providing pragmatic targets for numerical accuracy. We find that this procedure greatly accelerates code development and provides a great deal of flexibility in ones choice of physics.

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components

PubMed Central

Gardiner, Bruce S.; Wong, Kelvin K. L.; Joldes, Grand R.; Rich, Addison J.; Tan, Chin Wee; Burgess, Antony W.; Smith, David W.

2015-01-01

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory. PMID:26452000

Discrete Element Framework for Modelling Extracellular Matrix, Deformable Cells and Subcellular Components.

PubMed

Gardiner, Bruce S; Wong, Kelvin K L; Joldes, Grand R; Rich, Addison J; Tan, Chin Wee; Burgess, Antony W; Smith, David W

2015-10-01

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.

Modeling CO2 Storage in Fractured Reservoirs: Fracture-Matrix Interactions of Free-Phase and Dissolved CO2

NASA Astrophysics Data System (ADS)

Oldenburg, C. M.; Zhou, Q.; Birkholzer, J. T.

2017-12-01

The injection of supercritical CO2 (scCO2) in fractured reservoirs has been conducted at several storage sites. However, no site-specific dual-continuum modeling for fractured reservoirs has been reported and modeling studies have generally underestimated the fracture-matrix interactions. We developed a conceptual model for enhanced CO2 storage to take into account global scCO2 migration in the fracture continuum, local storage of scCO2 and dissolved CO2 (dsCO2) in the matrix continuum, and driving forces for scCO2 invasion and dsCO2 diffusion from fractures. High-resolution discrete fracture-matrix models were developed for a column of idealized matrix blocks bounded by vertical and horizontal fractures and for a km-scale fractured reservoir. The column-scale simulation results show that equilibrium storage efficiency strongly depends on matrix entry capillary pressure and matrix-matrix connectivity while the time scale to reach equilibrium is sensitive to fracture spacing and matrix flow properties. The reservoir-scale modeling results shows that the preferential migration of scCO2 through fractures is coupled with bulk storage in the rock matrix that in turn retards the fracture scCO2 plume. We also developed unified-form diffusive flux equations to account for dsCO2 storage in brine-filled matrix blocks and found solubility trapping is significant in fractured reservoirs with low-permeability matrix.

Bound states, scattering states, and resonant states in PT -symmetric open quantum systems

NASA Astrophysics Data System (ADS)

Garmon, Savannah; Gianfreda, Mariagiovanna; Hatano, Naomichi

2015-08-01

We study a simple open quantum system with a PT -symmetric defect potential as a prototype in order to illustrate a number of general features of PT -symmetric open quantum systems; however, the potential itself could be mimicked by a number of PT systems that have been experimentally studied quite recently. One key feature is the resonance in continuum (RIC), which appears in both the discrete spectrum and the scattering spectrum of such systems. The RIC wave function forms a standing wave extending throughout the spatial extent of the system and in this sense represents a resonance between the open environment associated with the leads of our model and the central PT -symmetric potential. We also illustrate that as one deforms the system parameters, the RIC may exit the continuum by splitting into a bound state and a virtual bound state at the band edge, a process which should be experimentally observable. We also study the exceptional points appearing in the discrete spectrum at which two eigenvalues coalesce; we categorize these as either EP2As, at which two real-valued solutions coalesce before becoming complex-valued, and EP2Bs, for which the two solutions are complex on either side of the exceptional point. The EP2As are associated with PT -symmetry breaking; we argue that these are more stable against parameter perturbation than the EP2Bs. We also study complex-valued solutions of the discrete spectrum for which the wave function is nevertheless spatially localized, something that is not allowed in traditional open quantum systems; we illustrate that these may form quasibound states in continuum under some circumstances. We also study the scattering properties of the system, including states that support invisible propagation and some general features of perfect transmission states. We finally use our model as a prototype for the construction of scattering states that satisfy PT -symmetric boundary conditions; while these states do not conserve the traditional probability current, we introduce the PT current which is preserved. The perfect transmission states appear as a special case of the PT -symmetric scattering states.

A comparison of the lattice discrete particle method to the finite-element method and the K&C material model for simulating the static and dynamic response of concrete.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Jovanca J.; Bishop, Joseph E.

2013-11-01

This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed atmore » Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.« less

Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

NASA Technical Reports Server (NTRS)

Leone, Frank A., Jr.

2015-01-01

A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

A Progressive Damage Model for Predicting Permanent Indentation and Impact Damage in Composite Laminates

NASA Astrophysics Data System (ADS)

Ji, Zhaojie; Guan, Zhidong; Li, Zengshan

2017-10-01

In this paper, a progressive damage model was established on the basis of ABAQUS software for predicting permanent indentation and impact damage in composite laminates. Intralaminar and interlaminar damage was modelled based on the continuum damage mechanics (CDM) in the finite element model. For the verification of the model, low-velocity impact tests of quasi-isotropic laminates with material system of T300/5228A were conducted. Permanent indentation and impact damage of the laminates were simulated and the numerical results agree well with the experiments. It can be concluded that an obvious knee point can be identified on the curve of the indentation depth versus impact energy. Matrix cracking and delamination develops rapidly with the increasing impact energy, while considerable amount of fiber breakage only occurs when the impact energy exceeds the energy corresponding to the knee point. Predicted indentation depth after the knee point is very sensitive to the parameter μ which is proposed in this paper, and the acceptable value of this parameter is in range from 0.9 to 1.0.

A damage analysis for brittle materials using stochastic micro-structural information

NASA Astrophysics Data System (ADS)

Lin, Shih-Po; Chen, Jiun-Shyan; Liang, Shixue

2016-03-01

In this work, a micro-crack informed stochastic damage analysis is performed to consider the failures of material with stochastic microstructure. The derivation of the damage evolution law is based on the Helmholtz free energy equivalence between cracked microstructure and homogenized continuum. The damage model is constructed under the stochastic representative volume element (SRVE) framework. The characteristics of SRVE used in the construction of the stochastic damage model have been investigated based on the principle of the minimum potential energy. The mesh dependency issue has been addressed by introducing a scaling law into the damage evolution equation. The proposed methods are then validated through the comparison between numerical simulations and experimental observations of a high strength concrete. It is observed that the standard deviation of porosity in the microstructures has stronger effect on the damage states and the peak stresses than its effect on the Young's and shear moduli in the macro-scale responses.

Prediction Of Formability In Sheet Metal Forming Processes Using A Local Damage Model

NASA Astrophysics Data System (ADS)

Teixeira, P.; Santos, Abel; César Sá, J.; Andrade Pires, F.; Barata da Rocha, A.

2007-05-01

The formability in sheet metal forming processes is mainly conditioned by ductile fracture resulting from geometric instabilities due to necking and strain localization. The macroscopic collapse associated with ductile failure is a result of internal degradation described throughout metallographic observations by the nucleation, growth and coalescence of voids and micro-cracks. Damage influences and is influenced by plastic deformation and therefore these two dissipative phenomena should be coupled at the constitutive level. In this contribution, Lemaitre's ductile damage model is coupled with Hill's orthotropic plasticity criterion. The coupling between damaging and material behavior is accounted for within the framework of Continuum Damage Mechanics (CDM). The resulting constitutive equations are implemented in the Abaqus/Explicit code, for the prediction of fracture onset in sheet metal forming processes. The damage evolution law takes into account the important effect of micro-crack closure, which dramatically decreases the rate of damage growth under compressive paths.

A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum.

PubMed Central

Dallon, J C; Othmer, H G

1997-01-01

Dictyostelium discoideum (Dd) is a widely studied model system from which fundamental insights into cell movement, chemotaxis, aggregation and pattern formation can be gained. In this system aggregation results from the chemotactic response by dispersed amoebae to a travelling wave of the chemoattractant cAMP. We have developed a model in which the cells are treated as discrete points in a continuum field of the chemoattractant, and transduction of the extracellular cAMP signal into the intracellular signal is based on the G protein model developed by Tang & Othmer. The model reproduces a number of experimental observations and gives further insight into the aggregation process. We investigate different rules for cell movement the factors that influence stream formation the effect on aggregation of noise in the choice of the direction of movement and when spiral waves of chemoattractant and cell density are likely to occur. Our results give new insight into the origin of spiral waves and suggest that streaming is due to a finite amplitude instability. PMID:9134569

Dynamics of basaltic glass dissolution - Capturing microscopic effects in continuum scale models

NASA Astrophysics Data System (ADS)

Aradóttir, E. S. P.; Sigfússon, B.; Sonnenthal, E. L.; Björnsson, G.; Jónsson, H.

2013-11-01

The method of 'multiple interacting continua' (MINC) was applied to include microscopic rate-limiting processes in continuum scale reactive transport models of basaltic glass dissolution. The MINC method involves dividing the system up to ambient fluid and grains, using a specific surface area to describe the interface between the two. The various grains and regions within grains can then be described by dividing them into continua separated by dividing surfaces. Millions of grains can thus be considered within the method without the need to explicity discretizing them. Four continua were used for describing a dissolving basaltic glass grain; the first one describes the ambient fluid around the grain, while the second, third and fourth continuum refer to a diffusive leached layer, the dissolving part of the grain and the inert part of the grain, respectively. The model was validated using the TOUGHREACT simulator and data from column flow through experiments of basaltic glass dissolution at low, neutral and high pH values. Successful reactive transport simulations of the experiments and overall adequate agreement between measured and simulated values provides validation that the MINC approach can be applied for incorporating microscopic effects in continuum scale basaltic glass dissolution models. Equivalent models can be used when simulating dissolution and alteration of other minerals. The study provides an example of how numerical modeling and experimental work can be combined to enhance understanding of mechanisms associated with basaltic glass dissolution. Column outlet concentrations indicated basaltic glass to dissolve stoichiometrically at pH 3. Predictive simulations with the developed MINC model indicated significant precipitation of secondary minerals within the column at neutral and high pH, explaining observed non-stoichiometric outlet concentrations at these pH levels. Clay, zeolite and hydroxide precipitation was predicted to be most abundant within the column.

Deterministic and Probabilistic Creep and Creep Rupture Enhancement to CARES/Creep: Multiaxial Creep Life Prediction of Ceramic Structures Using Continuum Damage Mechanics and the Finite Element Method

NASA Technical Reports Server (NTRS)

Jadaan, Osama M.; Powers, Lynn M.; Gyekenyesi, John P.

1998-01-01

High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep ripture criterion However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of stress, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions This creep life prediction methodology was preliminarily added to the integrated design code CARES/Creep (Ceramics Analysis and Reliability Evaluation of Structures/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of this methodology and the CARES/Creep program.

On the continuum limit for a semidiscrete Hirota equation

PubMed Central

Pickering, Andrew; Zhao, Hai-qiong

2016-01-01

In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step δ affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as δ→0. PMID:27956884

The dynamics of a forced coupled network of active elements

NASA Astrophysics Data System (ADS)

Parks, Helen F.; Ermentrout, Bard; Rubin, Jonathan E.

2011-03-01

This paper presents the derivation and analysis of mathematical models motivated by the experimental induction of contour phosphenes in the retina. First, a spatially discrete chain of periodically forced coupled oscillators is considered via reduction to a chain of scalar phase equations. Each isolated oscillator locks in a 1:2 manner with the forcing so that there is intrinsic bistability, with activity peaking on either the odd or even cycles of the forcing. If half the chain is started on the odd cycle and half on the even cycle (“split state”), then with sufficiently strong coupling, a wave can be produced that can travel in either direction due to symmetry. Numerical and analytic methods are employed to determine the size of coupling necessary for the split state solution to destabilize such that waves appear. Taking a continuum limit, we reduce the chain to a partial differential equation. We use a Melnikov function to compute, to leading order, the speed of the traveling wave solution to the partial differential equation as a function of the form of coupling and the forcing parameters and compare our result to the numerically computed discrete and continuum wave speeds.

Continuum approach for aerothermal flow through ablative porous material using discontinuous Galerkin discretization.

NASA Astrophysics Data System (ADS)

Schrooyen, Pierre; Chatelain, Philippe; Hillewaert, Koen; Magin, Thierry E.

2014-11-01

The atmospheric entry of spacecraft presents several challenges in simulating the aerothermal flow around the heat shield. Predicting an accurate heat-flux is a complex task, especially regarding the interaction between the flow in the free stream and the erosion of the thermal protection material. To capture this interaction, a continuum approach is developed to go progressively from the region fully occupied by fluid to a receding porous medium. The volume averaged Navier-Stokes equations are used to model both phases in the same computational domain considering a single set of conservation laws. The porosity is itself a variable of the computation, allowing to take volumetric ablation into account through adequate source terms. This approach is implemented within a computational tool based on a high-order discontinuous Galerkin discretization. The multi-dimensional tool has already been validated and has proven its efficient parallel implementation. Within this platform, a fully implicit method was developed to simulate multi-phase reacting flows. Numerical results to verify and validate the methodology are considered within this work. Interactions between the flow and the ablated geometry are also presented. Supported by Fund for Research Training in Industry and Agriculture.

Fracture simulation of restored teeth using a continuum damage mechanics failure model.

PubMed

Li, Haiyan; Li, Jianying; Zou, Zhenmin; Fok, Alex Siu-Lun

2011-07-01

The aim of this paper is to validate the use of a finite-element (FE) based continuum damage mechanics (CDM) failure model to simulate the debonding and fracture of restored teeth. Fracture testing of plastic model teeth, with or without a standard Class-II MOD (mesial-occusal-distal) restoration, was carried out to investigate their fracture behavior. In parallel, 2D FE models of the teeth are constructed and analyzed using the commercial FE software ABAQUS. A CDM failure model, implemented into ABAQUS via the user element subroutine (UEL), is used to simulate the debonding and/or final fracture of the model teeth under a compressive load. The material parameters needed for the CDM model to simulate fracture are obtained through separate mechanical tests. The predicted results are then compared with the experimental data of the fracture tests to validate the failure model. The failure processes of the intact and restored model teeth are successfully reproduced by the simulation. However, the fracture parameters obtained from testing small specimens need to be adjusted to account for the size effect. The results indicate that the CDM model is a viable model for the prediction of debonding and fracture in dental restorations. Copyright © 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Free energy change of a dislocation due to a Cottrell atmosphere

DOE PAGES

Sills, R. B.; Cai, W.

2018-03-07

The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. In this work, we show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel–hydrogen system, predictingmore » hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Lastly, the influence of the free energy change on a dislocation’s line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank–Read source using discrete dislocation dynamics.« less

Free energy change of a dislocation due to a Cottrell atmosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sills, R. B.; Cai, W.

The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. In this work, we show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel–hydrogen system, predictingmore » hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Lastly, the influence of the free energy change on a dislocation’s line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank–Read source using discrete dislocation dynamics.« less

Free energy change of a dislocation due to a Cottrell atmosphere

NASA Astrophysics Data System (ADS)

Sills, R. B.; Cai, W.

2018-06-01

The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. We show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel-hydrogen system, predicting hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Finally, the influence of the free energy change on a dislocation's line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank-Read source using discrete dislocation dynamics.

The discrete regime of flame propagation

NASA Astrophysics Data System (ADS)

Tang, Francois-David; Goroshin, Samuel; Higgins, Andrew

The propagation of laminar dust flames in iron dust clouds was studied in a low-gravity envi-ronment on-board a parabolic flight aircraft. The elimination of buoyancy-induced convection and particle settling permitted measurements of fundamental combustion parameters such as the burning velocity and the flame quenching distance over a wide range of particle sizes and in different gaseous mixtures. The discrete regime of flame propagation was observed by substitut-ing nitrogen present in air with xenon, an inert gas with a significantly lower heat conductivity. Flame propagation in the discrete regime is controlled by the heat transfer between neighbor-ing particles, rather than by the particle burning rate used by traditional continuum models of heterogeneous flames. The propagation mechanism of discrete flames depends on the spa-tial distribution of particles, and thus such flames are strongly influenced by local fluctuations in the fuel concentration. Constant pressure laminar dust flames were observed inside 70 cm long, 5 cm diameter Pyrex tubes. Equally-spaced plate assemblies forming rectangular chan-nels were placed inside each tube to determine the quenching distance defined as the minimum channel width through which a flame can successfully propagate. High-speed video cameras were used to measure the flame speed and a fiber optic spectrometer was used to measure the flame temperature. Experimental results were compared with predictions obtained from a numerical model of a three-dimensional flame developed to capture both the discrete nature and the random distribution of particles in the flame. Though good qualitative agreement was obtained between model predictions and experimental observations, residual g-jitters and the short reduced-gravity periods prevented further investigations of propagation limits in the dis-crete regime. The full exploration of the discrete flame phenomenon would require high-quality, long duration reduced gravity environment available only on orbital platforms.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles.

PubMed

Huang, Aiqun; Hsu, Hsiao-Ping; Bhattacharya, Aniket; Binder, Kurt

2015-12-28

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

On the relation between phase-field crack approximation and gradient damage modelling

NASA Astrophysics Data System (ADS)

Steinke, Christian; Zreid, Imadeddin; Kaliske, Michael

2017-05-01

The finite element implementation of a gradient enhanced microplane damage model is compared to a phase-field model for brittle fracture. Phase-field models and implicit gradient damage models share many similarities despite being conceived from very different standpoints. In both approaches, an additional differential equation and a length scale are introduced. However, while the phase-field method is formulated starting from the description of a crack in fracture mechanics, the gradient method starts from a continuum mechanics point of view. At first, the scope of application for both models is discussed to point out intersections. Then, the analysis of the employed mathematical methods and their rigorous comparison are presented. Finally, numerical examples are introduced to illustrate the findings of the comparison which are summarized in a conclusion at the end of the paper.

Conformation and dynamics of polymer chains on dirty surfaces: A discrete-to-continuum approach

NASA Astrophysics Data System (ADS)

Foo, Grace M.; Pandey, R. B.

1998-07-01

A discrete-to-continuum (DC) simulation approach is introduced to study the statics and dynamics of polymer chains in two dimensions with quenched barriers, a dirty surface. In our DC hybrid approach, the large-scale relaxation of polymer chains on a discrete disordered lattice is followed by off-lattice simulation using a bead-spring chain model with a finitely extensible nonlinear elastic (FENE) potential for covalent bonds and Lennard-Jones (LJ) potential for nonbonded interactions. Segregation/folding of chains, which occurs at low temperatures (T=0.2, 1.0) with LJ interaction, becomes more difficult as the concentration of barriers increases, due to a screening effect of the barriers. In contrast to the chains' contraction at high temperature (i.e., T=5) and their collapse in athermal systems, chains are elongated on increasing the barrier concentration—a barrier-induced stretching. Variations of the root-mean-square (rms) displacements of the center of mass (Rcm) of the chains and their center node (Rcn) with time (t) show power-law behaviors (Rcm˜tν1, Rcn˜tν2) with nonuniversal exponents in the range ν1≃0.40-0.05 and ν2≃0.30-0.05, respectively, depending on temperature and barrier concentration. The radius of gyration (Rg) and the average bond length () expand on increasing the barrier concentration at low temperature and contract at high temperature, which is consistent with the variation of the width of the radial distribution function.

Convergence of the Bouguer-Beer law for radiation extinction in particulate media

NASA Astrophysics Data System (ADS)

Frankel, A.; Iaccarino, G.; Mani, A.

2016-10-01

Radiation transport in particulate media is a common physical phenomenon in natural and industrial processes. Developing predictive models of these processes requires a detailed model of the interaction between the radiation and the particles. Resolving the interaction between the radiation and the individual particles in a very large system is impractical, whereas continuum-based representations of the particle field lend themselves to efficient numerical techniques based on the solution of the radiative transfer equation. We investigate radiation transport through discrete and continuum-based representations of a particle field. Exact solutions for radiation extinction are developed using a Monte Carlo model in different particle distributions. The particle distributions are then projected onto a concentration field with varying grid sizes, and the Bouguer-Beer law is applied by marching across the grid. We show that the continuum-based solution approaches the Monte Carlo solution under grid refinement, but quickly diverges as the grid size approaches the particle diameter. This divergence is attributed to the homogenization error of an individual particle across a whole grid cell. We remark that the concentration energy spectrum of a point-particle field does not approach zero, and thus the concentration variance must also diverge under infinite grid refinement, meaning that no grid-converged solution of the radiation transport is possible.

Cohesive Laws and Progressive Damage Analysis of Composite Bonded Joints, a Combined Numerical/Experimental Approach

NASA Technical Reports Server (NTRS)

Girolamo, Donato; Davila, Carlos G.; Leone, Frank A.; Lin, Shih-Yung

2015-01-01

The results of an experimental/numerical campaign aimed to develop progressive damage analysis (PDA) tools for predicting the strength of a composite bonded joint under tensile loads are presented. The PDA is based on continuum damage mechanics (CDM) to account for intralaminar damage, and cohesive laws to account for interlaminar and adhesive damage. The adhesive response is characterized using standard fracture specimens and digital image correlation (DIC). The displacement fields measured by DIC are used to calculate the J-integrals, from which the associated cohesive laws of the structural adhesive can be derived. A finite element model of a sandwich conventional splice joint (CSJ) under tensile loads was developed. The simulations, in agreement with experimental tests, indicate that the model is capable of predicting the interactions of damage modes that lead to the failure of the joint.

Development of morphogen gradient: The role of dimension and discreteness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teimouri, Hamid; Kolomeisky, Anatoly B.

2014-02-28

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuummore » descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.« less

Pulse propagation in discrete excitatory networks of integrate-and-fire neurons.

PubMed

Badel, Laurent; Tonnelier, Arnaud

2004-07-01

We study the propagation of solitary waves in a discrete excitatory network of integrate-and-fire neurons. We show the existence and the stability of a fast wave and a family of slow waves. Fast waves are similar to those already described in continuum networks. Stable slow waves have not been previously reported in purely excitatory networks and their propagation is particular to the discrete nature of the network. The robustness of our results is studied in the presence of noise.

Phase Field Modeling of Directional Fracture in Anisotropic Polycrystals

DTIC Science & Technology

2015-02-01

include [35–37]. The phase field description of fracture should be con- trasted with continuum damage mechanics descriptions such as [38,39] that do not...ARL-RP-0518 ● FEBRUARY 2015 US Army Research Laboratory Phase Field Modeling of Directional Fracture in Anisotropic Polycrystals...0518 ● FEBRUARY 2015 US Army Research Laboratory Phase Field Modeling of Directional Fracture in Anisotropic Polycrystals by JD Clayton

Simulating spontaneous aseismic and seismic slip events on evolving faults

NASA Astrophysics Data System (ADS)

Herrendörfer, Robert; van Dinther, Ylona; Pranger, Casper; Gerya, Taras

2017-04-01

Plate motion along tectonic boundaries is accommodated by different slip modes: steady creep, seismic slip and slow slip transients. Due to mainly indirect observations and difficulties to scale results from laboratory experiments to nature, it remains enigmatic which fault conditions favour certain slip modes. Therefore, we are developing a numerical modelling approach that is capable of simulating different slip modes together with the long-term fault evolution in a large-scale tectonic setting. We extend the 2D, continuum mechanics-based, visco-elasto-plastic thermo-mechanical model that was designed to simulate slip transients in large-scale geodynamic simulations (van Dinther et al., JGR, 2013). We improve the numerical approach to accurately treat the non-linear problem of plasticity (see also EGU 2017 abstract by Pranger et al.). To resolve a wide slip rate spectrum on evolving faults, we develop an invariant reformulation of the conventional rate-and-state dependent friction (RSF) and adapt the time step (Lapusta et al., JGR, 2000). A crucial part of this development is a conceptual ductile fault zone model that relates slip rates along discrete planes to the effective macroscopic plastic strain rates in the continuum. We test our implementation first in a simple 2D setup with a single fault zone that has a predefined initial thickness. Results show that deformation localizes in case of steady creep and for very slow slip transients to a bell-shaped strain rate profile across the fault zone, which suggests that a length scale across the fault zone may exist. This continuum length scale would overcome the common mesh-dependency in plasticity simulations and question the conventional treatment of aseismic slip on infinitely thin fault zones. We test the introduction of a diffusion term (similar to the damage description in Lyakhovsky et al., JMPS, 2011) into the state evolution equation and its effect on (de-)localization during faster slip events. We compare the slip spectrum in our simulations to conventional RSF simulations (Liu and Rice, JGR, 2007). We further demonstrate the capability of simulating the evolution of a fault zone and simultaneous occurrence of slip transients. From small random initial distributions of the state variable in an otherwise homogeneous medium, deformation localizes and forms curved zones of reduced states. These spontaneously formed fault zones host slip transients, which in turn contribute to the growth of the fault zone.

Nonholonomic Hamiltonian Method for Meso-macroscale Simulations of Reacting Shocks

NASA Astrophysics Data System (ADS)

Fahrenthold, Eric; Lee, Sangyup

2015-06-01

The seamless integration of macroscale, mesoscale, and molecular scale models of reacting shock physics has been hindered by dramatic differences in the model formulation techniques normally used at different scales. In recent research the authors have developed the first unified discrete Hamiltonian approach to multiscale simulation of reacting shock physics. Unlike previous work, the formulation employs reacting themomechanical Hamiltonian formulations at all scales, including the continuum. Unlike previous work, the formulation employs a nonholonomic modeling approach to systematically couple the models developed at all scales. Example applications of the method show meso-macroscale shock to detonation simulations in nitromethane and RDX. Research supported by the Defense Threat Reduction Agency.

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.

PubMed

Brocklehurst, Paul; Ni, Haibo; Zhang, Henggui; Ye, Jianqiao

2017-01-01

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation.

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue

PubMed Central

Zhang, Henggui

2017-01-01

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation. PMID:28510575

Insensitivity to Flaws Leads to Damage Tolerance in Brittle Architected Meta-Materials

NASA Astrophysics Data System (ADS)

Montemayor, L. C.; Wong, W. H.; Zhang, Y.-W.; Greer, J. R.

2016-02-01

Cellular solids are instrumental in creating lightweight, strong, and damage-tolerant engineering materials. By extending feature size down to the nanoscale, we simultaneously exploit the architecture and material size effects to substantially enhance structural integrity of architected meta-materials. We discovered that hollow-tube alumina nanolattices with 3D kagome geometry that contained pre-fabricated flaws always failed at the same load as the pristine specimens when the ratio of notch length (a) to sample width (w) is no greater than 1/3, with no correlation between failure occurring at or away from the notch. Samples with (a/w) > 0.3, and notch length-to-unit cell size ratios of (a/l) > 5.2, failed at a lower peak loads because of the higher sample compliance when fewer unit cells span the intact region. Finite element simulations show that the failure is governed by purely tensile loading for (a/w) < 0.3 for the same (a/l); bending begins to play a significant role in failure as (a/w) increases. This experimental and computational work demonstrates that the discrete-continuum duality of architected structural meta-materials may give rise to their damage tolerance and insensitivity of failure to the presence of flaws even when made entirely of intrinsically brittle materials.

Characteristics of shear damage for 60Sn-40Pb solder material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang, H.E.; Chow, C.L.; Wei, Y.

This paper presents an investigation of the development of a continuum damage model capable of accurately analyzing shear damage in 60Sn-40Pb solder material. Based on the theory of damage mechanics, an internal state variable known as the damage variable is introduced to characterize material degradation caused by the change of material microstructures under load. A damage surface in stress space is proposed to quantify damage initiation and its successive expanding surfaces to represent damage hardening. With the aid of irreversible thermodynamics, the damage-coupled constitutive equations and the damage evolution equations are established. A failure criterion is proposed based on themore » accumulation of overall damage in the material. The damage model is implemented in a general purpose finite element program ABAQUS through its user-defined material subroutine UMAT. The program is applied to predict shear deformation in a notched specimen. The predicted failure mode and maximum load agree well with those measured experimentally. The effect of finite element meshing on the numerical results is also examined and discussed.« less

Discrete and continuum modeling of solvent effects in a twisted intramolecular charge transfer system: The 4-N,N-dimethylaminobenzonitrile (DMABN) molecule.

PubMed

Modesto-Costa, Lucas; Borges, Itamar

2018-08-05

The 4-N,N-dimethylaminobenzonitrile (DMABN) molecule is a prototypical system displaying twisted intramolecular (TICT) charge transfer effects. The ground and the first four electronic excited states (S 1 -S 4 ) in gas phase and upon solvation were studied. Charge transfer values as function of the torsion angle between the donor group (dimethylamine) and the acceptor moiety (benzonitrile) were explicitly computed. Potential energy curves were also obtained. The algebraic diagrammatic construction method at the second-order [ADC(2)] ab initio wave function was employed. Three solvents of increased polarities (benzene, DMSO and water) were investigated using discrete (average solvent electrostatic configuration - ASEC) and continuum (conductor-like screening model - COSMO) models. The results for the S 3 and S 4 excited states and the S 1 -S 4 charge transfer curves were not previously available in the literature. Electronic gas phase and solvent vertical spectra are in good agreement with previous theoretical and experimental results. In the twisted (90°) geometry the optical oscillator strengths have negligible values even for the S 2 bright state. Potential energy curves show two distinct pairs of curves intersecting at decreasing angles or not crossing in the more polar solvents. Charge transfer and electric dipole values allowed the rationalization of these results. The former effects are mostly independent of the solvent model and polarity. Although COSMO and ASEC solvent models mostly lead to similar results, there is an important difference: some crossings of the excitation energy curves appear only in the ASEC solvation model, which has important implications to the photochemistry of DMABN. Copyright © 2018 Elsevier B.V. All rights reserved.

Finite Element Aircraft Simulation of Turbulence

NASA Technical Reports Server (NTRS)

McFarland, R. E.

1997-01-01

A turbulence model has been developed for realtime aircraft simulation that accommodates stochastic turbulence and distributed discrete gusts as a function of the terrain. This model is applicable to conventional aircraft, V/STOL aircraft, and disc rotor model helicopter simulations. Vehicle angular activity in response to turbulence is computed from geometrical and temporal relationships rather than by using the conventional continuum approximations that assume uniform gust immersion and low frequency responses. By using techniques similar to those recently developed for blade-element rotor models, the angular-rate filters of conventional turbulence models are not required. The model produces rotational rates as well as air mass translational velocities in response to both stochastic and deterministic disturbances, where the discrete gusts and turbulence magnitudes may be correlated with significant terrain features or ship models. Assuming isotropy, a two-dimensional vertical turbulence field is created. A novel Gaussian interpolation technique is used to distribute vertical turbulence on the wing span or lateral rotor disc, and this distribution is used to compute roll responses. Air mass velocities are applied at significant centers of pressure in the computation of the aircraft's pitch and roll responses.

Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement.

PubMed

Doblaré, M; García, J M

2001-09-01

In this work, a new model for internal anisotropic bone remodelling is applied to the study of the remodelling behaviour of the proximal femur before and after total hip replacement (THR). This model considers bone remodelling under the scope of a general damage-repair theory following the principles of continuum damage mechanics. A "damage-repair" tensor is defined in terms of the apparent density and Cowin's "fabric tensor", respectively, associated with porosity and directionality of the trabeculae. The different elements of a thermodynamically consistent damage theory are established, including resorption and apposition criteria, evolution law and rate of remodelling. All of these elements were introduced and discussed in detail in a previous paper (García, J. M., Martinez, M. A., Doblaré, M., 2001. An anisotrophic internal-external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies. Computer Methods in Biomechanics and Biomedical Engineering 4(4), 355-378.), including the definition of the proposed mechanical stimulus and the qualitative properties of the model. In this paper, the fundamentals of the proposed model are briefly reviewed and the computational aspects of its implementation are discussed. This model is then applied to the analysis of the remodelling behaviour of the intact femur obtaining densities and mass principal values and directions very close to the experimental data. The second application involved the proximal femoral extremity after THR and the inclusion of an Exeter prosthesis. As a result of the simulation process, some well-known features previously detected in medical clinics were recovered, such as the stress yielding effect in the proximal part of the implant or the enlargement of the cortical layer at the distal part of the implant. With respect to the anisotropic properties, bone microstructure and local stiffness are known to tend to align with the stress principal directions. This experimental fact is mathematically proved in the framework of this remodelling model and clearly shown in the results corresponding to the intact femur. After THR the degree of anisotropy decreases tending, specifically in the proximal femur, to a more isotropic behaviour.

A discrete element model for damage and fracture of geomaterials under fatigue loading

NASA Astrophysics Data System (ADS)

Gao, Xiaofeng; Koval, Georg; Chazallon, Cyrille

2017-06-01

Failure processes in geomaterials (concrete, asphalt concrete, masonry, etc.) under fatigue loading (repeated moving loads, cycles of temperature, etc.) are responsible for most of the dysfunctions in pavements, brick structures, etc. In the beginning of the lifetime of a structure, the material presents only inner defects (micro cracks, voids, etc.). Due to the effect of the cyclic loading, these small defects tend to grow in size and quantity which damage the material, reducing its stiffness. With a relatively high number of cycles, these growing micro cracks become large cracks, which characterizes the fracture behavior. From a theoretical point of view, both mechanisms are treated differently. Fracture is usually described locally, with the propagation of cracks defined by the energy release rate at the crack tip; damage is usually associated to non-local approaches. In the present work, damage and fracture mechanics are combined in a local discrete element approach.

Moment Tensor Descriptions for Simulated Explosions of the Source Physics Experiment (SPE)

NASA Astrophysics Data System (ADS)

Yang, X.; Rougier, E.; Knight, E. E.; Patton, H. J.

2014-12-01

In this research we seek to understand damage mechanisms governing the behavior of geo-materials in the explosion source region, and the role they play in seismic-wave generation. Numerical modeling tools can be used to describe these mechanisms through the development and implementation of appropriate material models. Researchers at Los Alamos National Laboratory (LANL) have been working on a novel continuum-based-viscoplastic strain-rate-dependent fracture material model, AZ_Frac, in an effort to improve the description of these damage sources. AZ_Frac has the ability to describe continuum fracture processes, and at the same time, to handle pre-existing anisotropic material characteristics. The introduction of fractures within the material generates further anisotropic behavior that is also accounted for within the model. The material model has been calibrated to a granitic medium and has been applied in a number of modeling efforts under the SPE project. In our modeling, we use a 2D, axisymmetric layered earth model of the SPE site consisting of a weathered layer on top of a half-space. We couple the hydrodynamic simulation code with a seismic simulation code and propagate the signals to distances of up to 2 km. The signals are inverted for time-dependent moment tensors using a modified inversion scheme that accounts for multiple sources at different depths. The inversion scheme is evaluated for its resolving power to determine a centroid depth and a moment tensor description of the damage source. The capabilities of the inversion method to retrieve such information from waveforms recorded on three SPE tests conducted to date are also being assessed.

Pore-scale and continuum simulations of solute transport micromodel benchmark experiments

DOE PAGES

Oostrom, M.; Mehmani, Y.; Romero-Gomez, P.; ...

2014-06-18

Four sets of nonreactive solute transport experiments were conducted with micromodels. Three experiments with one variable, i.e., flow velocity, grain diameter, pore-aspect ratio, and flow-focusing heterogeneity were in each set. The data sets were offered to pore-scale modeling groups to test their numerical simulators. Each set consisted of two learning experiments, for which our results were made available, and one challenge experiment, for which only the experimental description and base input parameters were provided. The experimental results showed a nonlinear dependence of the transverse dispersion coefficient on the Peclet number, a negligible effect of the pore-aspect ratio on transverse mixing,more » and considerably enhanced mixing due to flow focusing. Five pore-scale models and one continuum-scale model were used to simulate the experiments. Of the pore-scale models, two used a pore-network (PN) method, two others are based on a lattice Boltzmann (LB) approach, and one used a computational fluid dynamics (CFD) technique. Furthermore, we used the learning experiments, by the PN models, to modify the standard perfect mixing approach in pore bodies into approaches to simulate the observed incomplete mixing. The LB and CFD models used the learning experiments to appropriately discretize the spatial grid representations. For the continuum modeling, the required dispersivity input values were estimated based on published nonlinear relations between transverse dispersion coefficients and Peclet number. Comparisons between experimental and numerical results for the four challenge experiments show that all pore-scale models were all able to satisfactorily simulate the experiments. The continuum model underestimated the required dispersivity values, resulting in reduced dispersion. The PN models were able to complete the simulations in a few minutes, whereas the direct models, which account for the micromodel geometry and underlying flow and transport physics, needed up to several days on supercomputers to resolve the more complex problems.« less

Assessing the failure of continuum formula for solid-solid drag force using discrete element method in large size ratios

NASA Astrophysics Data System (ADS)

Jalali, Payman; Hyppänen, Timo

2017-06-01

In loose or moderately-dense particle mixtures, the contact forces between particles due to successive collisions create average volumetric solid-solid drag force between different granular phases (of different particle sizes). The derivation of the mathematical formula for this drag force is based on the homogeneity of mixture within the calculational control volume. This assumption especially fails when the size ratio of particles grows to a large value of 10 or greater. The size-driven inhomogeneity is responsible to the deviation of intergranular force from the continuum formula. In this paper, we have implemented discrete element method (DEM) simulations to obtain the volumetric mean force exchanged between the granular phases with the size ratios greater than 10. First, the force is calculated directly from DEM averaged over a proper time window. Second, the continuum formula is applied to calculate the drag forces using the DEM quantities. We have shown the two volumetric forces are in good agreement as long as the homogeneity condition is maintained. However, the relative motion of larger particles in a cloud of finer particles imposes the inhomogeneous distribution of finer particles around the larger ones. We have presented correction factors to the volumetric force from continuum formula.

Time dependence of breakdown in a global fiber-bundle model with continuous damage.

PubMed

Moral, L; Moreno, Y; Gómez, J B; Pacheco, A F

2001-06-01

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.

THMC Modeling of EGS Reservoirs -- Continuum through Discontinuum Representations. Capturing Reservoir Stimulation, Evolution and Induced Seismicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elsworth, Derek; Izadi, Ghazal; Gan, Quan

This work has investigated the roles of effective stress induced by changes in fluid pressure, temperature and chemistry in contributing to the evolution of permeability and induced seismicity in geothermal reservoirs. This work has developed continuum models [1] to represent the progress or seismicity during both stimulation [2] and production [3]. These methods have been used to resolve anomalous observations of induced seismicity at the Newberry Volcano demonstration project [4] through the application of modeling and experimentation. Later work then focuses on the occurrence of late stage seismicity induced by thermal stresses [5] including the codifying of the timing andmore » severity of such responses [6]. Furthermore, mechanistic linkages between observed seismicity and the evolution of permeability have been developed using data from the Newberry project [7] and benchmarked against field injection experiments. Finally, discontinuum models [8] incorporating the roles of discrete fracture networks have been applied to represent stimulation and then thermal recovery for new arrangements of geothermal wells incorporating the development of flow manifolds [9] in order to increase thermal output and longevity in EGS systems.« less

Discrete is it enough? The revival of Piola-Hencky keynotes to analyze three-dimensional Elastica

NASA Astrophysics Data System (ADS)

Turco, Emilio

2018-04-01

Complex problems such as those concerning the mechanics of materials can be confronted only by considering numerical simulations. Analytical methods are useful to build guidelines or reference solutions but, for general cases of technical interest, they have to be solved numerically, especially in the case of large displacements and deformations. Probably continuous models arose for producing inspiring examples and stemmed from homogenization techniques. These techniques allowed for the solution of some paradigmatic examples but, in general, always require a discretization method for solving problems dictated by the applications. Therefore, and also by taking into account that computing powers are nowadays more largely available and cheap, the question arises: why not using directly a discrete model for 3D beams? In other words, it could be interesting to formulate a discrete model without using an intermediate continuum one, as this last, at the end, has to be discretized in any case. These simple considerations immediately evoke some very basic models developed many years ago when the computing powers were practically inexistent but the problem of finding simple solutions to beam deformation problem was already an emerging one. Actually, in recent years, the keynotes of Hencky and Piola attracted a renewed attention [see, one for all, the work (Turco et al. in Zeitschrift für Angewandte Mathematik und Physik 67(4):1-28, 2016)]: generalizing their results, in the present paper, a novel directly discrete three-dimensional beam model is presented and discussed, in the framework of geometrically nonlinear analysis. Using a stepwise algorithm based essentially on Newton's method to compute the extrapolations and on the Riks' arc-length method to perform the corrections, we could obtain some numerical simulations showing the computational effectiveness of presented model: Indeed, it presents a convenient balance between accuracy and computational cost.

Breakage mechanics—Part I: Theory

NASA Astrophysics Data System (ADS)

Einav, Itai

2007-06-01

Different measures have been suggested for quantifying the amount of fragmentation in randomly compacted crushable aggregates. A most effective and popular measure is to adopt variants of Hardin's [1985. Crushing of soil particles. J. Geotech. Eng. ASCE 111(10), 1177-1192] definition of relative breakage ' Br'. In this paper we further develop the concept of breakage to formulate a new continuum mechanics theory for crushable granular materials based on statistical and thermomechanical principles. Analogous to the damage internal variable ' D' which is used in continuum damage mechanics (CDM), here the breakage internal variable ' B' is adopted. This internal variable represents a particular form of the relative breakage ' Br' and measures the relative distance of the current grain size distribution from the initial and ultimate distributions. Similar to ' D', ' B' varies from zero to one and describes processes of micro-fractures and the growth of surface area. However, unlike damage that is most suitable to tensioned solid-like materials, the breakage is aimed towards compressed granular matter. While damage effectively represents the opening of micro-cavities and cracks, breakage represents comminution of particles. We term the new theory continuum breakage mechanics (CBM), reflecting the analogy with CDM. A focus is given to developing fundamental concepts and postulates, and identifying the physical meaning of the various variables. In this part of the paper we limit the study to describe an ideal dissipative process that includes breakage without plasticity. Plastic strains are essential, however, in representing aspects that relate to frictional dissipation, and this is covered in Part II of this paper together with model examples.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas

The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies in one dimension demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. In conclusion, additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

Numerical simulation of deformation and failure processes of a complex technical object under impact loading

NASA Astrophysics Data System (ADS)

Kraus, E. I.; Shabalin, I. I.; Shabalin, T. I.

2018-04-01

The main points of development of numerical tools for simulation of deformation and failure of complex technical objects under nonstationary conditions of extreme loading are presented. The possibility of extending the dynamic method for construction of difference grids to the 3D case is shown. A 3D realization of discrete-continuum approach to the deformation and failure of complex technical objects is carried out. The efficiency of the existing software package for 3D modelling is shown.

Directed polymers versus directed percolation

NASA Astrophysics Data System (ADS)

Halpin-Healy, Timothy

1998-10-01

Universality plays a central role within the rubric of modern statistical mechanics, wherein an insightful continuum formulation rises above irrelevant microscopic details, capturing essential scaling behaviors. Nevertheless, occasions do arise where the lattice or another discrete aspect can constitute a formidable legacy. Directed polymers in random media, along with its close sibling, directed percolation, provide an intriguing case in point. Indeed, the deep blood relation between these two models may have sabotaged past efforts to fully characterize the Kardar-Parisi-Zhang universality class, to which the directed polymer belongs.

Elastic scattering and total reaction cross section of {sup 6}He+{sup 120}Sn

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faria, P. N. de; Lichtenthaeler, R.; Pires, K. C. C.

The elastic scattering of {sup 6}He on {sup 120}Sn has been measured at four energies above the Coulomb barrier using the {sup 6}He beam produced at the RIBRAS (Radioactive Ion Beams in Brasil) facility. The elastic angular distributions have been analyzed with the optical model and three- and four-body continuum-discretized coupled-channels calculations. The total reaction cross sections have been derived and compared with other systems of similar masses.

Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates.

PubMed

Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

2017-09-01

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

NASA Astrophysics Data System (ADS)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

The Thick Level-Set model for dynamic fragmentation

DOE PAGES

Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas

2017-01-04

The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies in one dimension demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. In conclusion, additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

Two-dimensional strain gradient damage modeling: a variational approach

NASA Astrophysics Data System (ADS)

Placidi, Luca; Misra, Anil; Barchiesi, Emilio

2018-06-01

In this paper, we formulate a linear elastic second gradient isotropic two-dimensional continuum model accounting for irreversible damage. The failure is defined as the condition in which the damage parameter reaches 1, at least in one point of the domain. The quasi-static approximation is done, i.e., the kinetic energy is assumed to be negligible. In order to deal with dissipation, a damage dissipation term is considered in the deformation energy functional. The key goal of this paper is to apply a non-standard variational procedure to exploit the damage irreversibility argument. As a result, we derive not only the equilibrium equations but, notably, also the Karush-Kuhn-Tucker conditions. Finally, numerical simulations for exemplary problems are discussed as some constitutive parameters are varying, with the inclusion of a mesh-independence evidence. Element-free Galerkin method and moving least square shape functions have been employed.

Effects of cell geometry on reversible vesicular transport

NASA Astrophysics Data System (ADS)

Karamched, Bhargav R.; Bressloff, Paul C.

2017-02-01

A major question in cell biology concerns the biophysical mechanism underlying delivery of newly synthesized macromolecules to specific targets within a cell. A recent modeling paper investigated this phenomenon in the context of vesicular delivery to en passant synapses in neurons (Bressloff and Levien 2015 Phys. Rev. Lett.). It was shown how reversibility in vesicular delivery to synapses could play a crucial role in achieving uniformity in the distribution of resources throughout an axon, which is consistent with experimental observations in C. elegans and Drosophila. In this work we generalize the previous model by investigating steady-state vesicular distributions on a Cayley tree, a disk, and a sphere. We show that for irreversible transport on a tree, branching increases the rate of decay of the steady-state distribution of vesicles. On the other hand, the steady-state profiles for reversible transport are similar to the 1D case. In the case of higher-dimensional geometries, we consider two distinct types of radially-symmetric microtubular network: (i) a continuum and (ii) a discrete set. In the continuum case, we model the motor-cargo dynamics using a phenomenologically-based advection-diffusion equation in polar (2D) and spherical (3D) coordinates. On the other-hand, in the discrete case, we derive the population model from a stochastic model of a single motor switching between ballistic motion and diffusion. For all of the geometries we find that reversibility in vesicular delivery to target sites allows for a more uniform distribution of vesicles, provided that cargo-carrying motors are not significantly slowed by their cargo. In each case we characterize the loss of uniformity as a function of the dispersion in velocities.

A gas kinetic scheme for hybrid simulation of partially rarefied flows

NASA Astrophysics Data System (ADS)

Colonia, S.; Steijl, R.; Barakos, G.

2017-06-01

Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work, analytically defined gas-kinetic schemes based on the Shakhov and Rykov models for monoatomic and diatomic gas flows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for high-speed rare¦ed gas flows it is necessary to take into account the nonequilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models including rotational relaxation process is a mandatory first step towards realistic simulations. Compared to previous works of Xu and coworkers, the presented scheme is de¦ned directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum flows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rarefied flows.

Development and Application of Methods for Estimating Operating Characteristics of Discrete Test Item Responses without Assuming any Mathematical Form.

ERIC Educational Resources Information Center

Samejima, Fumiko

In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent…

The fundamental theorem of asset pricing under default and collateral in finite discrete time

NASA Astrophysics Data System (ADS)

Alvarez-Samaniego, Borys; Orrillo, Jaime

2006-08-01

We consider a financial market where time and uncertainty are modeled by a finite event-tree. The event-tree has a length of N, a unique initial node at the initial date, and a continuum of branches at each node of the tree. Prices and returns of J assets are modeled, respectively, by a R2JxR2J-valued stochastic process . In this framework we prove a version of the Fundamental Theorem of Asset Pricing which applies to defaultable securities backed by exogenous collateral suffering a contingent linear depreciation.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less

Determining decision thresholds and evaluating indicators when conservation status is measured as a continuum.

PubMed

Connors, B M; Cooper, A B

2014-12-01

Categorization of the status of populations, species, and ecosystems underpins most conservation activities. Status is often based on how a system's current indicator value (e.g., change in abundance) relates to some threshold of conservation concern. Receiver operating characteristic (ROC) curves can be used to quantify the statistical reliability of indicators of conservation status and evaluate trade-offs between correct (true positive) and incorrect (false positive) classifications across a range of decision thresholds. However, ROC curves assume a discrete, binary relationship between an indicator and the conservation status it is meant to track, which is a simplification of the more realistic continuum of conservation status, and may limit the applicability of ROC curves in conservation science. We describe a modified ROC curve that treats conservation status as a continuum rather than a discrete state. We explored the influence of this continuum and typical sources of variation in abundance that can lead to classification errors (i.e., random variation and measurement error) on the true and false positive rates corresponding to varying decision thresholds and the reliability of change in abundance as an indicator of conservation status, respectively. We applied our modified ROC approach to an indicator of endangerment in Pacific salmon (Oncorhynchus nerka) (i.e., percent decline in geometric mean abundance) and an indicator of marine ecosystem structure and function (i.e., detritivore biomass). Failure to treat conservation status as a continuum when choosing thresholds for indicators resulted in the misidentification of trade-offs between true and false positive rates and the overestimation of an indicator's reliability. We argue for treating conservation status as a continuum when ROC curves are used to evaluate decision thresholds in indicators for the assessment of conservation status. © 2014 Society for Conservation Biology.

Studying the flow dynamics of a karst aquifer system with an equivalent porous medium model.

PubMed

Abusaada, Muath; Sauter, Martin

2013-01-01

The modeling of groundwater flow in karst aquifers is a challenge due to the extreme heterogeneity of its hydraulic parameters and the duality in their discharge behavior, that is, rapid response of highly conductive karst conduits and delayed drainage of the low-permeability fractured matrix after recharge events. There are a number of different modeling approaches for the simulation of the karst groundwater dynamics, applicable to different aquifer as well as modeling problem types, ranging from continuum models to double continuum models to discrete and hybrid models. This study presents the application of an equivalent porous model approach (EPM, single continuum model) to construct a steady-state numerical flow model for an important karst aquifer, that is, the Western Mountain Aquifer Basin (WMAB), shared by Israel and the West-Bank, using MODFLOW2000. The WMAB was used as a catchment since it is a well-constrained catchment with well-defined recharge and discharge components and therefore allows a control on the modeling approach, a very rare opportunity for karst aquifer modeling. The model demonstrates the applicability of equivalent porous medium models for the simulation of karst systems, despite their large contrast in hydraulic conductivities. As long as the simulated saturated volume is large enough to average out the local influence of karst conduits and as long as transport velocities are not an issue, EPM models excellently simulate the observed head distribution. The model serves as a starting basis that will be used as a reference for developing a long-term dynamic model for the WMAB, starting from the pre-development period (i.e., 1940s) up to date. © 2012, The Author(s). GroundWater © 2012, National Ground Water Association.

Mathematical model of macrophage-facilitated breast cancer cells invasion.

PubMed

Knútsdóttir, Hildur; Pálsson, Eirikur; Edelstein-Keshet, Leah

2014-09-21

Mortality from breast cancer stems from its tendency to invade into surrounding tissues and organs. Experiments have shown that this metastatic process is facilitated by macrophages in a short-ranged chemical signalling loop. Macrophages secrete epidermal growth factor, EGF, and respond to the colony stimulating factor 1, CSF-1. Tumor cells secrete CSF-1 and respond to EGF. In this way, the cells coordinate aggregation and cooperative migration. Here we investigate this process in a model for in vitro interactions using two distinct but related mathematical approaches. In the first, we analyze and simulate a set of partial differential equations to determine conditions for aggregation. In the second, we use a cell-based discrete 3D simulation to follow the fates and motion of individual cells during aggregation. Linear stability analysis of the PDE model reveals that decreasing the chemical secretion, chemotaxis coefficients or density of cells or increasing the chemical degradation in the model could eliminate the spontaneous aggregation of cells. Simulations with the discrete model show that the ratio between tumor cells and macrophages in aggregates increases when the EGF secretion parameter is increased. The results also show how CSF-1/CSF-1R autocrine signalling in tumor cells affects the ratio between the two cell types. Comparing the continuum results with simulations of a discrete cell-based model, we find good qualitative agreement. Copyright © 2014 Elsevier Ltd. All rights reserved.

A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system

NASA Astrophysics Data System (ADS)

Li, Chun-Xia; Lafortune, Stéphane; Shen, Shou-Feng

2016-05-01

We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation, respectively. Among these equations, we are mainly concerned with the semi-discrete bilinear Kadomtsev-Petviashvili (KP) equation which is seldomly studied in literature. We present both of its Casorati and Grammian determinant solutions. Through the Pfaffianization procedure proposed by Hirota and Ohta, we are able to derive the coupled integrable system for the semi-discrete KP equation.

Mimetic discretization of the Abelian Chern-Simons theory and link invariants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

Mimetic discretization of the Abelian Chern-Simons theory and link invariants

NASA Astrophysics Data System (ADS)

Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

2013-12-01

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

Wave generation by fracture initiation and propagation in geomaterials with internal rotations

NASA Astrophysics Data System (ADS)

Esin, Maxim; Pasternak, Elena; Dyskin, Arcady; Xu, Yuan

2016-04-01

Crack or fracture initiation and propagation in geomaterials are sources of waves and is important in both stability and fracture (e.g. hydraulic fracture) monitoring. Many geomaterials consist of particles or other constituents capable of rotating with respect to each other, either due to the absence of the binder phase (fragmented materials) or due to extensive damage of the cement between the constituents inflicted by previous loading. In investigating the wave generated in fracturing it is important to distinguish between the cases when the fracture is instantaneously initiated to its full length or propagates from a smaller initial crack. We show by direct physical experiments and discrete element modelling of 2D arrangements of unbonded disks that under compressive load fractures are initiated instantaneously as a result of the material instability and localisation. Such fractures generate waves as a single impulse impact. When the fractures propagate, they produce a sequence of impulses associated with the propagation steps. This manifests itself as acoustic (microseismic) emission whose temporal pattern contains the information of the fracture geometry, such as fractal dimension of the fracture. The description of this process requires formulating criteria of crack growth capable of taking into account the internal rotations. We developed an analytical solution based on the Cosserat continuum where each point of body has three translational and three rotational degrees of freedom. When the Cosserat characteristic lengths are comparable with the grain sizes, the simplified equations of small-scale Cosserat continuum can be used. We established that the order of singularity of the main asymptotic term for moment stress is higher than the order of singularity for conventional stress. Therefore, the mutual rotation of particles and related bending and/or twisting of the bonds between the particles represent an unconventional mechanism of crack propagation.

Frequency distributions from birth, death, and creation processes.

PubMed

Bartley, David L; Ogden, Trevor; Song, Ruiguang

2002-01-01

The time-dependent frequency distribution of groups of individuals versus group size was investigated within a continuum approximation, assuming a simplified individual growth, death and creation model. The analogy of the system to a physical fluid exhibiting both convection and diffusion was exploited in obtaining various solutions to the distribution equation. A general solution was approximated through the application of a Green's function. More specific exact solutions were also found to be useful. The solutions were continually checked against the continuum approximation through extensive simulation of the discrete system. Over limited ranges of group size, the frequency distributions were shown to closely exhibit a power-law dependence on group size, as found in many realizations of this type of system, ranging from colonies of mutated bacteria to the distribution of surnames in a given population. As an example, the modeled distributions were successfully fit to the distribution of surnames in several countries by adjusting the parameters specifying growth, death and creation rates.

Frontiers of Theoretical Research on Shape Memory Alloys: A General Overview

NASA Astrophysics Data System (ADS)

Chowdhury, Piyas

2018-03-01

In this concise review, general aspects of modeling shape memory alloys (SMAs) are recounted. Different approaches are discussed under four general categories, namely, (a) macro-phenomenological, (b) micromechanical, (c) molecular dynamics, and (d) first principles models. Macro-phenomenological theories, stemming from empirical formulations depicting continuum elastic, plastic, and phase transformation, are primarily of engineering interest, whereby the performance of SMA-made components is investigated. Micromechanical endeavors are generally geared towards understanding microstructural phenomena within continuum mechanics such as the accommodation of straining due to phase change as well as role of precipitates. By contrast, molecular dynamics, being a more recently emerging computational technique, concerns attributes of discrete lattice structures, and thus captures SMA deformation mechanism by means of empirically reconstructing interatomic bonding forces. Finally, ab initio theories utilize quantum mechanical framework to peek into atomistic foundation of deformation, and can pave the way for studying the role of solid-sate effects. With specific examples, this paper provides concise descriptions of each category along with their relative merits and emphases.

Robust Rocket Engine Concept

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.

1995-01-01

The potential for a revolutionary step in the durability of reusable rocket engines is made possible by the combination of several emerging technologies. The recent creation and analytical demonstration of life extending (or damage mitigating) control technology enables rapid rocket engine transients with minimum fatigue and creep damage. This technology has been further enhanced by the formulation of very simple but conservative continuum damage models. These new ideas when combined with recent advances in multidisciplinary optimization provide the potential for a large (revolutionary) step in reusable rocket engine durability. This concept has been named the robust rocket engine concept (RREC) and is the basic contribution of this paper. The concept also includes consideration of design innovations to minimize critical point damage.

A Numerical and Experimental Study of Damage Growth in a Composite Laminate

NASA Technical Reports Server (NTRS)

McElroy, Mark; Ratcliffe, James; Czabaj, Michael; Wang, John; Yuan, Fuh-Gwo

2014-01-01

The present study has three goals: (1) perform an experiment where a simple laminate damage process can be characterized in high detail; (2) evaluate the performance of existing commercially available laminate damage simulation tools by modeling the experiment; (3) observe and understand the underlying physics of damage in a composite honeycomb sandwich structure subjected to low-velocity impact. A quasi-static indentation experiment has been devised to provide detailed information about a simple mixed-mode damage growth process. The test specimens consist of an aluminum honeycomb core with a cross-ply laminate facesheet supported on a stiff uniform surface. When the sample is subjected to an indentation load, the honeycomb core provides support to the facesheet resulting in a gradual and stable damage growth process in the skin. This enables real time observation as a matrix crack forms, propagates through a ply, and then causes a delamination. Finite element analyses were conducted in ABAQUS/Explicit(TradeMark) 6.13 that used continuum and cohesive modeling techniques to simulate facesheet damage and a geometric and material nonlinear model to simulate core crushing. The high fidelity of the experimental data allows a detailed investigation and discussion of the accuracy of each numerical modeling approach.

Modeling and Characterization of Dynamic Failure of Soda-lime Glass Under High Speed Impact

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Wenning N.; Sun, Xin; Chen, Weinong W.

2012-05-27

In this paper, the impact-induced dynamic failure of a soda-lime glass block is studied using an integrated experimental/analytical approach. The Split Hopkinson Pressure Bar (SHPB) technique is used to conduct dynamic failure test of soda-lime glass first. The damage growth patterns and stress histories are reported for various glass specimen designs. Making use of a continuum damage mechanics (CDM)-based constitutive model, the initial failure and subsequent stiffness reduction of glass are simulated and investigated. Explicit finite element analyses are used to simulate the glass specimen impact event. A maximum shear stress-based damage evolution law is used in describing the glassmore » damage process under combined compression/shear loading. The impact test results are used to quantify the critical shear stress for the soda-lime glass under examination.« less

Failure prediction during backward flow forming of Ti6Al4V alloy

NASA Astrophysics Data System (ADS)

Singh, Abhishek Kumar; Narasimhan, K.; Singh, Ramesh

2018-05-01

The Flow forming process is a tube spinning process where the thickness of a tube is reduced with the help of spinning roller/s by keeping the internal diameter unchanged. A 3-D Finite element model for the flow-formability test has been developed by using Abaqus/explicit software. A coupled damage criterion based on continuum damage mechanics (CDM) has been studied in this research. The damage model is introduced by using FORTRAN based VUMAT subroutine which is developed through a stress integration algorithm. Further, the effect of reduction angle, friction coefficient, and coolant heat transfer coefficient on fracture has been studied. The results show that the formability improves with increase in reduction angle. Both, equivalent plastic strain and damage variable increases from inner to outer surface of flow formed tube.

Discrete-to-continuum simulation approach to polymer chain systems: Subdiffusion, segregation, and chain folding

NASA Astrophysics Data System (ADS)

Foo, Grace M.; Pandey, R. B.

1998-05-01

A discrete-to-continuum approach is introduced to study the static and dynamic properties of polymer chain systems with a bead-spring chain model in two dimensions. A finitely extensible nonlinear elastic potential is used for the bond between the consecutive beads with the Lennard-Jones (LJ) potential with smaller (Rc=21/6σ=0.95) and larger (Rc=2.5σ=2.1) values of the upper cutoff for the nonbonding interaction among the neighboring beads. We find that chains segregate at temperature T=1.0 with Rc=2.1 and remain desegregated with Rc=0.95. At low temperature (T=0.2), chains become folded, in a ribbonlike conformation, unlike random and self-avoiding walk conformations at T=1.0. The power-law dependence of the rms displacements of the center of mass (Rc.m.) of the chains and their center node (Rcn) with time are nonuniversal, with the range of exponents ν1~=0.45-0.25 and ν2~=0.30-0.10, respectively. Both radius of gyration (Rg) and average bond length () decrease on increasing the range of interaction (Rc), consistent with the extended state in good solvent to collapsed state in poor solvent description of the polymer chains. Analysis of the radial distribution function supports these observations.

Homoclinic snaking in the discrete Swift-Hohenberg equation

NASA Astrophysics Data System (ADS)

Kusdiantara, R.; Susanto, H.

2017-12-01

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

A Coupled/Uncoupled Computational Scheme for Deformation and Fatigue Damage Analysis of Unidirectional Metal-Matrix Composites

NASA Technical Reports Server (NTRS)

Wilt, Thomas E.; Arnold, Steven M.; Saleeb, Atef F.

1997-01-01

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum-based fatigue damage model for unidirectional metal-matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress that fully couples the fatigue damage calculations with the finite element deformation solution. Two applications using the fatigue damage algorithm are presented. First, an axisymmetric stress analysis of a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. Second, a micromechanics analysis of a fiber/matrix unit cell using both the finite element method and the generalized method of cells (GMC). Results are presented in the form of S-N curves and damage distribution plots.

A methodology to predict damage initiation, damage growth and residual strength in titanium matrix composites

NASA Technical Reports Server (NTRS)

Bakuckas, J. G., Jr.; Johnson, W. S.

1994-01-01

In this research, a methodology to predict damage initiation, damage growth, fatigue life, and residual strength in titanium matrix composites (TMC) is outlined. Emphasis was placed on micromechanics-based engineering approaches. Damage initiation was predicted using a local effective strain approach. A finite element analysis verified the prevailing assumptions made in the formulation of this model. Damage growth, namely, fiber-bridged matrix crack growth, was evaluated using a fiber bridging (FB) model which accounts for thermal residual stresses. This model combines continuum fracture mechanics and micromechanics analyses yielding stress-intensity factor solutions for fiber-bridged matrix cracks. It is assumed in the FB model that fibers in the wake of the matrix crack are idealized as a closure pressure, and an unknown constant frictional shear stress is assumed to act along the debond length of the bridging fibers. This frictional shear stress was used as a curve fitting parameter to the available experimental data. Fatigue life and post-fatigue residual strength were predicted based on the axial stress in the first intact 0 degree fiber calculated using the FB model and a three-dimensional finite element analysis.

A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature.

PubMed

McDougall, S R; Watson, M G; Devlin, A H; Mitchell, C A; Chaplain, M A J

2012-10-01

Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. However, there have been relatively few attempts to model angiogenesis associated with normal development, despite the availability of animal models with experimentally accessible and highly ordered vascular topologies: for example, growth and development of the vascular plexus layers in the murine retina. The current study aims to address this issue through the development of a hybrid discrete-continuum mathematical model of the developing retinal vasculature in neonatal mice that is closely coupled with an ongoing experimental programme. The model of the functional vasculature is informed by a range of morphological and molecular data obtained over a period of several days, from 6 days prior to birth to approximately 8 days after birth. The spatio-temporal formation of the superficial retinal vascular plexus (RVP) in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocytes migrate from the optic nerve over the surface of the inner retina in response to a chemotactic gradient of PDGF-A, formed at an earlier stage by migrating retinal ganglion cells (RGCs). Astrocytes express a variety of chemotactic and haptotactic proteins, including VEGF and fibronectin (respectively), which subsequently induce endothelial cell sprouting and modulate growth of the RVP. The developing RVP is not an inert structure; however, the vascular bed adapts and remodels in response to a wide variety of metabolic and biomolecular stimuli. The main focus of this investigation is to understand how these interacting cellular, molecular, and metabolic cues regulate RVP growth and formation. In an earlier one-dimensional continuum model of astrocyte and endothelial migration, we showed that the measured frontal velocities of the two cell types could be accurately reproduced by means of a system of five coupled partial differential equations (Aubert et al. in Bull. Math. Biol. 73:2430-2451, 2011). However, this approach was unable to generate spatial information and structural detail for the entire retinal surface. Building upon this earlier work, a more realistic two-dimensional hybrid PDE-discrete model is derived here that tracks the migration of individual astrocytes and endothelial tip cells towards the outer retinal boundary. Blood perfusion is included throughout plexus development and the emergent retinal architectures adapt and remodel in response to various biological factors. The resulting in silico RVP structures are compared with whole-mounted retinal vasculatures at various stages of development, and the agreement is found to be excellent. Having successfully benchmarked the model against wild-type data, the effect of transgenic over-expression of various genes is predicted, based on the ocular-specific expression of VEGF-A during murine development. These results can be used to help inform future experimental investigations of signalling pathways in ocular conditions characterised by aberrant angiogenesis.

Computation of the effective mechanical response of biological networks accounting for large configuration changes.

PubMed

El Nady, K; Ganghoffer, J F

2016-05-01

The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with FE simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes. Copyright © 2015 Elsevier Ltd. All rights reserved.

Student Engagements Help Educate and Boost Workforce Development -

Science.gov Websites

Continuum Magazine | NREL Two young men assemble the model of a house. Two students assemble the future by having students learn about building renewable energy technologies, as well as offering estimated $65 billion in damages. The disaster also inspired students from New Jersey's Stevens Institute of

DEM Particle Fracture Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Boning; Herbold, Eric B.; Homel, Michael A.

2015-12-01

An adaptive particle fracture model in poly-ellipsoidal Discrete Element Method is developed. The poly-ellipsoidal particle will break into several sub-poly-ellipsoids by Hoek-Brown fracture criterion based on continuum stress and the maximum tensile stress in contacts. Also Weibull theory is introduced to consider the statistics and size effects on particle strength. Finally, high strain-rate split Hopkinson pressure bar experiment of silica sand is simulated using this newly developed model. Comparisons with experiments show that our particle fracture model can capture the mechanical behavior of this experiment very well, both in stress-strain response and particle size redistribution. The effects of density andmore » packings o the samples are also studied in numerical examples.« less

9Be+120Sn scattering at near-barrier energies within a four-body model

NASA Astrophysics Data System (ADS)

Arazi, A.; Casal, J.; Rodríguez-Gallardo, M.; Arias, J. M.; Lichtenthäler Filho, R.; Abriola, D.; Capurro, O. A.; Cardona, M. A.; Carnelli, P. F. F.; de Barbará, E.; Fernández Niello, J.; Figueira, J. M.; Fimiani, L.; Hojman, D.; Martí, G. V.; Martínez Heimman, D.; Pacheco, A. J.

2018-04-01

Cross sections for elastic and inelastic scattering of the weakly bound 9Be nucleus on a 120Sn target have been measured at seven bombarding energies around and above the Coulomb barrier. The elastic angular distributions are analyzed with a four-body continuum-discretized coupled-channels (CDCC) calculation, which considers 9Be as a three-body projectile (α +α +n ). An optical model analysis using the São Paulo potential is also shown for comparison. The CDCC analysis shows that the coupling to the continuum part of the spectrum is important for the agreement with experimental data even at energies around the Coulomb barrier, suggesting that breakup is an important process at low energies. At the highest incident energies, two inelastic peaks are observed at 1.19(5) and 2.41(5) MeV. Coupled-channels (CC) calculations using a rotational model confirm that the first inelastic peak corresponds to the excitation of the 21+ state in 120Sn, while the second one likely corresponds to the excitation of the 31- state.

Singular unlocking transition in the Winfree model of coupled oscillators.

PubMed

Quinn, D Dane; Rand, Richard H; Strogatz, Steven H

2007-03-01

The Winfree model consists of a population of globally coupled phase oscillators with randomly distributed natural frequencies. As the coupling strength and the spread of natural frequencies are varied, the various stable states of the model can undergo bifurcations, nearly all of which have been characterized previously. The one exception is the unlocking transition, in which the frequency-locked state disappears abruptly as the spread of natural frequencies exceeds a critical width. Viewed as a function of the coupling strength, this critical width defines a bifurcation curve in parameter space. For the special case where the frequency distribution is uniform, earlier work had uncovered a puzzling singularity in this bifurcation curve. Here we seek to understand what causes the singularity. Using the Poincaré-Lindstedt method of perturbation theory, we analyze the locked state and its associated unlocking transition, first for an arbitrary distribution of natural frequencies, and then for discrete systems of N oscillators. We confirm that the bifurcation curve becomes singular for a continuum uniform distribution, yet find that it remains well behaved for any finite N , suggesting that the continuum limit is responsible for the singularity.

Nonlinear Fano interferences in open quantum systems: An exactly solvable model

NASA Astrophysics Data System (ADS)

Finkelstein-Shapiro, Daniel; Calatayud, Monica; Atabek, Osman; Mujica, Vladimiro; Keller, Arne

2016-06-01

We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 ×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

Development of a Continuum Damage Mechanics Material Model of a Graphite-Kevlar(Registered Trademark) Hybrid Fabric for Simulating the Impact Response of Energy Absorbing Kevlar(Registered Trademark) Hybrid Fabric for Simulating the Impact Response of Energy Absorbing

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Littell, Justin D.

2017-01-01

This paper describes the development of input properties for a continuum damage mechanics based material model, Mat 58, within LS-DYNA(Registered Trademark) to simulate the response of a graphite-Kevlar(Registered Trademark) hybrid plain weave fabric. A limited set of material characterization tests were performed on the hybrid graphite-Kevlar(Registered Trademark) fabric. Simple finite element models were executed in LS-DYNA(Registered Trademark) to simulate the material characterization tests and to verify the Mat 58 material model. Once verified, the Mat 58 model was used in finite element models of two composite energy absorbers: a conical-shaped design, designated the "conusoid," fabricated of four layers of hybrid graphite-Kevlar(Registered Trademark) fabric; and, a sinusoidal-shaped foam sandwich design, designated the "sinusoid," fabricated of the same hybrid fabric face sheets with a foam core. Dynamic crush tests were performed on components of the two energy absorbers, which were designed to limit average vertical accelerations to 25- to 40-g, to minimize peak crush loads, and to generate relatively long crush stroke values under dynamic loading conditions. Finite element models of the two energy absorbers utilized the Mat 58 model that had been verified through material characterization testing. Excellent predictions of the dynamic crushing response were obtained.

Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses.

PubMed

Guerrier, Claire; Holcman, David

2016-10-18

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.

The Finite Strain Johnson Cook Plasticity and Damage Constitutive Model in ALEGRA.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez, Jason James

A finite strain formulation of the Johnson Cook plasticity and damage model and it's numerical implementation into the ALEGRA code is presented. The goal of this work is to improve the predictive material failure capability of the Johnson Cook model. The new implementation consists of a coupling of damage and the stored elastic energy as well as the minimum failure strain criteria for spall included in the original model development. This effort establishes the necessary foundation for a thermodynamically consistent and complete continuum solid material model, for which all intensive properties derive from a common energy. The motivation for developingmore » such a model is to improve upon ALEGRA's present combined model framework. Several applications of the new Johnson Cook implementation are presented. Deformation driven loading paths demonstrate the basic features of the new model formulation. Use of the model produces good comparisons with experimental Taylor impact data. Localized deformation leading to fragmentation is produced for expanding ring and exploding cylinder applications.« less

The Micromechanics of the Moving Contact Line

NASA Technical Reports Server (NTRS)

Han, Minsub; Lichter, Seth; Lin, Chih-Yu; Perng, Yeong-Yan

1996-01-01

The proposed research is divided into three components concerned with molecular structure, molecular orientation, and continuum averages of discrete systems. In the experimental program, we propose exploring how changes in interfacial molecular structure generate contact line motion. Rather than rely on the electrostatic and electrokinetic fields arising from the molecules themselves, we augment their interactions by an imposed field at the solid/liquid interface. By controling the field, we can manipulate the molecular structure at the solid/liquid interface. In response to controlled changes in molecular structure, we observe the resultant contact line motion. In the analytical portion of the proposed research we seek to formulate a system of equations governing fluid motion which accounts for the orientation of fluid molecules. In preliminary work, we have focused on describing how molecular orientation affects the forces generated at the moving contact line. Ideally, as assumed above, the discrete behavior of molecules can be averaged into a continuum theory. In the numerical portion of the proposed research, we inquire whether the contact line region is, in fact, large enough to possess a well-defined average. Additionally, we ask what types of behavior distinguish discrete systems from continuum systems. Might the smallness of the contact line region, in itself, lead to behavior different from that in the bulk? Taken together, our proposed research seeks to identify and accurately account for some of the molecular dynamics of the moving contact line, and attempts to formulate a description from which one can compute the forces at the moving contact line.

A continuum theory of grain size evolution and damage

NASA Astrophysics Data System (ADS)

Ricard, Y.; Bercovici, D.

2009-01-01

Lithospheric shear localization, as occurs in the formation of tectonic plate boundaries, is often associated with diminished grain size (e.g., mylonites). Grain size reduction is typically attributed to dynamic recrystallization; however, theoretical models of shear localization arising from this hypothesis are problematic because (1) they require the simultaneous action of two creep mechanisms (diffusion and dislocation creep) that occur in different deformation regimes (i.e., in grain size stress space) and (2) the grain growth ("healing") laws employed by these models are derived from normal grain growth or coarsening theory, which are valid in the absence of deformation, although the shear localization setting itself requires deformation. Here we present a new first principles grained-continuum theory, which accounts for both coarsening and damage-induced grain size reduction in a monomineralic assemblage undergoing irrecoverable deformation. Damage per se is the generic process for generation of microcracks, defects, dislocations (including recrystallization), subgrains, nuclei, and cataclastic breakdown of grains. The theory contains coupled macroscopic continuum mechanical and grain-scale statistical components. The continuum level of the theory considers standard mass, momentum, and energy conservation, as well as entropy production, on a statistically averaged grained continuum. The grain-scale element of the theory describes both the evolution of the grain size distribution and mechanisms for both continuous grain growth and discontinuous grain fracture and coalescence. The continuous and discontinuous processes of grain size variation are prescribed by nonequilibrium thermodynamics (in particular, the treatment of entropy production provides the phenomenological laws for grain growth and reduction); grain size evolution thus incorporates the free energy differences between grains, including both grain boundary surface energy (which controls coarsening) and the contribution of deformational work to these free energies (which controls damage). In the absence of deformation, only two mechanisms that increase the average grain size are allowed by the second law of thermodynamics. One mechanism, involving continuous diffusive mass transport from small to large grains, captures the essential components of normal grain growth theories of Lifshitz-Slyosov and Hillert. The second mechanism involves the aggregation of grains and is described using a Smoluchovski formalism. With the inclusion of deformational work and damage, the theory predicts two mechanisms for which the thermodynamic requirement of entropy positivity always forces large grains to shrink and small ones to grow. The first such damage-driven mechanism involving continuous mass transfer from large to small grains tends to homogenize the distribution of grain size toward its initial mean grain size. The second damage mechanism favors the creation of small grains by discontinuous division of larger grains and reduces the mean grain size with time. When considered separately, most of these mechanisms allow for self-similar grain size distributions whose scales (i.e., statistical moments such as the mean, variance, and skewness) can all be described by a single grain scale, such as the mean or maximum. However, the combination of mechanisms, e.g., one that captures the competition between continuous coarsening and mean grain size reduction by breakage, does not generally permit a self-similar solution for the grain size distribution, which contradicts the classic assumption that grain growth laws allowing for both coarsening and recrystallization can be treated with a single grain scale such as the mean size.

Critical flavor number of the Thirring model in three dimensions

NASA Astrophysics Data System (ADS)

Wellegehausen, Björn H.; Schmidt, Daniel; Wipf, Andreas

2017-11-01

The Thirring model is a four-fermion theory with a current-current interaction and U (2 N ) chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition, it serves as a toy model to study chiral symmetry breaking. In the limit of flavor number N →1 /2 it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalization group methods, and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavors, but no symmetry breaking for large N . But there is no consensus on the critical flavor number Ncr above which there is no phase transition anymore and on further details of the critical behavior. Values of N found in the literature vary between 2 and 7. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behavior for even and odd flavor numbers is very different: for even flavor numbers, chiral and parity symmetry are always unbroken; for odd flavor numbers, parity symmetry is spontaneously broken below the critical flavor number Nircr=9 , while chiral symmetry is still unbroken.

Mechanical behavior in living cells consistent with the tensegrity model

NASA Technical Reports Server (NTRS)

Wang, N.; Naruse, K.; Stamenovic, D.; Fredberg, J. J.; Mijailovich, S. M.; Tolic-Norrelykke, I. M.; Polte, T.; Mannix, R.; Ingber, D. E.

2001-01-01

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.

The numerical high cycle fatigue damage model of fillet weld joint under weld-induced residual stresses

NASA Astrophysics Data System (ADS)

Nguyen Van Do, Vuong

2018-04-01

In this study, a development of nonlinear continuum damage mechanics (CDM) model for multiaxial high cycle fatigue is proposed in which the cyclic plasticity constitutive model has been incorporated in the finite element (FE) framework. T-joint FE simulation of fillet welding is implemented to characterize sequentially coupled three-dimensional (3-D) of thermo-mechanical FE formulation and simulate the welding residual stresses. The high cycle fatigue damage model is then taken account into the fillet weld joints under the various cyclic fatigue load types to calculate the fatigue life considering the residual stresses. The fatigue crack initiation and the propagation in the present model estimated for the total fatigue is compared with the experimental results. The FE results illustrated that the proposed high cycle fatigue damage model in this study could become a powerful tool to effectively predict the fatigue life of the welds. Parametric studies in this work are also demonstrated that the welding residual stresses cannot be ignored in the computation of the fatigue life of welded structures.

Comparative study on predicting Young's modulus of graphene sheets using nano-scale continuum mechanics approach

NASA Astrophysics Data System (ADS)

Rafiee, Roham; Eskandariyun, Amirali

2017-06-01

In this research, nano-scale continuum modeling is employed to predict Young's modulus of graphene sheet. The lattice nano-structure of a graphene sheet is replaced with a discrete space-frame structure simulating carbon-carbon bonds with either beam or spring elements. A comparative study is carried out to check the influence of employed elements on estimated Young's moduli of graphene sheets in both horizontal and vertical directions. A detailed analysis is also conducted to investigate the influence of graphene sheet sizes on its Young's modulus and corresponding aspect ratios that unwelcomed end effects disappear on the results are extracted. At the final stage, defected graphene sheets suffering from vacancy defects are investigated through a stochastic analysis taking into account both number of defects and their locations as random parameters. The reduction level in the Young's moduli of defected graphene sheets compared with non-defected ones is analyzed and reported.

Classification of proteins: available structural space for molecular modeling.

PubMed

Andreeva, Antonina

2012-01-01

The wealth of available protein structural data provides unprecedented opportunity to study and better understand the underlying principles of protein folding and protein structure evolution. A key to achieving this lies in the ability to analyse these data and to organize them in a coherent classification scheme. Over the past years several protein classifications have been developed that aim to group proteins based on their structural relationships. Some of these classification schemes explore the concept of structural neighbourhood (structural continuum), whereas other utilize the notion of protein evolution and thus provide a discrete rather than continuum view of protein structure space. This chapter presents a strategy for classification of proteins with known three-dimensional structure. Steps in the classification process along with basic definitions are introduced. Examples illustrating some fundamental concepts of protein folding and evolution with a special focus on the exceptions to them are presented.

A Temperature-Dependent Phase-Field Model for Phase Separation and Damage

NASA Astrophysics Data System (ADS)

Heinemann, Christian; Kraus, Christiane; Rocca, Elisabetta; Rossi, Riccarda

2017-07-01

In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature concerning phase separation and damage processes in elastic media, in our model we encompass thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More particularly, we prove the existence of "entropic weak solutions", resorting to a solvability concept first introduced in Feireisl (Comput Math Appl 53:461-490, 2007) in the framework of Fourier-Navier-Stokes systems and then recently employed in Feireisl et al. (Math Methods Appl Sci 32:1345-1369, 2009) and Rocca and Rossi (Math Models Methods Appl Sci 24:1265-1341, 2014) for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.

A study of a diffusive model of asset returns and an empirical analysis of financial markets

NASA Astrophysics Data System (ADS)

Alejandro Quinones, Angel Luis

A diffusive model for market dynamics is studied and the predictions of the model are compared to real financial markets. The model has a non-constant diffusion coefficient which depends both on the asset value and the time. A general solution for the distribution of returns is obtained and shown to match the results of computer simulations for two simple cases, piecewise linear and quadratic diffusion. The effects of discreteness in the market dynamics on the model are also studied. For the quadratic diffusion case, a type of phase transition leading to fat tails is observed as the discrete distribution approaches the continuum limit. It is also found that the model captures some of the empirical stylized facts observed in real markets, including fat-tails and scaling behavior in the distribution of returns. An analysis of empirical data for the EUR/USD currency exchange rate and the S&P 500 index is performed. Both markets show time scaling behavior consistent with a value of 1/2 for the Hurst exponent. Finally, the results show that the distribution of returns for the two markets is well fitted by the model, and the corresponding empirical diffusion coefficients are determined.

Nonelastic nuclear reactions and accompanying gamma radiation

NASA Technical Reports Server (NTRS)

Snow, R.; Rosner, H. R.; George, M. C.; Hayes, J. D.

1971-01-01

Several aspects of nonelastic nuclear reactions which proceed through the formation of a compound nucleus are dealt with. The full statistical model and the partial statistical model are described and computer programs based on these models are presented along with operating instructions and input and output for sample problems. A theoretical development of the expression for the reaction cross section for the hybrid case which involves a combination of the continuum aspects of the full statistical model with the discrete level aspects of the partial statistical model is presented. Cross sections for level excitation and gamma production by neutron inelastic scattering from the nuclei Al-27, Fe-56, Si-28, and Pb-208 are calculated and compared with avaliable experimental data.

Strong Local-Nonlocal Coupling for Integrated Fracture Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Littlewood, David John; Silling, Stewart A.; Mitchell, John A.

Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling,"more » completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves conver- gence behavior. Finally, a novel approach for modeling ductile failure has been developed, moti- vated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software im- plementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.« less

Finite Element Creep Damage Analyses and Life Prediction of P91 Pipe Containing Local Wall Thinning Defect

NASA Astrophysics Data System (ADS)

Xue, Jilin; Zhou, Changyu

2016-03-01

Creep continuum damage finite element (FE) analyses were performed for P91 steel pipe containing local wall thinning (LWT) defect subjected to monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment by orthogonal experimental design method. The creep damage lives of pipe containing LWT defect under different load conditions were obtained. Then, the creep damage life formulas were regressed based on the creep damage life results from FE method. At the same time a skeletal point rupture stress was found and used for life prediction which was compared with creep damage lives obtained by continuum damage analyses. From the results, the failure lives of pipe containing LWT defect can be obtained accurately by using skeletal point rupture stress method. Finally, the influence of LWT defect geometry was analysed, which indicated that relative defect depth was the most significant factor for creep damage lives of pipe containing LWT defect.

Modified fluctuation-dissipation and Einstein relation at nonequilibrium steady states

NASA Astrophysics Data System (ADS)

Chaudhuri, Debasish; Chaudhuri, Abhishek

2012-02-01

Starting from the pioneering work of Agarwal [G. S. Agarwal, Zeitschrift für PhysikEPJAFV1434-600110.1007/BF01391621 252, 25 (1972)], we present a unified derivation of a number of modified fluctuation-dissipation relations (MFDR) that relate response to small perturbations around nonequilibrium steady states to steady-state correlations. Using this formalism we show the equivalence of velocity forms of MFDR derived using continuum Langevin and discrete master equation dynamics. The resulting additive correction to the Einstein relation is exemplified using a flashing ratchet model of molecular motors.

Calculation of Vibrational Spectra for Coordinated Thiocyanate Ion in Acetonitrile

NASA Astrophysics Data System (ADS)

Mikhailov, G. P.

2016-07-01

The impact of the association of lithium cation with NCS- ion in acetonitrile on the vibrational spectrum was studied by the density-functional method in the B3LYP/6-31+G(d,p) approximation. The best agreement between experimental and calculated ionic association data was achieved taking into account the nonspecific solvation, oversolvation, and solubility of ionic complexes within the discrete-continuum model. The microstructures of the thiocyanate ion in a contact ion pair with lithium cation and ion-pair dimer and trimer in acetonitrile were established.

Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kraloua, B.; Hennad, A.

The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

On the Extension of Goal-Oriented Error Estimation and Hierarchical Modeling to Discrete Lattice Models

DTIC Science & Technology

2004-08-04

rewrite the residual as: R(u0,p) = R(u0,p0) + R(u0, ε0) (22) = R(u0,p0) + B(e0, ε0) (23) where p0 = Πp0, p0 being the influence function for the surrogate...lattice solutions are shown in Fig. 5 for the 11 × 11 and 31 × 31 lattices. We show in Figs. 6 and 7 the continuum influence function p0 and lattice...the influence function becomes more localized as the lattice width decreases since, in all cases, the quantity of interest is defined with respect to

Discretization of 3d gravity in different polarizations

NASA Astrophysics Data System (ADS)

Dupuis, Maïté; Freidel, Laurent; Girelli, Florian

2017-10-01

We study the discretization of three-dimensional gravity with Λ =0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows us to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical nontrivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows us to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

MESOSCALE MODELING OF DEFLAGRATION-INDUCED DECONSOLIDATION IN POLYMER-BONDED EXPLOSIVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Springer, H K; Glascoe, E A; Reaugh, J E

Initially undamaged polymer-bonded explosives can transition from conductive burning to more violent convective burning via rapid deconsolidation at higher pressures. The pressure-dependent infiltration of cracks and pores, i.e., damage, by product gases at the burn-front is a key step in the transition to convective burning. However, the relative influence of pre-existing damage and the evolution of deflagration-induced damage during the transition to convective burning is not well understood. The objective of this study is to investigate the role of microstructure and initial pressurization on deconsolidation. We performed simulations using the multi-physics hydrocode, ALE3D. HMX-Viton A served as our model explosive.more » A Prout-Tompkins chemical kinetic model, Vielle's Law pressure-dependent burning, Gruneisen equation-of-state, and simplified strength model were used for the HMX. The propensity for deconsolidation increased with increasing defect size and decreasing initial pressurization, as measured by the increase in burning surface area. These studies are important because they enable the development of continuum-scale damage models and the design of inherently safer explosives.« less

Coupling crystal plasticity and phase-field damage to simulate β-HMX-based polymer-bonded explosive under shock load

NASA Astrophysics Data System (ADS)

Grilli, Nicolo; Dandekar, Akshay; Koslowski, Marisol

2017-06-01

The development of high explosive materials requires constitutive models that are able to predict the influence of microstructure and loading conditions on shock sensitivity. In this work a model at the continuum-scale for the polymer-bonded explosive constituted of β-HMX particles embedded in a Sylgard matrix is developed. It includes a Murnaghan equation of state, a crystal plasticity model, based on power-law slip rate and hardening, and a phase field damage model based on crack regularization. The temperature increase due to chemical reactions is introduced by a heat source term, which is validated using results from reactive molecular dynamics simulations. An initial damage field representing pre-existing voids and cracks is used in the simulations to understand the effect of these inhomogeneities on the damage propagation and shock sensitivity. We show the predictions of the crystal plasticity model and the effect of the HMX crystal orientation on the shock initiation and on the dissipated plastic work and damage propagation. The simulation results are validated with ultra-fast dynamic transmission electron microscopy experiments and x-ray experiments carried out at Purdue University. Membership Pending.

Effect of Electrostatic Discharge on Electrical Characteristics of Discrete Electronic Components

NASA Technical Reports Server (NTRS)

Wysocki, Phil; Vashchenko, Vladislav; Celaya, Jose; Saha, Sankalita; Goebel, Kai

2009-01-01

This article reports on preliminary results of a study conducted to examine how temporary electrical overstress seed fault conditions in discrete power electronic components that cannot be detected with reliability tests but impact longevity of the device. These defects do not result in formal parametric failures per datasheet specifications, but result in substantial change in the electrical characteristics when compared with pristine device parameters. Tests were carried out on commercially available 600V IGBT devices using transmission line pulse (TLP) and system level ESD stress. It was hypothesized that the ESD causes local damage during the ESD discharge which may greatly accelerate degradation mechanisms and thus reduce the life of the components. This hypothesis was explored in simulation studies where different types of damage were imposed to different parts of the device. Experimental results agree qualitatively with the simulation for a number of tests which will motivate more in-depth modeling of the damage.

Modeling postshock evolution of large electropores

NASA Astrophysics Data System (ADS)

Neu, John C.; Krassowska, Wanda

2003-02-01

The Smoluchowski equation (SE), which describes the evolution of pores created by electric shocks, cannot be applied to modeling large and long-lived pores for two reasons: (1) it does not predict pores of radius above 20 nm without also predicting membrane rupture; (2) it does not predict postshock growth of pores. This study proposes a model in which pores are coupled by membrane tension, resulting in a nonlinear generalization of SE. The predictions of the model are explored using examples of homogeneous (all pore radii r are equal) and heterogeneous (0⩽r⩽rmax) distributions of pores. Pores in a homogeneous population either shrink to zero or assume a stable radius corresponding to the minimum of the bilayer energy. For a heterogeneous population, such a stable radius does not exist. All pores, except rmax, shrink to zero and rmax grows to infinity. However, the unbounded growth of rmax is not physical because the number of pores per cell decreases in time and the continuum model loses validity. When the continuum formulation is replaced by the discrete one, the model predicts the coarsening process: all pores, except rmax, shrink to zero and rmax assumes a stable radius. Thus, the model with tension-coupled pores does not predict membrane rupture and the predicted postshock growth of pores is consistent with experimental evidence.

Combining cellular automata and Lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition.

PubMed

Alemani, Davide; Pappalardo, Francesco; Pennisi, Marzio; Motta, Santo; Brusic, Vladimir

2012-02-28

In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach. Copyright © 2011 Elsevier B.V. All rights reserved.

Computational Implementation of a Thermodynamically Based Work Potential Model For Progressive Microdamage and Transverse Cracking in Fiber-Reinforced Laminates

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Bednarcyk, Brett A.; Collier, Craig S.

2012-01-01

A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.

The continuum of spreading depolarizations in acute cortical lesion development: Examining Leão’s legacy

PubMed Central

Shuttleworth, C William; Kirov, Sergei A; Ayata, Cenk; Hinzman, Jason M; Foreman, Brandon; Andrew, R David; Boutelle, Martyn G; Brennan, KC; Carlson, Andrew P; Dahlem, Markus A; Drenckhahn, Christoph; Dohmen, Christian; Fabricius, Martin; Farkas, Eszter; Feuerstein, Delphine; Graf, Rudolf; Helbok, Raimund; Lauritzen, Martin; Major, Sebastian; Oliveira-Ferreira, Ana I; Richter, Frank; Rosenthal, Eric S; Sakowitz, Oliver W; Sánchez-Porras, Renán; Santos, Edgar; Schöll, Michael; Strong, Anthony J; Urbach, Anja; Westover, M Brandon; Winkler, Maren KL; Witte, Otto W; Woitzik, Johannes; Dreier, Jens P

2016-01-01

A modern understanding of how cerebral cortical lesions develop after acute brain injury is based on Aristides Leão’s historic discoveries of spreading depression and asphyxial/anoxic depolarization. Treated as separate entities for decades, we now appreciate that these events define a continuum of spreading mass depolarizations, a concept that is central to understanding their pathologic effects. Within minutes of acute severe ischemia, the onset of persistent depolarization triggers the breakdown of ion homeostasis and development of cytotoxic edema. These persistent changes are diagnosed as diffusion restriction in magnetic resonance imaging and define the ischemic core. In delayed lesion growth, transient spreading depolarizations arise spontaneously in the ischemic penumbra and induce further persistent depolarization and excitotoxic damage, progressively expanding the ischemic core. The causal role of these waves in lesion development has been proven by real-time monitoring of electrophysiology, blood flow, and cytotoxic edema. The spreading depolarization continuum further applies to other models of acute cortical lesions, suggesting that it is a universal principle of cortical lesion development. These pathophysiologic concepts establish a working hypothesis for translation to human disease, where complex patterns of depolarizations are observed in acute brain injury and appear to mediate and signal ongoing secondary damage. PMID:27328690

The notion of a plastic material spin in atomistic simulations

NASA Astrophysics Data System (ADS)

Dickel, D.; Tenev, T. G.; Gullett, P.; Horstemeyer, M. F.

2016-12-01

A kinematic algorithm is proposed to extend existing constructions of strain tensors from atomistic data to decouple elastic and plastic contributions to the strain. Elastic and plastic deformation and ultimately the plastic spin, useful quantities in continuum mechanics and finite element simulations, are computed from the full, discrete deformation gradient and an algorithm for the local elastic deformation gradient. This elastic deformation gradient algorithm identifies a crystal type using bond angle analysis (Ackland and Jones 2006 Phys. Rev. B 73 054104) and further exploits the relationship between bond angles to determine the local deformation from an ideal crystal lattice. Full definitions of plastic deformation follow directly using a multiplicative decomposition of the deformation gradient. The results of molecular dynamics simulations of copper in simple shear and torsion are presented to demonstrate the ability of these new discrete measures to describe plastic material spin in atomistic simulation and to compare them with continuum theory.

Characteristics of Creep Damage for 60Sn-40Pb Solder Material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Y.; Chow, C.L.; Fang, H.E.

This paper presents a viscoplasticity model taking into account the effects of change in grain or phase size and damage on the characterization of creep damage in 60Sn-40Pb solder. Based on the theory of damage mechanics, a two-scalar damage model is developed for isotropic materials by introducing the free energy equivalence principle. The damage evolution equations are derived in terms of the damage energy release rates. In addition, a failure criterion is developed based on the postulation that a material element is said to have ruptured when the total damage accumulated in the element reaches a critical value. The damagemore » coupled viscoplasticity model is discretized and coded in a general-purpose finite element program known as ABAQUS through its user-defined material subroutine UMAT. To illustrate the application of the model, several example cases are introduced to analyze, both numerically and experimentally, the tensile creep behaviors of the material at three stress levels. The model is then applied to predict the deformation of a notched specimen under monotonic tension at room temperature (22 C). The results demonstrate that the proposed model can successfully predict the viscoplastic behavior of the solder material.« less

Discrete Spring Model for Predicting Delamination Growth in Z-Fiber Reinforced DCB Specimens

NASA Technical Reports Server (NTRS)

Ratcliffe, James G.; OBrien, T. Kevin

2004-01-01

Beam theory analysis was applied to predict delamination growth in Double Cantilever Beam (DCB) specimens reinforced in the thickness direction with pultruded pins, known as Z-fibers. The specimen arms were modeled as cantilever beams supported by discrete springs, which were included to represent the pins. A bi-linear, irreversible damage law was used to represent Z-fiber damage, the parameters of which were obtained from previous experiments. Closed-form solutions were developed for specimen compliance and displacements corresponding to Z-fiber row locations. A solution strategy was formulated to predict delamination growth, in which the parent laminate mode I critical strain energy release rate was used as the criterion for delamination growth. The solution procedure was coded into FORTRAN 90, giving a dedicated software tool for performing the delamination prediction. Comparison of analysis results with previous analysis and experiment showed good agreement, yielding an initial verification for the analytical procedure.

Discrete Spring Model for Predicting Delamination Growth in Z-Fiber Reinforced DCB Specimens

NASA Technical Reports Server (NTRS)

Ratcliffe, James G.; O'Brien, T. Kevin

2004-01-01

Beam theory analysis was applied to predict delamination growth in DCB specimens reinforced in the thickness direction with pultruded pins, known as Z-fibers. The specimen arms were modeled as cantilever beams supported by discrete springs, which were included to represent the pins. A bi-linear, irreversible damage law was used to represent Z-fiber damage, the parameters of which were obtained from previous experiments. Closed-form solutions were developed for specimen compliance and displacements corresponding to Z-fiber row locations. A solution strategy was formulated to predict delamination growth, in which the parent laminate mode I fracture toughness was used as the criterion for delamination growth. The solution procedure was coded into FORTRAN 90, giving a dedicated software tool for performing the delamination prediction. Comparison of analysis results with previous analysis and experiment showed good agreement, yielding an initial verification for the analytical procedure.

Generalized continuum modeling of scale-dependent crystalline plasticity

NASA Astrophysics Data System (ADS)

Mayeur, Jason R.

The use of metallic material systems (e.g. pure metals, alloys, metal matrix composites) in a wide range of engineering applications from medical devices to electronic components to automobiles continues to motivate the development of improved constitutive models to meet increased performance demands while minimizing cost. Emerging technologies often incorporate materials in which the dominant microstructural features have characteristic dimensions reaching into the submicron and nanometer regime. Metals comprised of such fine microstructures often exhibit unique and size-dependent mechanical response, and classical approaches to constitutive model development at engineering (continuum) scales, being local in nature, are inadequate for describing such behavior. Therefore, traditional modeling frameworks must be augmented and/or reformulated to account for such phenomena. Crystal plasticity constitutive models have proven quite capable of capturing first-order microstructural effects such as grain orientation (elastic/plastic anisotropy), grain morphology, phase distribution, etc. on the deformation behavior of both single and polycrystals, yet suffer from the same limitations as other local continuum theories with regard to capturing scale-dependent mechanical response. This research is focused on the development, numerical implementation, and application of a generalized (nonlocal) theory of single crystal plasticity capable of describing the scale-dependent mechanical response of both single and polycrystalline metals that arises as a result of heterogeneous deformation. This research developed a dislocation-based theory of micropolar single crystal plasticity. The majority of nonlocal crystal plasticity theories are predicated on the connection between gradients of slip and geometrically necessary dislocations. Due to the diversity of existing nonlocal crystal plasticity theories, a review, summary, and comparison of representative model classes is presented in Chapter 2 from a unified dislocation-based perspective. The discussion of the continuum crystal plasticity theories is prefaced by a brief review of discrete dislocation plasticity, which facilitates the comparison of certain model aspects and also serves as a reference for latter segments of the research which make connection to this constitutive description. Chapter 2 has utility not only as a literature review, but also as a synthesis and analysis of competing and alternative nonlocal crystal plasticity modeling strategies from a common viewpoint. The micropolar theory of single crystal plasticity is presented in Chapter 3. Two different types of flow criteria are considered - the so-called single and multicriterion theories, and several variations of the dislocation-based strength models appropriate for each theory are presented and discussed. The numerical implementation of the two-dimensional version of the constitutive theory is given in Chapter 4. A user element subroutine for the implicit commercial finite element code Abaqus/Standard is developed and validated through the solution of initial-boundary value problems with closed-form solutions. Convergent behavior of the subroutine is also demonstrated for an initial-boundary value problem exhibiting strain localization. In Chapter 5, the models are employed to solve several standard initial-boundary value problems for heterogeneously deforming single crystals including simple shearing of a semi-infinite constrained thin film, pure bending of thin films, and simple shearing of a metal matrix composite with elastic inclusions. The simulation results are compared to those obtained from the solution of equivalent boundary value problems using discrete dislocation dynamics and alternative generalized crystal plasticity theories. Comparison and calibration with respect to the former provides guidance in the specification of non-traditional material parameters that arise in the model formulation and demonstrates its effectiveness at capturing the heterogeneous deformation fields and size-dependent mechanical behavior predicted by a finer scale constitutive description. Finally, in Chapter 6, the models are applied to simulate the deformation behavior of small polycrystalline ensembles. Several grain boundary constitutive descriptions are explored and the response characteristics are analyzed with respect to experimental observations as well as results obtained from discrete dislocation dynamics and alternative nonlocal crystal plasticity theories. Particular attention is focused on how the various grain boundary descriptions serve to either locally concentrate or diffuse deformation heterogeneity as a function of grain size.

A hybrid computational model to explore the topological characteristics of epithelial tissues.

PubMed

González-Valverde, Ismael; García-Aznar, José Manuel

2017-11-01

Epithelial tissues show a particular topology where cells resemble a polygon-like shape, but some biological processes can alter this tissue topology. During cell proliferation, mitotic cell dilation deforms the tissue and modifies the tissue topology. Additionally, cells are reorganized in the epithelial layer and these rearrangements also alter the polygon distribution. We present here a computer-based hybrid framework focused on the simulation of epithelial layer dynamics that combines discrete and continuum numerical models. In this framework, we consider topological and mechanical aspects of the epithelial tissue. Individual cells in the tissue are simulated by an off-lattice agent-based model, which keeps the information of each cell. In addition, we model the cell-cell interaction forces and the cell cycle. Otherwise, we simulate the passive mechanical behaviour of the cell monolayer using a material that approximates the mechanical properties of the cell. This continuum approach is solved by the finite element method, which uses a dynamic mesh generated by the triangulation of cell polygons. Forces generated by cell-cell interaction in the agent-based model are also applied on the finite element mesh. Cell movement in the agent-based model is driven by the displacements obtained from the deformed finite element mesh of the continuum mechanical approach. We successfully compare the results of our simulations with some experiments about the topology of proliferating epithelial tissues in Drosophila. Our framework is able to model the emergent behaviour of the cell monolayer that is due to local cell-cell interactions, which have a direct influence on the dynamics of the epithelial tissue. Copyright © 2017 John Wiley & Sons, Ltd.

Continuum models of cohesive stochastic swarms: The effect of motility on aggregation patterns

NASA Astrophysics Data System (ADS)

Hughes, Barry D.; Fellner, Klemens

2013-10-01

Mathematical models of swarms of moving agents with non-local interactions have many applications and have been the subject of considerable recent interest. For modest numbers of agents, cellular automata or related algorithms can be used to study such systems, but in the present work, instead of considering discrete agents, we discuss a class of one-dimensional continuum models, in which the agents possess a density ρ(x,t) at location x at time t. The agents are subject to a stochastic motility mechanism and to a global cohesive inter-agent force. The motility mechanisms covered include classical diffusion, nonlinear diffusion (which may be used to model, in a phenomenological way, volume exclusion or other short-range local interactions), and a family of linear redistribution operators related to fractional diffusion equations. A variety of exact analytic results are discussed, including equilibrium solutions and criteria for unimodality of equilibrium distributions, full time-dependent solutions, and transitions between asymptotic collapse and asymptotic escape. We address the behaviour of the system for diffusive motility in the low-diffusivity limit for both smooth and singular interaction potentials and show how this elucidates puzzling behaviour in fully deterministic non-local particle interaction models. We conclude with speculative remarks about extensions and applications of the models.

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

NASA Technical Reports Server (NTRS)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Yan-Rong; Wang, Jian-Min; Bai, Jin-Ming, E-mail: liyanrong@mail.ihep.ac.cn

Broad emission lines of active galactic nuclei stem from a spatially extended region (broad-line region, BLR) that is composed of discrete clouds and photoionized by the central ionizing continuum. The temporal behaviors of these emission lines are blurred echoes of continuum variations (i.e., reverberation mapping, RM) and directly reflect the structures and kinematic information of BLRs through the so-called transfer function (also known as the velocity-delay map). Based on the previous works of Rybicki and Press and Zu et al., we develop an extended, non-parametric approach to determine the transfer function for RM data, in which the transfer function ismore » expressed as a sum of a family of relatively displaced Gaussian response functions. Therefore, arbitrary shapes of transfer functions associated with complicated BLR geometry can be seamlessly included, enabling us to relax the presumption of a specified transfer function frequently adopted in previous studies and to let it be determined by observation data. We formulate our approach in a previously well-established framework that incorporates the statistical modeling of continuum variations as a damped random walk process and takes into account long-term secular variations which are irrelevant to RM signals. The application to RM data shows the fidelity of our approach.« less

Numerical modelling of bedload sediment transport

NASA Astrophysics Data System (ADS)

Langlois, Vincent J.

2010-05-01

We present a numerical study of sediment transport in the bedload regime. Classical bedload transport laws only describe the variation of the vertically integrated flux of grains as a function of the Shields number. However, these relations are only valid if the moving layer of the bed is at equilibrium with the external flow. Besides, they do not contain enough information for many geomorphological applications. For instance, understanding inertial effects in the moving bed requires models that are able to account for the variability of hydrodynamical conditions, and the discrete nature of the sediment material. We developped a numerical modelling of the behaviour of a three-dimensional bed of grains sheared by a unidirectional fluid flow. These simulations are based on a combination of discrete and continuum approaches: sediment particles are modelled by hard spheres interacting through simple contact forces, whereas the fluid flow is described by a 'mean field' model. Both the drag exerted on grains by the fluid and the retroactive effect of the presence of grains on the flow are accounted for, allowing the system to converge to its equilibrium state (no assumption is made on the fluid velocity profile inside the layer of moving grains). Above the motion threshold, the variation of the flux of grains in the steady state is found to vary like the cube of the Shields number (as predicted by Bagnold). Besides, our simulations allow us to obtain new insights into the detailed mechanisms of bedload transport, by giving access to non-integral quantities, such as the trajectories of each individual grains, the detailed velocity and packing fraction profiles inside the granular bed, etc. It is therefore possible to investigate some effects that are not accounted for in usual continuum models, such as the polydispersity of grains, the ageing of the bed, the response to a variation of the flowrate, etc.

Geometry of the Gene Expression Space of Individual Cells

PubMed Central

Korem, Yael; Szekely, Pablo; Hart, Yuval; Sheftel, Hila; Hausser, Jean; Mayo, Avi; Rothenberg, Michael E.; Kalisky, Tomer; Alon, Uri

2015-01-01

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks. PMID:26161936

Systematic continuum-discretized coupled-channels calculations of total fusion for 6Li with targets 28Si, 59Co, 96Zr, 198Pt, and 209Bi: Effect of resonance states

NASA Astrophysics Data System (ADS)

Gómez Camacho, A.; Wang, Bing; Zhang, H. Q.

2018-05-01

Continuum discretized coupled-channel (CDCC) calculations of total fusion cross sections for reactions induced by the weakly bound nucleus 6Li with targets 28Si, 59Co, 96Zr, 198Pt, and 209Bi at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li→α +d , short-range absorption potentials are considered for the interactions between the α and d fragments with the targets. The effect of resonance (l =2 , Jπ=3+,2+,1+ ) and nonresonance states of 6Li on fusion is studied by using two approaches: (1) by omitting the resonance states from the full discretized CDCC breakup space and (2) by considering only the resonance subspace. A systematic analysis of the effect on fusion from resonance breakup couplings is carried out from light to heavy mass targets. Among other things, it is found that resonance breakup states produce strong repulsive polarization potentials that lead to fusion suppression. Couplings from nonresonance states give place to weak repulsive potentials at high energies; however, these become attractive for the heavier targets at low energies.

Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone.

PubMed

Levrero-Florencio, Francesc; Pankaj, Pankaj

2018-01-01

Realistic macro-level finite element simulations of the mechanical behavior of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenization-based multiscale finite element simulations on bone micro-structure. While homogenization has been fairly successful in the elastic regime and, to some extent, in modeling the macroscopic plastic response, it has remained a challenge with respect to modeling damage. This study uses a homogenization scheme to upscale the damage behavior from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenized results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.

Finite Element Methods and Multiphase Continuum Theory for Modeling 3D Air-Water-Sediment Interactions

NASA Astrophysics Data System (ADS)

Kees, C. E.; Miller, C. T.; Dimakopoulos, A.; Farthing, M.

2016-12-01

The last decade has seen an expansion in the development and application of 3D free surface flow models in the context of environmental simulation. These models are based primarily on the combination of effective algorithms, namely level set and volume-of-fluid methods, with high-performance, parallel computing. These models are still computationally expensive and suitable primarily when high-fidelity modeling near structures is required. While most research on algorithms and implementations has been conducted in the context of finite volume methods, recent work has extended a class of level set schemes to finite element methods on unstructured methods. This work considers models of three-phase flow in domains containing air, water, and granular phases. These multi-phase continuum mechanical formulations show great promise for applications such as analysis of coastal and riverine structures. This work will consider formulations proposed in the literature over the last decade as well as new formulations derived using the thermodynamically constrained averaging theory, an approach to deriving and closing macroscale continuum models for multi-phase and multi-component processes. The target applications require the ability to simulate wave breaking and structure over-topping, particularly fully three-dimensional, non-hydrostatic flows that drive these phenomena. A conservative level set scheme suitable for higher-order finite element methods is used to describe the air/water phase interaction. The interaction of these air/water flows with granular materials, such as sand and rubble, must also be modeled. The range of granular media dynamics targeted including flow and wave transmision through the solid media as well as erosion and deposition of granular media and moving bed dynamics. For the granular phase we consider volume- and time-averaged continuum mechanical formulations that are discretized with the finite element method and coupled to the underlying air/water flow via operator splitting (fractional step) schemes. Particular attention will be given to verification and validation of the numerical model and important qualitative features of the numerical methods including phase conservation, wave energy dissipation, and computational efficiency in regimes of interest.

Parallel algorithm for multiscale atomistic/continuum simulations using LAMMPS

NASA Astrophysics Data System (ADS)

Pavia, F.; Curtin, W. A.

2015-07-01

Deformation and fracture processes in engineering materials often require simultaneous descriptions over a range of length and time scales, with each scale using a different computational technique. Here we present a high-performance parallel 3D computing framework for executing large multiscale studies that couple an atomic domain, modeled using molecular dynamics and a continuum domain, modeled using explicit finite elements. We use the robust Coupled Atomistic/Discrete-Dislocation (CADD) displacement-coupling method, but without the transfer of dislocations between atoms and continuum. The main purpose of the work is to provide a multiscale implementation within an existing large-scale parallel molecular dynamics code (LAMMPS) that enables use of all the tools associated with this popular open-source code, while extending CADD-type coupling to 3D. Validation of the implementation includes the demonstration of (i) stability in finite-temperature dynamics using Langevin dynamics, (ii) elimination of wave reflections due to large dynamic events occurring in the MD region and (iii) the absence of spurious forces acting on dislocations due to the MD/FE coupling, for dislocations further than 10 Å from the coupling boundary. A first non-trivial example application of dislocation glide and bowing around obstacles is shown, for dislocation lengths of ∼50 nm using fewer than 1 000 000 atoms but reproducing results of extremely large atomistic simulations at much lower computational cost.

Rhelogical constraints on ridge formation on Icy Satellites

NASA Astrophysics Data System (ADS)

Rudolph, M. L.; Manga, M.

2010-12-01

The processes responsible for forming ridges on Europa remain poorly understood. We use a continuum damage mechanics approach to model ridge formation. The main objectives of this contribution are to constrain (1) choice of rheological parameters and (2) maximum ridge size and rate of formation. The key rheological parameters to constrain appear in the evolution equation for a damage variable (D): ˙ {D} = B <<σ >>r}(1-D){-k-α D (p)/(μ ) and in the equation relating damage accumulation to volumetric changes, Jρ 0 = δ (1-D). Similar damage evolution laws have been applied to terrestrial glaciers and to the analysis of rock mechanics experiments. However, it is reasonable to expect that, like viscosity, the rheological constants B, α , and δ depend strongly on temperature, composition, and ice grain size. In order to determine whether the damage model is appropriate for Europa’s ridges, we must find values of the unknown damage parameters that reproduce ridge topography. We perform a suite of numerical experiments to identify the region of parameter space conducive to ridge production and show the sensitivity to changes in each unknown parameter.

Comparison of the Marcus and Pekar partitions in the context of non-equilibrium, polarizable-continuum solvation models

DOE Office of Scientific and Technical Information (OSTI.GOV)

You, Zhi-Qiang; Herbert, John M., E-mail: herbert@chemistry.ohio-state.edu; Mewes, Jan-Michael

2015-11-28

The Marcus and Pekar partitions are common, alternative models to describe the non-equilibrium dielectric polarization response that accompanies instantaneous perturbation of a solute embedded in a dielectric continuum. Examples of such a perturbation include vertical electronic excitation and vertical ionization of a solution-phase molecule. Here, we provide a general derivation of the accompanying polarization response, for a quantum-mechanical solute described within the framework of a polarizable continuum model (PCM) of electrostatic solvation. Although the non-equilibrium free energy is formally equivalent within the two partitions, albeit partitioned differently into “fast” versus “slow” polarization contributions, discretization of the PCM integral equations failsmore » to preserve certain symmetries contained in these equations (except in the case of the conductor-like models or when the solute cavity is spherical), leading to alternative, non-equivalent matrix equations. Unlike the total equilibrium solvation energy, however, which can differ dramatically between different formulations, we demonstrate that the equivalence of the Marcus and Pekar partitions for the non-equilibrium solvation correction is preserved to high accuracy. Differences in vertical excitation and ionization energies are <0.2 eV (and often <0.01 eV), even for systems specifically selected to afford a large polarization response. Numerical results therefore support the interchangeability of the Marcus and Pekar partitions, but also caution against relying too much on the fast PCM charges for interpretive value, as these charges differ greatly between the two partitions, especially in polar solvents.« less

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales.

PubMed

Unterberger, Michael J; Holzapfel, Gerhard A

2014-11-01

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.

Multiscale Simulation Platform Linking Lithium Ion Battery Electrode Fabrication Process with Performance at the Cell Level.

PubMed

Ngandjong, Alain C; Rucci, Alexis; Maiza, Mariem; Shukla, Garima; Vazquez-Arenas, Jorge; Franco, Alejandro A

2017-12-07

A novel multiscale modeling platform is proposed to demonstrate the importance of particle assembly during battery electrode fabrication by showing its effect on battery performance. For the first time, a discretized three-dimensional (3D) electrode resulting from the simulation of its fabrication has been incorporated within a 3D continuum performance model. The study used LiNi 0.5 Co 0.2 Mn 0.3 O 2 as active material, and the effect of changes of electrode formulation is explored for three cases, namely 85:15, 90:10, and 95:5 ratios between active material and carbon-binder domains. Coarse-grained molecular dynamics is used to simulate the electrode fabrication. The resulting electrode mesostructure is characterized in terms of active material surface coverage by the carbon-binder domains and porosity. The trends observed are nonintuitive, indicating a high degree of complexity of the system. These structures are subsequently implemented into a 3D continuum model which displays distinct discharge behaviors for the three cases. The study offers a method for developing a coherent theoretical understanding of electrode fabrication that can help optimize battery performance.

Soft Wall Ion Channel in Continuum Representation with Application to Modeling Ion Currents in α-Hemolysin

PubMed Central

Simakov, Nikolay A.

2010-01-01

A soft repulsion (SR) model of short range interactions between mobile ions and protein atoms is introduced in the framework of continuum representation of the protein and solvent. The Poisson-Nernst-Plank (PNP) theory of ion transport through biological channels is modified to incorporate this soft wall protein model. Two sets of SR parameters are introduced: the first is parameterized for all essential amino acid residues using all atom molecular dynamic simulations; the second is a truncated Lennard – Jones potential. We have further designed an energy based algorithm for the determination of the ion accessible volume, which is appropriate for a particular system discretization. The effects of these models of short-range interaction were tested by computing current-voltage characteristics of the α-hemolysin channel. The introduced SR potentials significantly improve prediction of channel selectivity. In addition, we studied the effect of choice of some space-dependent diffusion coefficient distributions on the predicted current-voltage properties. We conclude that the diffusion coefficient distributions largely affect total currents and have little effect on rectifications, selectivity or reversal potential. The PNP-SR algorithm is implemented in a new efficient parallel Poisson, Poisson-Boltzman and PNP equation solver, also incorporated in a graphical molecular modeling package HARLEM. PMID:21028776

A Progressive Damage Model for unidirectional Fibre Reinforced Composites with Application to Impact and Penetration Simulation

NASA Astrophysics Data System (ADS)

Kerschbaum, M.; Hopmann, C.

2016-06-01

The computationally efficient simulation of the progressive damage behaviour of continuous fibre reinforced plastics is still a challenging task with currently available computer aided engineering methods. This paper presents an original approach for an energy based continuum damage model which accounts for stress-/strain nonlinearities, transverse and shear stress interaction phenomena, quasi-plastic shear strain components, strain rate effects, regularised damage evolution and consideration of load reversal effects. The physically based modelling approach enables experimental determination of all parameters on ply level to avoid expensive inverse analysis procedures. The modelling strategy, implementation and verification of this model using commercially available explicit finite element software are detailed. The model is then applied to simulate the impact and penetration of carbon fibre reinforced cross-ply specimens with variation of the impact speed. The simulation results show that the presented approach enables a good representation of the force-/displacement curves and especially well agreement with the experimentally observed fracture patterns. In addition, the mesh dependency of the results were assessed for one impact case showing only very little change of the simulation results which emphasises the general applicability of the presented method.

The role of microstructure on deformation and damage mechanisms in a Nickel-based superalloy at elevated temperatures

NASA Astrophysics Data System (ADS)

Maciejewski, Kimberly E.

The overall objective of this research work is the development and implementation of a mechanistic based time-dependent crack growth model which considers the role of creep, fatigue and environment interactions on both the bulk and the grain boundary phase in ME3 disk material. The model is established by considering a moving crack tip along a grain boundary path in which damage events are described in terms of the grain boundary deformation and related accommodation processes. Modeling of these events was achieved by adapting a cohesive zone approach (an interface with internal singular surfaces) in which the grain boundary dislocation network is smeared into a Newtonian fluid element. The deformation behavior of this element is controlled by the continuum in both far field (internal state variable model) and near field (crystal plasticity model) and the intrinsic grain boundary viscosity which is characterized by microstructural parameters, including grain boundary precipitates and morphology, and is able to define the mobility of the element by scaling the motion of dislocations into a mesoscopic scale. Within the cohesive zone element, the motion of gliding dislocations in the tangential direction relates to the observed grain boundary sliding displacement, the rate of which is limited by the climb of dislocations over grain boundary obstacles. Effects of microstructural variation and orientation of the surrounding continuum are embedded in the tangential stress developing in the grain boundary. The mobility of the element in the tangential direction (i.e. by grain boundary sliding) characterizes the accumulation of irreversible displacement while the vertical movement (migration), although present, is assumed to alter stress by relaxation and, thus, is not considered a contributing factor in the damage process. This process is controlled by the rate at which the time-dependent sliding reaches a critical displacement and as such, a damage criterion is introduced by considering the mobility limit in the tangential direction leading to strain incompatibility and failure. This limit is diminished by environmental effects which are introduced as a dynamic embrittlement process that hinders grain boundary mobility due to oxygen diffusion. The concepts described herein indicate that implementation of the cohesive zone model requires the knowledge of the grain boundary external and internal deformation fields. The external field is generated by developing and coupling two continuum constitutive models including (i) a microstructure-explicit coarse scale crystal plasticity model with strength provided by tertiary and secondary gamma' precipitates. This scale is appropriate for the representation of the continuum region at the immediate crack tip, and (ii) a macroscopic internal state variable model for the purpose of modeling the response of the far field region located several grains away from the crack path. The hardening contributions of the gamma' precipitates consider dislocation/precipitate interactions in terms of gamma' particles shearing and/or Orowan by-passing mechanisms. The material parameters for these models are obtained from results of low cycle fatigue tests which were performed at three temperatures; 650, 704 and 760°C. Furthermore, a series of microstructure controlled experiments were carried out in order to develop and validate the microstructure dependency feature of the continuum constitutive models. The second requirement in the implementation of the cohesive zone model is a grain boundary deformation model which has been developed, as described above, on the basis of viscous flow rules of the boundary material. This model is supported by dwell crack growth experiments carried out at the three temperatures mentioned above, in both air and vacuum environments. Results of these tests have identified the frequency range in which the grain boundary cohesive zone model is applicable and also provided data to calculate the grain boundary activation energy as well as identifying the relative contributions of creep and environment in the critical sliding displacement leading to failure. Validation of the cohesive zone model has been carried out by comparing the simulated crack growth data with that obtained experimentally. This comparison is used to optimize the different model components and to provide a route to assess the relative significance of each of these components in relation to the intergranular damage associated with dwell fatigue crack growth in the ME3 alloy. For this purpose, a set of case studies were performed in order to illustrate the sensitivity of the cohesive zone model to variations in microstructure parameters (gamma ' statistics and grain boundary morphology) examined within the range of temperatures utilized in this study.

Micromechanics Fatigue Damage Analysis Modeling for Fabric Reinforced Ceramic Matrix Composites

NASA Technical Reports Server (NTRS)

Min, J. B.; Xue, D.; Shi, Y.

2013-01-01

A micromechanics analysis modeling method was developed to analyze the damage progression and fatigue failure of fabric reinforced composite structures, especially for the brittle ceramic matrix material composites. A repeating unit cell concept of fabric reinforced composites was used to represent the global composite structure. The thermal and mechanical properties of the repeating unit cell were considered as the same as those of the global composite structure. The three-phase micromechanics, the shear-lag, and the continuum fracture mechanics models were integrated with a statistical model in the repeating unit cell to predict the progressive damages and fatigue life of the composite structures. The global structure failure was defined as the loss of loading capability of the repeating unit cell, which depends on the stiffness reduction due to material slice failures and nonlinear material properties in the repeating unit cell. The present methodology is demonstrated with the analysis results evaluated through the experimental test performed with carbon fiber reinforced silicon carbide matrix plain weave composite specimens.

How important is exact knowledge of preferential flowpath locations and orientations for understanding spatiotemporally integrated spring hydrologic and transport response?

NASA Astrophysics Data System (ADS)

Henson, W.; De Rooij, R.; Graham, W. D.

2016-12-01

The Upper Floridian Aquifer is hydrogeologically complex; limestone dissolution has led to vertical and horizontal preferential flow paths. Locations of karst conduits are unknown and conduit properties are poorly constrained. Uncertainty in effects of conduit location, size, and density, network geometry and connectivity on hydrologic and transport responses is not well quantified, leading to limited use of discrete-continuum models that incorporate conduit networks for regional-scale hydrologic regulatory models. However, conduit networks typically dominate flow and contaminant transport in karst aquifers. We evaluated sensitivity of simulated water and nitrate fluxes and flow paths to karst conduit geometry in a springshed representative of Silver Springs, Florida, using a novel calcite dissolution conduit-generation algorithm coupled with a discrete-continuum flow and transport model (DisCo). Monte Carlo simulations of conduit generation, groundwater flow, and conservative solute transport indicate that, if a first magnitude spring system conduit network developed (i.e., spring flow >2.8 m3/s), the uncertainty in hydraulic and solute pulse response metrics at the spring vent was minimally related to locational uncertainty of network elements. Across the ensemble of realizations for various distributions of conduits, first magnitude spring hydraulic pulse metrics (e.g., steady-flow, peak flow, and recession coefficients) had < 0.01 coefficient of variation (CV). Similarly, spring solute breakthrough curve moments had low CV (<0.08); peak arrival had CV=0.06, mean travel time had CV=0.05, and travel time standard deviation had CV=0.08. Nevertheless, hydraulic and solute pulse response metrics were significantly different than those predicted by an equivalent porous-media model. These findings indicate that regional-scale decision models that incorporate karst preferential flow paths within an uncertainty framework can be used to better constrain aquifer-vulnerability estimates, despite lacking information about actual conduit locations.

Evaluation of Strain-Life Fatigue Curve Estimation Methods and Their Application to a Direct-Quenched High-Strength Steel

NASA Astrophysics Data System (ADS)

Dabiri, M.; Ghafouri, M.; Rohani Raftar, H. R.; Björk, T.

2018-03-01

Methods to estimate the strain-life curve, which were divided into three categories: simple approximations, artificial neural network-based approaches and continuum damage mechanics models, were examined, and their accuracy was assessed in strain-life evaluation of a direct-quenched high-strength steel. All the prediction methods claim to be able to perform low-cycle fatigue analysis using available or easily obtainable material properties, thus eliminating the need for costly and time-consuming fatigue tests. Simple approximations were able to estimate the strain-life curve with satisfactory accuracy using only monotonic properties. The tested neural network-based model, although yielding acceptable results for the material in question, was found to be overly sensitive to the data sets used for training and showed an inconsistency in estimation of the fatigue life and fatigue properties. The studied continuum damage-based model was able to produce a curve detecting early stages of crack initiation. This model requires more experimental data for calibration than approaches using simple approximations. As a result of the different theories underlying the analyzed methods, the different approaches have different strengths and weaknesses. However, it was found that the group of parametric equations categorized as simple approximations are the easiest for practical use, with their applicability having already been verified for a broad range of materials.

A discrete element and ray framework for rapid simulation of acoustical dispersion of microscale particulate agglomerations

NASA Astrophysics Data System (ADS)

Zohdi, T. I.

2016-03-01

In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.

Improved Strength and Damage Modeling of Geologic Materials

NASA Astrophysics Data System (ADS)

Stewart, Sarah; Senft, Laurel

2007-06-01

Collisions and impact cratering events are important processes in the evolution of planetary bodies. The time and length scales of planetary collisions, however, are inaccessible in the laboratory and require the use of shock physics codes. We present the results from a new rheological model for geological materials implemented in the CTH code [1]. The `ROCK' model includes pressure, temperature, and damage effects on strength, as well as acoustic fluidization during impact crater collapse. We demonstrate that the model accurately reproduces final crater shapes, tensile cracking, and damaged zones from laboratory to planetary scales. The strength model requires basic material properties; hence, the input parameters may be benchmarked to laboratory results and extended to planetary collision events. We show the effects of varying material strength parameters, which are dependent on both scale and strain rate, and discuss choosing appropriate parameters for laboratory and planetary situations. The results are a significant improvement in models of continuum rock deformation during large scale impact events. [1] Senft, L. E., Stewart, S. T. Modeling Impact Cratering in Layered Surfaces, J. Geophys. Res., submitted.

Micro-Macro Analysis and Phenomenological Modelling of Salt Viscous Damage and Application to Salt Caverns

NASA Astrophysics Data System (ADS)

Zhu, Cheng; Pouya, Ahmad; Arson, Chloé

2015-11-01

This paper aims to gain fundamental understanding of the microscopic mechanisms that control the transition between secondary and tertiary creep around salt caverns in typical geological storage conditions. We use a self-consistent inclusion-matrix model to homogenize the viscoplastic deformation of halite polycrystals and predict the number of broken grains in a Representative Elementary Volume of salt. We use this micro-macro modeling framework to simulate creep tests under various axial stresses, which gives us the critical viscoplastic strain at which grain breakage (i.e., tertiary creep) is expected to occur. The comparison of simulation results for short-term and long-term creep indicates that the initiation of tertiary creep depends on the stress and the viscoplastic strain. We use the critical viscoplastic deformation as a yield criterion to control the transition between secondary and tertiary creep in a phenomenological viscoplastic model, which we implement into the Finite Element Method program POROFIS. We model a 850-m-deep salt cavern of irregular shape, in axis-symmetric conditions. Simulations of cavern depressurization indicate that a strain-dependent damage evolution law is more suitable than a stress-dependent damage evolution law, because it avoids high damage concentrations and allows capturing the formation of a damaged zone around the cavity. The modeling framework explained in this paper is expected to provide new insights to link grain breakage to phenomenological damage variables used in Continuum Damage Mechanics.

On the lagrangian 1-form structure of the hyperbolic calogero-moser system

NASA Astrophysics Data System (ADS)

Jairuk, Umpon; Tanasittikosol, Monsit; Yoo-Kong, Sikarin

2017-06-01

In this work, we present the Lagrangian 1-form structure of the hyperbolic Calogero-Moser system in both discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. Furthermore, it is shown that the hyperbolic Calogero-Moser system possesses the key relation, known as the discrete-time closure relation. This relation is a consequence of the compatibility property of the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained by taking two successive continuum limits, namely, the skewed limit and full limit. With these successive limits, the continuous-time closure relation is also obtained and is shown to hold at the continuous level.

Effects of a semi-infinite stratification on the Rayleigh-Taylor instability in an interface with surface tension

NASA Astrophysics Data System (ADS)

de Andrea González, Ángel; González-Gutiérrez, Leo M.

2017-09-01

The Rayleigh-Taylor instability (RTI) in an infinite slab where a constant density lower fluid is initially separated from an upper stratified fluid is discussed in linear regime. The upper fluid is of increasing exponential density and surface tension is considered between both of them. It was found useful to study stability by using the initial value problem approach (IVP), so that we ensure the inclusion of certain continuum modes, otherwise neglected. This methodology includes the branch cut in the complex plane, consequently, in addition to discrete modes (surface RTI modes), a set of continuum modes (internal RTI modes) also appears. As a result, the usual information given by the normal mode method is now complete. Furthermore, a new role is found for surface tension: to transform surface RTI modes (discrete spectrum) into internal RTI modes belonging to a continuous spectrum at a critical wavenumber. As a consequence, the cut-off wavenumber disappears: i.e. the growth rate of the RTI surface mode does not decay to zero at the cut-off wavenumber, as previous researchers used to believe. Finally, we found that, due to the continuum, the asymptotic behavior of the perturbation with respect to time is slower than the exponential when only the continuous spectrum exists.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

NASA Astrophysics Data System (ADS)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Meso-Scale Progressive Damage Behavior Characterization of Triaxial Braided Composites under Quasi-Static Tensile Load

NASA Astrophysics Data System (ADS)

Ren, Yiru; Zhang, Songjun; Jiang, Hongyong; Xiang, Jinwu

2018-04-01

Based on continuum damage mechanics (CDM), a sophisticated 3D meso-scale finite element (FE) model is proposed to characterize the progressive damage behavior of 2D Triaxial Braided Composites (2DTBC) with 60° braiding angle under quasi-static tensile load. The modified Von Mises strength criterion and 3D Hashin failure criterion are used to predict the damage initiation of the pure matrix and fiber tows. A combining interface damage and friction constitutive model is applied to predict the interface damage behavior. Murakami-Ohno stiffness degradation scheme is employed to predict the damage evolution process of each constituent. Coupling with the ordinary and translational symmetry boundary conditions, the tensile elastic response including tensile strength and failure strain of 2DTBC are in good agreement with the available experiment data. The numerical results show that the main failure modes of the composites under axial tensile load are pure matrix cracking, fiber and matrix tension failure in bias fiber tows, matrix tension failure in axial fiber tows and interface debonding; the main failure modes of the composites subjected to transverse tensile load are free-edge effect, matrix tension failure in bias fiber tows and interface debonding.

{Γ}-Convergence Analysis of a Generalized XY Model: Fractional Vortices and String Defects

NASA Astrophysics Data System (ADS)

Badal, Rufat; Cicalese, Marco; De Luca, Lucia; Ponsiglione, Marcello

2018-03-01

We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by {Γ}-convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The {Γ}-limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity.

Numerical model of a single nanocrystal devoted to the study of disordered nanocrystal floating gates of new flash memories

NASA Astrophysics Data System (ADS)

Leroy, Yann; Armeanu, Dumitru; Cordan, Anne-Sophie

2011-05-01

The improvement of our model concerning a single nanocrystal that belongs to a nanocrystal floating gate of a flash memory is presented. In order to extend the gate voltage range applicability of the model, the 3D continuum of states of either metallic or semiconducting electrodes is discretized into 2D subbands. Such an approach gives precise information about the mechanisms behind the charging or release processes of the nanocrystal. Then, the self-energy and screening effects of an electron within the nanocrystal are evaluated and introduced in the model. This enables a better determination of the operating point of the nanocrystal memory. The impact of those improvements on the charging or release time of the nanocrystal is discussed.

Packaging double-helical DNA into viral capsids.

PubMed

LaMarque, Jaclyn C; Le, Thuc-Vy L; Harvey, Stephen C

2004-02-15

DNA packaging in bacteriophage P4 has been examined using a molecular mechanics model with a reduced representation containing one pseudoatom per turn of the double helix. The model is a discretized version of an elastic continuum model. The DNA is inserted piecewise into the model capsid, with the structure being reoptimized after each piece is inserted. Various optimization protocols were investigated, and it was found that molecular dynamics at a very low temperature (0.3 K) produces the optimal packaged structure. This structure is a concentric spool, rather than the coaxial spool that has been commonly accepted for so many years. This geometry, which was originally suggested by Hall and Schellman in 1982 (Biopolymers Vol. 21, pp. 2011-2031), produces a lower overall elastic energy than coaxial spooling. Copyright 2003 Wiley Periodicals, Inc.

Fluctuation-controlled front propagation

NASA Astrophysics Data System (ADS)

Ridgway, Douglas Thacher

1997-09-01

A number of fundamental pattern-forming systems are controlled by fluctuations at the front. These problems involve the interaction of an infinite dimensional probability distribution with a strongly nonlinear, spatially extended pattern-forming system. We have examined fluctuation-controlled growth in the context of the specific problems of diffusion-limited growth and biological evolution. Mean field theory of diffusion-limited growth exhibits a finite time singularity. Near the leading edge of a diffusion-limited front, this leads to acceleration and blowup. This may be resolved, in an ad hoc manner, by introducing a cutoff below which growth is weakened or eliminated (8). This model, referred to as the BLT model, captures a number of qualitative features of global pattern formation in diffusion-limited aggregation: contours of the mean field match contours of averaged particle density in simulation, and the modified mean field theory can form dendritic features not possible in the naive mean field theory. The morphology transition between dendritic and non-dendritic global patterns requires that BLT fronts have a Mullins-Sekerka instability of the wavefront shape, in order to form concave patterns. We compute the stability of BLT fronts numerically, and compare the results to fronts without a cutoff. A significant morphological instability of the BLT fronts exists, with a dominant wavenumber on the scale of the front width. For standard mean field fronts, no instability is found. The naive and ad hoc mean field theories are continuum-deterministic models intended to capture the behavior of a discrete stochastic system. A transformation which maps discrete systems into a continuum model with a singular multiplicative noise is known, however numerical simulations of the continuum stochastic system often give mean field behavior instead of the critical behavior of the discrete system. We have found a new interpretation of the singular noise, based on maintaining the symmetry of the absorbing state, but which is unsuccessful at capturing the behavior of diffusion-limited growth. In an effort to find a simpler model system, we turned to modelling fitness increases in evolution. The work was motivated by an experiment on vesicular stomatitis virus, a short (˜9600bp) single-stranded RNA virus. A highly bottlenecked viral population increases in fitness rapidly until a certain point, after which the fitness increases at a slower rate. This is well modeled by a constant population reproducing and mutating on a smooth fitness landscape. Mean field theory of this system displays the same infinite propagation velocity blowup as mean field diffusion-limited aggregation. However, we have been able to make progress on a number of fronts. One is solving systems of moment equations, where a hierarchy of moments is truncated arbitrarily at some level. Good results for front propagation velocity are found with just two moments, corresponding to inclusion of the basic finite population clustering effect ignored by mean field theory. In addition, for small mutation rates, most of the population will be entirely on a single site or two adjacent sites, and the density of these cases can be described and solved. (Abstract shortened by UMI.)

Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage

NASA Astrophysics Data System (ADS)

Han, Weimin; Shillor, Meir; Sofonea, Mircea

2001-12-01

We consider a model for quasistatic frictional contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. The contact is modeled with the normal compliance condition and the associated version of Coulomb's law of dry friction. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions.

An Enriched Shell Finite Element for Progressive Damage Simulation in Composite Laminates

NASA Technical Reports Server (NTRS)

McElroy, Mark W.

2016-01-01

A formulation is presented for an enriched shell nite element capable of progressive damage simulation in composite laminates. The element uses a discrete adaptive splitting approach for damage representation that allows for a straightforward model creation procedure based on an initially low delity mesh. The enriched element is veri ed for Mode I, Mode II, and mixed Mode I/II delamination simulation using numerical benchmark data. Experimental validation is performed using test data from a delamination-migration experiment. Good correlation was found between the enriched shell element model results and the numerical and experimental data sets. The work presented in this paper is meant to serve as a rst milestone in the enriched element's development with an ultimate goal of simulating three-dimensional progressive damage processes in multidirectional laminates.

Discrete Element Modeling of Impact Damage on Thermal Barrier Coatings

NASA Astrophysics Data System (ADS)

Minor, Peter Michel

Natural gas turbines have become an increasingly important part of the energy landscape in the United States, currently accounting for 19% of all electricity production. Efforts to increase thermal efficiency in gas turbines has led to the adoption of highly porous ceramic thermal barrier coatings (TBCs), which are susceptible to erosion and foreign object impact damage. Despite significant investment to improve the design of TBCs, few numerical tools exist which are capable of both accurately capturing the specific failure mechanisms inherent to TBCs and iterating design parameters without the requirement for coupled experimental data. To overcome these limitations, a discrete element model (DEM) was created to simulate the microstructure of a TBC using a large-scale assembly of bonded particles. Acting as Lagrangian nodes, the particles can be combined to create accurate representations of TBC geometry and porosity. The inclusion of collision-driven particle dynamics and bonds derived from displacement-dependent force functions endow the microstructure model with the ability to deform and reproduce damage in a highly physical manner. Typical TBC damage mechanisms such as compaction, fracture and spallation occur automatically, without having to tune the model based on experimental observation. Therefore, the first order performance of novel TBC designs and materials can be determined numerically, greatly decreasing the cost of development. To verify the utility and effectiveness of the proposed damage model framework, a nanoindentation materials test simulation was developed to serve as a test case. By varying model parameters, such as the porosity of the TBC and maximum applied indenter force, nanoindentation data from more than one hundred distinct permutations was gathered and analyzed. This data was used to calculate the elastic modulus (E) and hardness (H) of the simulated microstructure, which could then be compared to known experimental material property values. A good correlation was found between the predicted properties calculated by the model and those found through experimental nanoindentation tests. Furthermore, conforming to the benefits of DEM, the model was able to accurately recreate the same material damage characteristics observed in literature, such as the onset of inelastic deformation from fracture.

Numerical investigation of diesel exhaust particle transport and deposition in the CT-scan based lung airway

NASA Astrophysics Data System (ADS)

Islam, Mohammad S.; Saha, Suvash C.; Sauret, Emilie; Gu, Y. T.; Molla, Md Mamun

2017-06-01

Diesel exhaust particulates matter (DEPM) is a compound mixture of gasses and fine particles that contain more than 40 toxic air pollutants including benzene, formaldehyde, and nitrogen oxides. Exposure of DEPM to human lung airway during respiratory inhalation causes severe health hazards like diverse pulmonary diseases. This paper studies the DEPM transport and deposition in upper three generations of the realistic lung airways. A 3-D digital airway bifurcation model is constructed from the computerized tomography (CT) scan data of a healthy adult man. The Euler-Lagrange approach is used to solve the continuum and disperse phases of the calculation. Local averaged Navier-Stokes equations are solved to calculate the transport of the continuum phase. Lagrangian based Discrete Phase Model (DPM) is used to investigate the particle transport and deposition in the current anatomical model. The effects of size specific monodispersed particles on deposition are extensively investigated during different breathing pattern. The numerical results illustrate that particle diameter and breathing pattern have a substantial impact on particles transport and deposition in the tracheobronchial airways. The present realistic bifurcation model also depicts a new deposition hot spot which could advance the understanding of the therapeutic drug delivery system to the specific position of the respiratory airways.

Analysis Methods for Progressive Damage of Composite Structures

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Davila, Carlos G.; Leone, Frank A.

2013-01-01

This document provides an overview of recent accomplishments and lessons learned in the development of general progressive damage analysis methods for predicting the residual strength and life of composite structures. These developments are described within their State-of-the-Art (SoA) context and the associated technology barriers. The emphasis of the authors is on developing these analysis tools for application at the structural level. Hence, modeling of damage progression is undertaken at the mesoscale, where the plies of a laminate are represented as a homogenous orthotropic continuum. The aim of the present effort is establish the ranges of validity of available models, to identify technology barriers, and to establish the foundations of the future investigation efforts. Such are the necessary steps towards accurate and robust simulations that can replace some of the expensive and time-consuming "building block" tests that are currently required for the design and certification of aerospace structures.

Localized end states in density modulated quantum wires and rings.

PubMed

Gangadharaiah, Suhas; Trifunovic, Luka; Loss, Daniel

2012-03-30

We study finite quantum wires and rings in the presence of a charge-density wave gap induced by a periodic modulation of the chemical potential. We show that the Tamm-Shockley bound states emerging at the ends of the wire are stable against weak disorder and interactions, for discrete open chains and for continuum systems. The low-energy physics can be mapped onto the Jackiw-Rebbi equations describing massive Dirac fermions and bound end states. We treat interactions via the continuum model and show that they increase the charge gap and further localize the end states. The electrons placed in the two localized states on the opposite ends of the wire can interact via exchange interactions and this setup can be used as a double quantum dot hosting spin qubits. The existence of these states could be experimentally detected through the presence of an unusual 4π Aharonov-Bohm periodicity in the spectrum and persistent current as a function of the external flux.

Continuum-based DFN-consistent numerical framework for the simulation of oxygen infiltration into fractured crystalline rocks

NASA Astrophysics Data System (ADS)

Trinchero, Paolo; Puigdomenech, Ignasi; Molinero, Jorge; Ebrahimi, Hedieh; Gylling, Björn; Svensson, Urban; Bosbach, Dirk; Deissmann, Guido

2017-05-01

We present an enhanced continuum-based approach for the modelling of groundwater flow coupled with reactive transport in crystalline fractured rocks. In the proposed formulation, flow, transport and geochemical parameters are represented onto a numerical grid using Discrete Fracture Network (DFN) derived parameters. The geochemical reactions are further constrained by field observations of mineral distribution. To illustrate how the approach can be used to include physical and geochemical complexities into reactive transport calculations, we have analysed the potential ingress of oxygenated glacial-meltwater in a heterogeneous fractured rock using the Forsmark site (Sweden) as an example. The results of high-performance reactive transport calculations show that, after a quick oxygen penetration, steady state conditions are attained where abiotic reactions (i.e. the dissolution of chlorite and the homogeneous oxidation of aqueous iron(II) ions) counterbalance advective oxygen fluxes. The results show that most of the chlorite becomes depleted in the highly conductive deformation zones where higher mineral surface areas are available for reactions.

Crack layer theory

NASA Technical Reports Server (NTRS)

Chudnovsky, A.

1984-01-01

A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.

Crack layer theory

NASA Technical Reports Server (NTRS)

Chudnovsky, A.

1987-01-01

A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.

Stochastic-Strength-Based Damage Simulation Tool for Ceramic Matrix and Polymer Matrix Composite Structures

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Bednarcyk, Brett A.; Pineda, Evan J.; Walton, Owen J.; Arnold, Steven M.

2016-01-01

Stochastic-based, discrete-event progressive damage simulations of ceramic-matrix composite and polymer matrix composite material structures have been enabled through the development of a unique multiscale modeling tool. This effort involves coupling three independently developed software programs: (1) the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), (2) the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/ Life), and (3) the Abaqus finite element analysis (FEA) program. MAC/GMC contributes multiscale modeling capabilities and micromechanics relations to determine stresses and deformations at the microscale of the composite material repeating unit cell (RUC). CARES/Life contributes statistical multiaxial failure criteria that can be applied to the individual brittle-material constituents of the RUC. Abaqus is used at the global scale to model the overall composite structure. An Abaqus user-defined material (UMAT) interface, referred to here as "FEAMAC/CARES," was developed that enables MAC/GMC and CARES/Life to operate seamlessly with the Abaqus FEA code. For each FEAMAC/CARES simulation trial, the stochastic nature of brittle material strength results in random, discrete damage events, which incrementally progress and lead to ultimate structural failure. This report describes the FEAMAC/CARES methodology and discusses examples that illustrate the performance of the tool. A comprehensive example problem, simulating the progressive damage of laminated ceramic matrix composites under various off-axis loading conditions and including a double notched tensile specimen geometry, is described in a separate report.

An Analytical Model of Nanometer Scale Viscoelastic Properties of Polymer Surfaces Measured Using an Atomic Force Microscope

DTIC Science & Technology

2011-03-01

efficient partially buoyant cargo airlifters, fuel-efficient hybrid wing- body aircraft, and hyperprecision low-collateral damage munitions [17]. In order to...between the tip and the surface, or between the tip and the small layer of condensed water on the surface [78]. The third method is a continuum model...crystal near the ringing conditions. The second is by applying an alternating voltage to the piezo crystal in the z-direction. The third method is to

An implementation of discrete electron transport models for gold in the Geant4 simulation toolkit

NASA Astrophysics Data System (ADS)

Sakata, D.; Incerti, S.; Bordage, M. C.; Lampe, N.; Okada, S.; Emfietzoglou, D.; Kyriakou, I.; Murakami, K.; Sasaki, T.; Tran, H.; Guatelli, S.; Ivantchenko, V. N.

2016-12-01

Gold nanoparticle (GNP) boosted radiation therapy can enhance the biological effectiveness of radiation treatments by increasing the quantity of direct and indirect radiation-induced cellular damage. As the physical effects of GNP boosted radiotherapy occur across energy scales that descend down to 10 eV, Monte Carlo simulations require discrete physics models down to these very low energies in order to avoid underestimating the absorbed dose and secondary particle generation. Discrete physics models for electron transportation down to 10 eV have been implemented within the Geant4-DNA low energy extension of Geant4. Such models allow the investigation of GNP effects at the nanoscale. At low energies, the new models have better agreement with experimental data on the backscattering coefficient, and they show similar performance for transmission coefficient data as the Livermore and Penelope models already implemented in Geant4. These new models are applicable in simulations focussed towards estimating the relative biological effectiveness of radiation in GNP boosted radiotherapy applications with photon and electron radiation sources.

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface.

PubMed

Chen, Duan; Chen, Zhan; Wei, Guo-Wei

2012-01-01

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.

Granular materials interacting with thin flexible rods

NASA Astrophysics Data System (ADS)

Neto, Alfredo Gay; Campello, Eduardo M. B.

2017-04-01

In this work, we develop a computational model for the simulation of problems wherein granular materials interact with thin flexible rods. We treat granular materials as a collection of spherical particles following a discrete element method (DEM) approach, while flexible rods are described by a large deformation finite element (FEM) rod formulation. Grain-to-grain, grain-to-rod, and rod-to-rod contacts are fully permitted and resolved. A simple and efficient strategy is proposed for coupling the motion of the two types (discrete and continuum) of materials within an iterative time-stepping solution scheme. Implementation details are shown and discussed. Validity and applicability of the model are assessed by means of a few numerical examples. We believe that robust, efficiently coupled DEM-FEM schemes can be a useful tool to the simulation of problems wherein granular materials interact with thin flexible rods, such as (but not limited to) bombardment of grains on beam structures, flow of granular materials over surfaces covered by threads of hair in many biological processes, flow of grains through filters and strainers in various industrial segregation processes, and many others.

Understanding earthquake from the granular physics point of view — Causes of earthquake, earthquake precursors and predictions

NASA Astrophysics Data System (ADS)

Lu, Kunquan; Hou, Meiying; Jiang, Zehui; Wang, Qiang; Sun, Gang; Liu, Jixing

2018-03-01

We treat the earth crust and mantle as large scale discrete matters based on the principles of granular physics and existing experimental observations. Main outcomes are: A granular model of the structure and movement of the earth crust and mantle is established. The formation mechanism of the tectonic forces, which causes the earthquake, and a model of propagation for precursory information are proposed. Properties of the seismic precursory information and its relevance with the earthquake occurrence are illustrated, and principle of ways to detect the effective seismic precursor is elaborated. The mechanism of deep-focus earthquake is also explained by the jamming-unjamming transition of the granular flow. Some earthquake phenomena which were previously difficult to understand are explained, and the predictability of the earthquake is discussed. Due to the discrete nature of the earth crust and mantle, the continuum theory no longer applies during the quasi-static seismological process. In this paper, based on the principles of granular physics, we study the causes of earthquakes, earthquake precursors and predictions, and a new understanding, different from the traditional seismological viewpoint, is obtained.

Multiporosity flow in fractured low-permeability rocks: Extension to shale hydrocarbon reservoirs

DOE PAGES

Kuhlman, Kristopher L.; Malama, Bwalya; Heath, Jason E.

2015-02-05

We presented a multiporosity extension of classical double and triple-porosity fractured rock flow models for slightly compressible fluids. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo steady state and transient interporosity flow double-porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probability mass function. Semianalytical cylindrically symmetric solutions to the multiporosity mathematical model are developed using the Laplace transform tomore » illustrate its behavior. Furthermore, the multiporosity model presented here is conceptually simple, yet flexible enough to simulate common conceptualizations of double and triple-porosity flow. This combination of generality and simplicity makes the multiporosity model a good choice for flow modelling in low-permeability fractured rocks.« less

Constitutive modeling of fiber-reinforced cement composites

NASA Astrophysics Data System (ADS)

Boulfiza, Mohamed

The role of fibers in the enhancement of the inherently low tensile stress and strain capacities of fiber reinforced cementitious composites (FRC) has been addressed through both the phenomenological, using concepts of continuum damage mechanics, and micro-mechanical approaches leading to the development of a closing pressure that could be used in a cohesive crack analysis. The observed enhancements in the matrix behavior is assumed to be related to the ability of the material to transfer stress across cracks. In the micromechanics approach, this is modeled by the introduction of a nonlinear closing pressure at the crack lips. Due to the different nature of cracking in the pre-peak and post peak regimes, two different micro-mechanical models of the cohesive pressure have been proposed, one for the strain hardening stage and another for the strain softening regime. This cohesive pressure is subsequently incorporated into a finite element code so that a nonlinear fracture analysis can be carried out. On top of the fact that a direct fracture analysis has been performed to predict the response of some FRC structural elements, a numerical procedure for the homogenization of FRC materials has been proposed. In this latter approach, a link is established between the cracking taking place at the meso-scale and its mechanical characteristics as represented by the Young's modulus. A parametric study has been carried out to investigate the effect of crack patterning and fiber volume fractions on the overall Young's modulus and the thermodynamic force associated with the tensorial damage variable. After showing the usefulness and power of phenomenological continuum damage mechanics (PCDM) in the prediction of ERC materials' response to a stimuli (loading), a combined PCDM-NLFMsp1 approach is proposed to model (predict, forecast) the complete response of the composite up to failure. Based on experimental observations, this approach assumes that damage mechanics which predicts a diffused damage is more appropriate in the pre-peak regime whereas, NLFM is more suitable in the post-peak stage where the opening and propagation of a major crack will control the response of the material and not a deformation in a continuum sense as opposed to the pre-cracking zone. Tensile and compressive tests have been carried out for the sole purpose of calibrating the constitutive models proposed and/or developed in this thesis for FRC materials. The suitability of the models in predicting the response of different structural members has been performed by comparing the models' forecasts with experimental results carried out by the author, as well as experimental results from the literature. The different models proposed in this thesis have the possibility to account for the presence of fibers in the matrix, and give fairly good results for both high fiber volume fractions (vsb{f}≥2%) and low fiber volume fractions (vsb{f}<2%). Use of interface elements in a finite element code has been shown to be a powerful tool in analyzing the behavior of concrete substrate-FRC repair materials by the introduction of a zero thickness layer of interface elements to account for the interface properties which usually control the effectiveness of the repair material. ftnsp1NLFM: Non Linear Fracture Mechanics.

Interrogating concepts of care in the HIV care continuum: ethnographic insights from the implementation of a "Universal Test and Treat" approach in South Africa.

PubMed

Wademan, Dillon T; Reynolds, Lindsey J

2016-01-01

South Africa currently sustains the largest antiretroviral treatment (ART) programme in the world. The number of people on ART is set to grow even more in the coming years as incidence remains stable, people on ART stay healthy, and guidelines for initiation become increasingly inclusive. The South African public health sector has increasingly relied on community- and home-based lay and professional "carers" to carry out the everyday tasks of rolling out the ART programme. Drawing on ethnographic research in one locality in the Western Cape, the paper explores the care practices of two such groups of carers implementing a 'Universal Test and Treat' (UTT) approach. The UTT approach being evlauated in this place is based on one model of the HIV treatment cascade, or care continuum, which focuses on the steps necessary to identify and link HIV-positive individuals to care and retain them in lifelong HIV treatment. In this context, community-based care workers are responsible for carrying out several discrete steps in the HIV care continuum, including testing people for HIV, linking HIV-positive individuals to care, and supporting adherence. In order to retain clients within the continuum, however, carers also perform other forms of labour that stretch their care work beyond more bounded notions of a stepwise progression of care. These broader forms of care, which can be material, emotional, social or physical in nature, appear alongside the more structured technical and biomedical tasks formally expected of carers. We argue that understanding the dynamics of these more distributed and relational forms of care is essential for the effective implementation of the care continuum, and of the UTT approach, in diverse contexts.

The respective roles of bulk friction and slip velocity during a granular mass flow

NASA Astrophysics Data System (ADS)

Staron, Lydie

2016-04-01

Catastrophic granular mass flows form an important natural hazard. Mitigation has motivated numerous studies on the properties of natural granular flows, and in particular, their ability to travel long distances away from the release point. The mobility of granular flows is commonly characterised through the definition of rheological properties and effective friction. Yet, it is widely accepted that the description in term of effective friction may include various lubrication effects, softening at the base of the flow and large slip velocities being a most likely one. In this case, flow bulk properties may obliterate the flow boundary conditions. In this contribution, we investigate how disentangling bulk properties from boundary conditions may improve our understanding of the flow. Using discrete simulations, we induce increasing slip velocities in different flow configurations. We show that increased mobility may be achieved without changing bulk properties. The results are interpreted in terms of a Robin-Navier slip condition and implemented in a continuum Navier-Stokes solver. We quantify the respective role of rheological bulk properties and boundary conditions in the general behaviour of a transient mass flow. We show that omitting the description of boundary conditions leads to misinterpretation of the flow properties. The outcome is discussed in terms of models reliability. References P.-Y. Lagrée et al, The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes model with the mu(I) rheology, J. Fluid Mech. 686, 378-408 (2011) L. Staron and E. Lajeunesse, Understanding how the volume affects the mobility of dry debris flows, Geophys. Res. Lett. 36, L12402 (2009) L. Staron, Mobility of long-runout rock flows: a discrete numerical investigation, Geophys. J. Int. 172, 455-463 (2008)

Turbulent and Laminar Flow in Karst Conduits Under Unsteady Flow Conditions: Interpretation of Pumping Tests by Discrete Conduit-Continuum Modeling

NASA Astrophysics Data System (ADS)

Giese, M.; Reimann, T.; Bailly-Comte, V.; Maréchal, J.-C.; Sauter, M.; Geyer, T.

2018-03-01

Due to the duality in terms of (1) the groundwater flow field and (2) the discharge conditions, flow patterns of karst aquifer systems are complex. Estimated aquifer parameters may differ by several orders of magnitude from local (borehole) to regional (catchment) scale because of the large contrast in hydraulic parameters between matrix and conduit, their heterogeneity and anisotropy. One approach to deal with the scale effect problem in the estimation of hydraulic parameters of karst aquifers is the application of large-scale experiments such as long-term high-abstraction conduit pumping tests, stimulating measurable groundwater drawdown in both, the karst conduit system as well as the fractured matrix. The numerical discrete conduit-continuum modeling approach MODFLOW-2005 Conduit Flow Process Mode 1 (CFPM1) is employed to simulate laminar and nonlaminar conduit flow, induced by large-scale experiments, in combination with Darcian matrix flow. Effects of large-scale experiments were simulated for idealized settings. Subsequently, diagnostic plots and analyses of different fluxes are applied to interpret differences in the simulated conduit drawdown and general flow patterns. The main focus is set on the question to which extent different conduit flow regimes will affect the drawdown in conduit and matrix depending on the hydraulic properties of the conduit system, i.e., conduit diameter and relative roughness. In this context, CFPM1 is applied to investigate the importance of considering turbulent conditions for the simulation of karst conduit flow. This work quantifies the relative error that results from assuming laminar conduit flow for the interpretation of a synthetic large-scale pumping test in karst.

Modeling and Characterization of Damage Processes in Metallic Materials

NASA Technical Reports Server (NTRS)

Glaessgen, E. H.; Saether, E.; Smith, S. W.; Hochhalter, J. D.; Yamakov, V. I.; Gupta, V.

2011-01-01

This paper describes a broad effort that is aimed at understanding the fundamental mechanisms of crack growth and using that understanding as a basis for designing materials and enabling predictions of fracture in materials and structures that have small characteristic dimensions. This area of research, herein referred to as Damage Science, emphasizes the length scale regimes of the nanoscale and the microscale for which analysis and characterization tools are being developed to predict the formation, propagation, and interaction of fundamental damage mechanisms. Examination of nanoscale processes requires atomistic and discrete dislocation plasticity simulations, while microscale processes can be examined using strain gradient plasticity, crystal plasticity and microstructure modeling methods. Concurrent and sequential multiscale modeling methods are being developed to analytically bridge between these length scales. Experimental methods for characterization and quantification of near-crack tip damage are also being developed. This paper focuses on several new methodologies in these areas and their application to understanding damage processes in polycrystalline metals. On-going and potential applications are also discussed.

Revisiting the continuum hypothesis: toward an in-depth exploration of executive functions in korsakoff syndrome.

PubMed

Brion, Mélanie; Pitel, Anne-Lise; Beaunieux, Hélène; Maurage, Pierre

2014-01-01

Korsakoff syndrome (KS) is a neurological state mostly caused by alcohol-dependence and leading to disproportionate episodic memory deficits. KS patients present more severe anterograde amnesia than Alcohol-Dependent Subjects (ADS), which led to the continuum hypothesis postulating a progressive increase in brain and cognitive damages during the evolution from ADS to KS. This hypothesis has been extensively examined for memory but is still debated for other abilities, notably executive functions (EF). EF have up to now been explored by unspecific tasks in KS, and few studies explored their interactions with memory. Exploring EF in KS by specific tasks based on current EF models could thus renew the exploration of the continuum hypothesis. This paper will propose a research program aiming at: (1) clarifying the extent of executive dysfunctions in KS by tasks focusing on specific EF subcomponents; (2) determining the differential EF deficits in ADS and KS; (3) exploring EF-memory interactions in KS with innovative tasks. At the fundamental level, this exploration will test the continuum hypothesis beyond memory. At the clinical level, it will propose new rehabilitation tools focusing on the EF specifically impaired in KS.

Revisiting the Continuum Hypothesis: Toward an In-Depth Exploration of Executive Functions in Korsakoff Syndrome

PubMed Central

Brion, Mélanie; Pitel, Anne-Lise; Beaunieux, Hélène; Maurage, Pierre

2014-01-01

Korsakoff syndrome (KS) is a neurological state mostly caused by alcohol-dependence and leading to disproportionate episodic memory deficits. KS patients present more severe anterograde amnesia than Alcohol-Dependent Subjects (ADS), which led to the continuum hypothesis postulating a progressive increase in brain and cognitive damages during the evolution from ADS to KS. This hypothesis has been extensively examined for memory but is still debated for other abilities, notably executive functions (EF). EF have up to now been explored by unspecific tasks in KS, and few studies explored their interactions with memory. Exploring EF in KS by specific tasks based on current EF models could thus renew the exploration of the continuum hypothesis. This paper will propose a research program aiming at: (1) clarifying the extent of executive dysfunctions in KS by tasks focusing on specific EF subcomponents; (2) determining the differential EF deficits in ADS and KS; (3) exploring EF-memory interactions in KS with innovative tasks. At the fundamental level, this exploration will test the continuum hypothesis beyond memory. At the clinical level, it will propose new rehabilitation tools focusing on the EF specifically impaired in KS. PMID:25071526

Correcting X-ray spectra obtained from the AXAF VETA-I mirror calibration for pileup, continuum, background and deadtime

NASA Technical Reports Server (NTRS)

Chartas, G.; Flanagan, K.; Hughes, J. P.; Kellogg, E. M.; Nguyen, D.; Zombek, M.; Joy, M.; Kolodziejezak, J.

1993-01-01

The VETA-I mirror was calibrated with the use of a collimated soft X-ray source produced by electron bombardment of various anode materials. The FWHM, effective area and encircled energy were measured with the use of proportional counters that were scanned with a set of circular apertures. The pulsers from the proportional counters were sent through a multichannel analyzer that produced a pulse height spectrum. In order to characterize the properties of the mirror at different discrete photon energies one desires to extract from the pulse height distribution only those photons that originated from the characteristic line emission of the X-ray target source. We have developed a code that fits a modeled spectrum to the observed X-ray data, extracts the counts that originated from the line emission, and estimates the error in these counts. The function that is fitted to the X-ray spectra includes a Prescott function for the resolution of the detector a second Prescott function for a pileup peak and a X-ray continuum function. The continuum component is determined by calculating the absorption of the target Bremsstrahlung through various filters, correcting for the reflectivity of the mirror and convolving with the detector response.

Correcting x ray spectra obtained from the AXAF VETA-I mirror calibration for pileup, continuum, background and deadtime

NASA Technical Reports Server (NTRS)

Chartas, G.; Flanagan, Kathy; Hughes, John P.; Kellogg, Edwin M.; Nguyen, D.; Zombeck, M.; Joy, M.; Kolodziejezak, J.

1992-01-01

The VETA-I mirror was calibrated with the use of a collimated soft X-ray source produced by electron bombardment of various anode materials. The FWHM, effective area and encircled energy were measured with the use of proportional counters that were scanned with a set of circular apertures. The pulsers from the proportional counters were sent through a multichannel analyzer that produced a pulse height spectrum. In order to characterize the properties of the mirror at different discrete photon energies one desires to extract from the pulse height distribution only those photons that originated from the characteristic line emission of the X-ray target source. We have developed a code that fits a modeled spectrum to the observed X-ray data, extracts the counts that originated from the line emission, and estimates the error in these counts. The function that is fitted to the X-ray spectra includes a Prescott function for the resolution of the detector a second Prescott function for a pileup peak and a X-ray continuum function. The continuum component is determined by calculating the absorption of the target Bremsstrahlung through various filters correcting for the reflectivity of the mirror and convolving with the detector response.

A Non-parametric Approach to Constrain the Transfer Function in Reverberation Mapping

NASA Astrophysics Data System (ADS)

Li, Yan-Rong; Wang, Jian-Min; Bai, Jin-Ming

2016-11-01

Broad emission lines of active galactic nuclei stem from a spatially extended region (broad-line region, BLR) that is composed of discrete clouds and photoionized by the central ionizing continuum. The temporal behaviors of these emission lines are blurred echoes of continuum variations (I.e., reverberation mapping, RM) and directly reflect the structures and kinematic information of BLRs through the so-called transfer function (also known as the velocity-delay map). Based on the previous works of Rybicki and Press and Zu et al., we develop an extended, non-parametric approach to determine the transfer function for RM data, in which the transfer function is expressed as a sum of a family of relatively displaced Gaussian response functions. Therefore, arbitrary shapes of transfer functions associated with complicated BLR geometry can be seamlessly included, enabling us to relax the presumption of a specified transfer function frequently adopted in previous studies and to let it be determined by observation data. We formulate our approach in a previously well-established framework that incorporates the statistical modeling of continuum variations as a damped random walk process and takes into account long-term secular variations which are irrelevant to RM signals. The application to RM data shows the fidelity of our approach.

Neutron Capture Gamma-Ray Libraries for Nuclear Applications

NASA Astrophysics Data System (ADS)

Sleaford, B. W.; Firestone, R. B.; Summers, N.; Escher, J.; Hurst, A.; Krticka, M.; Basunia, S.; Molnar, G.; Belgya, T.; Revay, Z.; Choi, H. D.

2011-06-01

The neutron capture reaction is useful in identifying and analyzing the gamma-ray spectrum from an unknown assembly as it gives unambiguous information on its composition. This can be done passively or actively where an external neutron source is used to probe an unknown assembly. There are known capture gamma-ray data gaps in the ENDF libraries used by transport codes for various nuclear applications. The Evaluated Gamma-ray Activation file (EGAF) is a new thermal neutron capture database of discrete line spectra and cross sections for over 260 isotopes that was developed as part of an IAEA Coordinated Research Project. EGAF is being used to improve the capture gamma production in ENDF libraries. For medium to heavy nuclei the quasi continuum contribution to the gamma cascades is not experimentally resolved. The continuum contains up to 90% of all the decay energy and is modeled here with the statistical nuclear structure code DICEBOX. This code also provides a consistency check of the level scheme nuclear structure evaluation. The calculated continuum is of sufficient accuracy to include in the ENDF libraries. This analysis also determines new total thermal capture cross sections and provides an improved RIPL database. For higher energy neutron capture there is less experimental data available making benchmarking of the modeling codes more difficult. We are investigating the capture spectra from higher energy neutrons experimentally using surrogate reactions and modeling this with Hauser-Feshbach codes. This can then be used to benchmark CASINO, a version of DICEBOX modified for neutron capture at higher energy. This can be used to simulate spectra from neutron capture at incident neutron energies up to 20 MeV to improve the gamma-ray spectrum in neutron data libraries used for transport modeling of unknown assemblies.

A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods

NASA Technical Reports Server (NTRS)

Saether, E.; Yamakov, V.; Glaessgen, E.

2007-01-01

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.

Effective particle size from molecular dynamics simulations in fluids

NASA Astrophysics Data System (ADS)

Ju, Jianwei; Welch, Paul M.; Rasmussen, Kim Ø.; Redondo, Antonio; Vorobieff, Peter; Kober, Edward M.

2018-04-01

We report molecular dynamics simulations designed to investigate the effective size of colloidal particles suspended in a fluid in the vicinity of a rigid wall where all interactions are defined by smooth atomic potential functions. These simulations are used to assess how the behavior of this system at the atomistic length scale compares to continuum mechanics models. In order to determine the effective size of the particles, we calculate the solvent forces on spherical particles of different radii as a function of different positions near and overlapping with the atomistically defined wall and compare them to continuum models. This procedure also then determines the effective position of the wall. Our analysis is based solely on forces that the particles sense, ensuring self-consistency of the method. The simulations were carried out using both Weeks-Chandler-Andersen and modified Lennard-Jones (LJ) potentials to identify the different contributions of simple repulsion and van der Waals attractive forces. Upon correction for behavior arising the discreteness of the atomic system, the underlying continuum physics analysis appeared to be correct down to much less than the particle radius. For both particle types, the effective radius was found to be ˜ 0.75σ , where σ defines the length scale of the force interaction (the LJ diameter). The effective "hydrodynamic" radii determined by this means are distinct from commonly assumed values of 0.5σ and 1.0σ , but agree with a value developed from the atomistic analysis of the viscosity of such systems.

Effective particle size from molecular dynamics simulations in fluids

NASA Astrophysics Data System (ADS)

Ju, Jianwei; Welch, Paul M.; Rasmussen, Kim Ø.; Redondo, Antonio; Vorobieff, Peter; Kober, Edward M.

2017-12-01

We report molecular dynamics simulations designed to investigate the effective size of colloidal particles suspended in a fluid in the vicinity of a rigid wall where all interactions are defined by smooth atomic potential functions. These simulations are used to assess how the behavior of this system at the atomistic length scale compares to continuum mechanics models. In order to determine the effective size of the particles, we calculate the solvent forces on spherical particles of different radii as a function of different positions near and overlapping with the atomistically defined wall and compare them to continuum models. This procedure also then determines the effective position of the wall. Our analysis is based solely on forces that the particles sense, ensuring self-consistency of the method. The simulations were carried out using both Weeks-Chandler-Andersen and modified Lennard-Jones (LJ) potentials to identify the different contributions of simple repulsion and van der Waals attractive forces. Upon correction for behavior arising the discreteness of the atomic system, the underlying continuum physics analysis appeared to be correct down to much less than the particle radius. For both particle types, the effective radius was found to be ˜ 0.75σ , where σ defines the length scale of the force interaction (the LJ diameter). The effective "hydrodynamic" radii determined by this means are distinct from commonly assumed values of 0.5σ and 1.0σ , but agree with a value developed from the atomistic analysis of the viscosity of such systems.

Fluid-Structure Interaction in Continuum Models of Bacterial Biofilms

NASA Astrophysics Data System (ADS)

Hicks, Jared A.

Bacterial biofilms are aggregates of cells that adhere to nearly any solid-fluid interface. While many have harmful effects, such as industrial damage and nosocomial infections, certain biofilm species are now generating renewable energy as the fundamental components of Microbial Fuel Cells (MFCs). In an MFC, bacteria consume organic waste and, as they respire, produce free electrons. To do so efficiently, the bacteria must operate at peak metabolic activity, and so require an ample supply of nutrients. But existing MFC systems face several nutrient delivery problems, including clogging and downstream depletion. Ameliorating these problems will require a better understanding of the interplay between structural development and the surrounding fluid flow. In addition to delivering nutrients that affect biofilm growth, the fluid also exerts stresses that cause erosion, detachment, and deformation. These structural changes, in turn, affect the flow and alter the nutrient distribution. To account for this feedback effect, I have developed a continuum model that couples the growth and deformation processes. My model augments an existing growth model with evolution equations derived from Morphoelasticity Theory, by showing that the growth tensor can be directly related to the biofilm velocity potential. This result helps overcome one of the major practical limitations of Morphoelasticity--there is no physical framework for specifying the growth tensor. Through further analysis of the growth tensor, I define the related adjugate and anisotropic growth tensors, which can be more meaningful measures of growth for some models. Under the assumption of small strain, I show that there exists a small correction to the biofilm growth velocity (the accommodation velocity) that represents the effect of the elastic response on the evolution of the biofilm shape. I derive a solvability condition for the accommodation velocity, and show that it leads to a novel evolution equation for stress and strain in the biofilm, which couples the growth and deformation processes. Furthermore, I show that the introduction of a vorticity allows the accommodation velocity to be described by a system of Poisson equations, and that this vorticity arises naturally from Morphoelasticity theory and is related to the velocity solvability condition. I apply the modeling approach to a one-dimensional biofilm, and show that (a) the coupled growth process affects the evolution of the biofilm shape as expected, and (b) a non-coupled approach to biofilm strain introduces an error that grows over time. Numerical analysis of the one-dimensional strain evolution equation leads to several insights that inform the development of numerical methods for the two-dimensional case, including a split-step approach that reduces the fifth-order PDE to an advection equation for strain and a biharmonic equation for stress. Finally, I discuss some useful numerical methods for the simulation of elastic biofilm growth, particularly the discretization of the strain evolution equation(s). My overall approach is to track the evolving biofilm surface using a combination of the level-set method coupled with the eXtended Finite Element Method (XFEM). The major result is a novel mixed-XFEM discretization of the clamped-plate biharmonic equation, which I show to be first-order accurate for the trace of the solution on the interface.