Nonlinear creep damage constitutive model for soft rocks
NASA Astrophysics Data System (ADS)
Liu, H. Z.; Xie, H. Q.; He, J. D.; Xiao, M. L.; Zhuo, L.
2016-06-01
In some existing nonlinear creep damage models, it may be less rigorous to directly introduce a damage variable into the creep equation when the damage variable of the viscous component is a function of time or strain. In this paper, we adopt the Kachanov creep damage rate and introduce a damage variable into a rheological differential constitutive equation to derive an analytical integral solution for the creep damage equation of the Bingham model. We also propose a new nonlinear viscous component which reflects nonlinear properties related to the axial stress of soft rock in the steady-state creep stage. Furthermore, we build an improved Nishihara model by using this new component in series with the correctional Nishihara damage model that describes the accelerating creep, and deduce the rheological constitutive relation of the improved model. Based on superposition principle, we obtain the damage creep equation for conditions of both uniaxial and triaxial compression stress, and study the method for determining the model parameters. Finally, this paper presents the laboratory test results performed on mica-quartz schist in parallel with, or vertical to the schistosity direction, and applies the improved Nishihara model to the parameter identification of mica-quartz schist. Using a comparative analysis with test data, results show that the improved model has a superior ability to reflect the creep properties of soft rock in the decelerating creep stage, the steady-state creep stage, and particularly within the accelerating creep stage, in comparison with the traditional Nishihara model.
Constitutive modeling of solid propellant materials with evolving microstructural damage
NASA Astrophysics Data System (ADS)
Xu, F.; Aravas, N.; Sofronis, P.
Solid propellants are composite materials with complex microstructure. In a generic form, the material consists of polymeric binder, crystal oxidizer (e.g., ammonium perchlorate), and fuel particles (e.g., aluminum). Severe stressing and extreme temperatures induce damage which is manifested in particle cracking, dewetting along particle/polymer interfaces, void nucleation and growth. Damage complicates the overall constitutive response of a solid propellant over and above the complexities associated with the differing constitutive properties of the particle and binder phases. Using rigorous homogenization theory for composite materials, we propose a general 3-D nonlinear macroscopic constitutive law that models microstructural damage evolution upon straining through continuous void formation and growth. The law addresses the viscous deformation rate within the framework of additive decomposition of the deformation rate and the concept of back stress is used to improve the model performance in stress relaxation. No restriction is placed on the magnitude of the strains. Experimental data from the standard relaxation and uniaxial tension tests are used to calibrate the model parameters in the case of a high elongation solid propellant. It is emphasized that the model parameters are descriptors of individual phase constitutive response and criticality conditions for particle decohesion which can systematically be determined through experiment. The model is used to predict the response of the material under more complex loading paths and to investigate the effect of crack tip damage on the mechanical behavior of a compact tension fracture specimen.
Stender, Michael E; Regueiro, Richard A; Klisch, Stephen M; Ferguson, Virginia L
2015-08-01
Traumatic injuries and gradual wear-and-tear of articular cartilage (AC) that can lead to osteoarthritis (OA) have been hypothesized to result from tissue damage to AC. In this study, a previous equilibrium constitutive model of AC was extended to a constitutive damage articular cartilage (CDAC) model. In particular, anisotropic collagen (COL) fibril damage and isotropic glycosaminoglycan (GAG) damage were considered in a 3D formulation. In the CDAC model, time-dependent effects, such as viscoelasticity and poroelasticity, were neglected, and thus all results represent the equilibrium response after all time-dependent effects have dissipated. The resulting CDAC model was implemented in two different finite-element models. The first simulated uniaxial tensile loading to failure, while the second simulated spherical indentation with a rigid indenter displaced into a bilayer AC sample. Uniaxial tension to failure simulations were performed for three COL fibril Lagrangian failure strain (i.e., the maximum elastic COL fibril strain) values of 15%, 30%, and 45%, while spherical indentation simulations were performed with a COL fibril Lagrangian failure strain of 15%. GAG damage parameters were held constant for all simulations. Our results indicated that the equilibrium postyield tensile response of AC and the macroscopic tissue failure strain are highly dependent on COL fibril Lagrangian failure strain. The uniaxial tensile response consisted of an initial nonlinear ramp region due to the recruitment of intact fibrils followed by a rapid decrease in tissue stress at initial COL fibril failure, as a result of COL fibril damage which continued until ultimate tissue failure. In the spherical indentation simulation, damage to both the COL fibril and GAG constituents was located only in the superficial zone (SZ) and near the articular surface with tissue thickening following unloading. Spherical indentation simulation results are in agreement with published experimental
A procedure for utilization of a damage-dependent constitutive model for laminated composites
NASA Technical Reports Server (NTRS)
Lo, David C.; Allen, David H.; Harris, Charles E.
1992-01-01
Described here is the procedure for utilizing a damage constitutive model to predict progressive damage growth in laminated composites. In this model, the effects of the internal damage are represented by strain-like second order tensorial damage variables and enter the analysis through damage dependent ply level and laminate level constitutive equations. The growth of matrix cracks due to fatigue loading is predicted by an experimentally based damage evolutionary relationship. This model is incorporated into a computer code called FLAMSTR. This code is capable of predicting the constitutive response and matrix crack damage accumulation in fatigue loaded laminated composites. The structure and usage of FLAMSTR are presented along with sample input and output files to assist the code user. As an example problem, an analysis of crossply laminates subjected to two stage fatigue loading was conducted and the resulting damage accumulation and stress redistribution were examined to determine the effect of variations in fatigue load amplitude applied during the first stage of the load history. It was found that the model predicts a significant loading history effect on damage evolution.
Constitutive and damage material modeling in a high pressure hydrogen environment
NASA Astrophysics Data System (ADS)
Russell, D. A.; Fritzemeier, L. G.
1991-05-01
Numerous components in reusable space propulsion systems such as the SSME are exposed to high pressure gaseous hydrogen environments. Flow areas and passages in the fuel turbopump, fuel and oxidizer preburners, main combustion chamber, and injector assembly contain high pressure hydrogen either high in purity or as hydrogen rich steam. Accurate constitutive and damage material models applicable to high pressure hydrogen environments are therefore needed for engine design and analysis. Existing constitutive and cyclic crack initiation models were evaluated only for conditions of oxidizing environments. The main objective is to evaluate these models for applicability to high pressure hydrogen environments.
Constitutive and damage material modeling in a high pressure hydrogen environment
NASA Technical Reports Server (NTRS)
Russell, D. A.; Fritzemeier, L. G.
1991-01-01
Numerous components in reusable space propulsion systems such as the SSME are exposed to high pressure gaseous hydrogen environments. Flow areas and passages in the fuel turbopump, fuel and oxidizer preburners, main combustion chamber, and injector assembly contain high pressure hydrogen either high in purity or as hydrogen rich steam. Accurate constitutive and damage material models applicable to high pressure hydrogen environments are therefore needed for engine design and analysis. Existing constitutive and cyclic crack initiation models were evaluated only for conditions of oxidizing environments. The main objective is to evaluate these models for applicability to high pressure hydrogen environments.
A damage-softening statistical constitutive model considering rock residual strength
NASA Astrophysics Data System (ADS)
Wang, Zhi-liang; Li, Yong-chi; Wang, J. G.
2007-01-01
Under stress, the microcracks in rock evolve (initiation, growth and coalescence) from damage to fracture with a continuous process. In order to describe this continuous process, a damage-softening statistical constitutive model for rock was proposed based on the Weibull distribution of mesoscopic element strength. This model usually adopts the Drucker-Prager criterion as its distribution parameter of mesoscopic element strength, which may produce larger damage zone in numerical simulations. This paper mainly studies the effects of strength criteria and residual strength on the performance of this damage-softening statistical constitutive model of rock. Main works include following three aspects: Firstly, the mechanical behaviors of rock are comparatively studied when the Drucker-Prager and the Mohr-Coulomb criteria are employed, respectively, as the distribution parameter. Then, a coefficient is introduced to make this constitutive model be capable of describing the residual strength of rock. Finally, a user-defined subroutine is concisely developed for this model and checked through typical strain paths. The current work lays a good foundation for further application of this model in geotechnics and geosciences.
Ma, Songyun; Scheider, Ingo; Bargmann, Swantje
2016-09-01
An anisotropic constitutive model is proposed in the framework of finite deformation to capture several damage mechanisms occurring in the microstructure of dental enamel, a hierarchical bio-composite. It provides the basis for a homogenization approach for an efficient multiscale (in this case: multiple hierarchy levels) investigation of the deformation and damage behavior. The influence of tension-compression asymmetry and fiber-matrix interaction on the nonlinear deformation behavior of dental enamel is studied by 3D micromechanical simulations under different loading conditions and fiber lengths. The complex deformation behavior and the characteristics and interaction of three damage mechanisms in the damage process of enamel are well captured. The proposed constitutive model incorporating anisotropic damage is applied to the first hierarchical level of dental enamel and validated by experimental results. The effect of the fiber orientation on the damage behavior and compressive strength is studied by comparing micro-pillar experiments of dental enamel at the first hierarchical level in multiple directions of fiber orientation. A very good agreement between computational and experimental results is found for the damage evolution process of dental enamel. PMID:27294283
NASA Astrophysics Data System (ADS)
Augustins, L.; Billardon, R.; Hild, F.
2016-01-01
The present paper details an elasto-viscoplastic constitutive model for automotive brake discs made of flake graphite cast iron. In a companion paper (Augustins et al. in Contin Mech Thermodyn, 2015), the authors proposed a one-dimensional setting appropriate for representing the complex behavior of the material (i.e., asymmetry between tensile and compressive loadings) under anisothermal conditions. The generalization of this 1D model to 3D cases on a volume element and the associated challenges are addressed. A direct transposition is not possible, and an alternative solution without unilateral conditions is first proposed. Induced anisotropic damage and associated constitutive laws are then introduced. The transition from the volume element to the real structure and the numerical implementation require a specific basis change. Brake disc simulations with this constitutive model show that unilateral conditions are needed for the friction bands. A damage deactivation procedure is therefore defined.
NASA Astrophysics Data System (ADS)
Revil-Baudard, Benoit; Cazacu, Oana; Flater, Philip; Chandola, Nitin; Alves, J. L.
2016-03-01
In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen, and is diffuse; the level of damage close to failure being very low. On the other hand, for a notched specimen subject to the same loading the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.
NASA Astrophysics Data System (ADS)
Chaabane, Makram; Chaabane, Makram; Dalverny, Olivier; Deramecourt, Arnaud; Mistou, SÃ©bastien
The super-pressure balloons developed by CNES are a great challenge in scientific ballooning. Whatever the balloon type considered (spherical, pumpkin...), it is necessary to have good knowledge of the mechanical behavior of the envelope regarding to the flight level and the lifespan of the balloon. It appears during the working stages of the super pressure balloons that these last can exploded prematurely in the course of the first hours of flight. For this reason CNES and LGP are carrying out research programs about experimentations and modelling in order to predict a good stability of the balloons flight and guarantee a life time in adequacy with the technical requirement. This study deals with multilayered polymeric film damage which induce balloons failure. These experimental and numerical study aims, are a better understanding and predicting of the damage mechanisms bringing the premature explosion of balloons. The following damages phenomena have different origins. The firsts are simple and triple wrinkles owed during the process and the stocking stages of the balloons. The second damage phenomenon is associated to the creep of the polymeric film during the flight of the balloon. The first experimental results we present in this paper, concern the mechanical characterization of three different damage phenomena. The severe damage induced by the wrinkles of the film involves a significant loss of mechanical properties. In a second part the theoretical study, concerns the choice and the development of a non linear viscoelastic coupled damage behavior model in a finite element code.
Interpretation of the Superpave IDT strength test using a viscoelastic-damage constitutive model
NASA Astrophysics Data System (ADS)
Onifade, Ibrahim; Balieu, Romain; Birgisson, Bjorn
2016-03-01
This paper presents a new interpretation for the Superpave IDT strength test based on a viscoelastic-damage framework. The framework is based on continuum damage mechanics and the thermodynamics of irreversible processes with an anisotropic damage representation. The new approach introduces considerations for the viscoelastic effects and the damage accumulation that accompanies the fracture process in the interpretation of the Superpave IDT strength test for the identification of the Dissipated Creep Strain Energy (DCSE) limit from the test result. The viscoelastic model is implemented in a Finite Element Method (FEM) program for the simulation of the Superpave IDT strength test. The DCSE values obtained using the new approach is compared with the values obtained using the conventional approach to evaluate the validity of the assumptions made in the conventional interpretation of the test results. The result shows that the conventional approach over-estimates the DCSE value with increasing estimation error at higher deformation rates.
Interpretation of the Superpave IDT strength test using a viscoelastic-damage constitutive model
NASA Astrophysics Data System (ADS)
Onifade, Ibrahim; Balieu, Romain; Birgisson, Bjorn
2016-08-01
This paper presents a new interpretation for the Superpave IDT strength test based on a viscoelastic-damage framework. The framework is based on continuum damage mechanics and the thermodynamics of irreversible processes with an anisotropic damage representation. The new approach introduces considerations for the viscoelastic effects and the damage accumulation that accompanies the fracture process in the interpretation of the Superpave IDT strength test for the identification of the Dissipated Creep Strain Energy (DCSE) limit from the test result. The viscoelastic model is implemented in a Finite Element Method (FEM) program for the simulation of the Superpave IDT strength test. The DCSE values obtained using the new approach is compared with the values obtained using the conventional approach to evaluate the validity of the assumptions made in the conventional interpretation of the test results. The result shows that the conventional approach over-estimates the DCSE value with increasing estimation error at higher deformation rates.
Probabilistic constitutive law for damage in ligaments.
Guo, Zheying; De Vita, Raffaella
2009-11-01
A new constitutive equation is presented to describe the damage evolution process in parallel-fibered collagenous tissues such as ligaments. The model is formulated by accounting for the fibrous structure of the tissues. The tissue's stress is defined as the average of the collagen fiber's stresses. The fibers are assumed to be undulated and straightened out at different stretches that are randomly defined according to a Weibull distribution. After becoming straight, each collagen fiber is assumed to be linear elastic. Damage is defined as a reduction in collagen fiber's stiffness and occurs at different stretches that are also randomly defined by a Weibull distribution. Due to the lack of experimental data, the predictions of the constitutive equation are analyzed by varying the values of its structural parameters. Moreover, the results are compared with the available stress-strain data in the biomechanics literature that evaluate damage produced by subfailure stretches in rat medial collateral ligaments. PMID:19665914
Crushed Salt Constitutive Model
Callahan, G.D.
1999-02-01
The constitutive model used to describe the deformation of crushed salt is presented in this report. Two mechanisms -- dislocation creep and grain boundary diffusional pressure solution -- are combined to form the basis for the constitutive model governing the deformation of crushed salt. The constitutive model is generalized to represent three-dimensional states of stress. Upon complete consolidation, the crushed-salt model reproduces the Multimechanism Deformation (M-D) model typically used for the Waste Isolation Pilot Plant (WIPP) host geological formation salt. New shear consolidation tests are combined with an existing database that includes hydrostatic consolidation and shear consolidation tests conducted on WIPP and southeastern New Mexico salt. Nonlinear least-squares model fitting to the database produced two sets of material parameter values for the model -- one for the shear consolidation tests and one for a combination of the shear and hydrostatic consolidation tests. Using the parameter values determined from the fitted database, the constitutive model is validated against constant strain-rate tests. Shaft seal problems are analyzed to demonstrate model-predicted consolidation of the shaft seal crushed-salt component. Based on the fitting statistics, the ability of the model to predict the test data, and the ability of the model to predict load paths and test data outside of the fitted database, the model appears to capture the creep consolidation behavior of crushed salt reasonably well.
The constitutive representation of high-temperature creep damage
NASA Technical Reports Server (NTRS)
Chan, K. S.
1988-01-01
The elastic-viscoplastic constitutive equations of Bodner-Partom were applied to modeling creep damage in a high temperature Ni-alloy, B1900 + Hf. Both tertiary creep in bulk materials and creep crack growth in flawed materials were considered. In the latter case, the energy rate line integral was used for characterizing the crack driving force, and the rate of crack extension was computed using a local damage formulation that assumed fracture was controlled by cavitation occurring within the crack-tip process zone. The results of this investigation were used to assess the evolution equation for isotropic damage utilized in the Bodner-Partom constitutive equations.
Constitutive representation of damage development and healing in WIPP salt
Chan, K.S.; Bodner, S.R.; Fossum, A.F
1994-12-31
There has been considerable interest in characterizing and modeling the constitutive behavior of rock salt with particular reference to long-term creep and creep failure. The interest is motivated by the projected use of excavated rooms in salt rock formations as repositories for nuclear waste. It is presumed that closure of those rooms by creep ultimately would encapsulate the waste material, resulting in its effective isolation. A continuum mechanics approach for treating damage healing is formulated as part of a constitutive model for describing coupled creep, fracture, and healing in rock salt. Formulation of the healing term is, described and the constitutive model is evaluated against experimental data of rock salt from the Waste Isolation Pilot Plant (WIPP) site. The results indicate that healing anistropy in WIPP salt can be modeled with an appropriate power-conjugate equivalent stress, kinetic equation, and evolution equation for damage healing.
Hammerand, Daniel Carl; Scherzinger, William Mark
2007-09-01
The Library of Advanced Materials for Engineering (LAME) provides a common repository for constitutive models that can be used in computational solid mechanics codes. A number of models including both hypoelastic (rate) and hyperelastic (total strain) constitutive forms have been implemented in LAME. The structure and testing of LAME is described in Scherzinger and Hammerand ([3] and [4]). The purpose of the present report is to describe the material models which have already been implemented into LAME. The descriptions are designed to give useful information to both analysts and code developers. Thus far, 33 non-ITAR/non-CRADA protected material models have been incorporated. These include everything from the simple isotropic linear elastic models to a number of elastic-plastic models for metals to models for honeycomb, foams, potting epoxies and rubber. A complete description of each model is outside the scope of the current report. Rather, the aim here is to delineate the properties, state variables, functions, and methods for each model. However, a brief description of some of the constitutive details is provided for a number of the material models. Where appropriate, the SAND reports available for each model have been cited. Many models have state variable aliases for some or all of their state variables. These alias names can be used for outputting desired quantities. The state variable aliases available for results output have been listed in this report. However, not all models use these aliases. For those models, no state variable names are listed. Nevertheless, the number of state variables employed by each model is always given. Currently, there are four possible functions for a material model. This report lists which of these four methods are employed in each material model. As far as analysts are concerned, this information is included only for the awareness purposes. The analyst can take confidence in the fact that model has been properly implemented
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Lindholm, U. S.
1984-01-01
A state-of-the-art review of applicable constitutive models with selection of two for detailed comparison with a wide range of experimental tests was conducted. The experimental matrix contained uniaxial and biaxial tensile, creep, stress relaxation, and cyclic fatigue tests at temperatures to 1093 C and strain rates from .0000001 to .001/sec. Some nonisothermal cycles will also be run. The constitutive models will be incorporated into the MARC finite element structural analysis program with a demonstration computation made for advanced turbine blade configuration. In the code development work, particular emphasis is being placed on developing efficient integration algorithms for the highly nonlinear and stiff constitutive equations. Another area of emphasis is the appropriate and efficient methodology for determing constitutive constants from a minimum extent of experimental data.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Lindholm, Ulric S.
1985-01-01
The objective is to develop a unified constitutive model for finite element structural analysis of turbine engine hot-section components. This effort constitutes a different approach for non-linear finite-element computer codes which have heretofore been based on classical inelastic methods. The unified constitutive theory to be developed will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. During the first two years of the program, extensive experimental correlations were made with two representative unified models. The experiments were both uniaxial and biaxial at temperatures up to 1093 C (2000 F). In addition, the unified models were adopted to the MARC finite element code and used for stress analysis of notched bar and turbine blade geometries.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Chan, K. S.; Lindholm, U. S.; Bodner, S. R.
1988-01-01
The third and fourth years of a 4-year research program, part of the NASA HOST Program, are described. The program goals were: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analysis of hot section components of gas turbine engines. The unified models selected for development and evaluation were those of Bodner-Partom and of Walker. The unified approach for elastic-viscoplastic constitutive equations is a viable method for representing and predicting material response characteristics in the range where strain rate and temperature dependent inelastic deformations are experienced. This conclusion is reached by extensive comparison of model calculations against the experimental results of a test program of two high temperature Ni-base alloys, B1900+Hf and Mar-M247, over a wide temperature range for a variety of deformation and thermal histories including uniaxial, multiaxial, and thermomechanical loading paths. The applicability of the Bodner-Partom and the Walker models for structural applications has been demonstrated by implementing these models into the MARC finite element code and by performing a number of analyses including thermomechanical histories on components of hot sections of gas turbine engines and benchmark notch tensile specimens. The results of the 4-year program have been published in four annual reports. The results of the base program are summarized in this report. The tasks covered include: (1) development of material test procedures, (2) thermal history effects, and (3) verification of the constitutive model for an alternative material.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Lindholm, Ulric S.; Chan, Kwai S.
1986-01-01
The objective of the program is to evaluate and develop existing constitutive models for use in finite-element structural analysis of turbine engine hot section components. The class of constitutive equation studied is considered unified in that all inelastic deformation including plasticity, creep, and stress relaxation are treated in a single term rather than a classical separation of plasticity (time independent) and creep (time dependent) behavior. The unified theories employed also do not utilize the classical yield surface or plastic potential concept. The models are constructed from an appropriate flow law, a scalar kinetic relation between strain rate, temperature and stress, and evolutionary equations for internal variables describing strain or work hardening, both isotropic and directional (kinematic). This and other studies have shown that the unified approach is particularly suited for determining the cyclic behavior of superalloy type blade and vane materials and is entirely compatible with three-dimensional inelastic finite-element formulations. The behavior was examined of a second nickel-base alloy, MAR-M247, and compared it with the Bodner-Partom model, further examined procedures for determining the material-specific constants in the models, and exercised the MARC code for a turbine blade under simulated flight spectrum loading. Results are summarized.
Testing of constitutive models in LAME.
Hammerand, Daniel Carl; Scherzinger, William Mark
2007-09-01
Constitutive models for computational solid mechanics codes are in LAME--the Library of Advanced Materials for Engineering. These models describe complex material behavior and are used in our finite deformation solid mechanics codes. To ensure the correct implementation of these models, regression tests have been created for constitutive models in LAME. A selection of these tests is documented here. Constitutive models are an important part of any solid mechanics code. If an analysis code is meant to provide accurate results, the constitutive models that describe the material behavior need to be implemented correctly. Ensuring the correct implementation of constitutive models is the goal of a testing procedure that is used with the Library of Advanced Materials for Engineering (LAME) (see [1] and [2]). A test suite for constitutive models can serve three purposes. First, the test problems provide the constitutive model developer a means to test the model implementation. This is an activity that is always done by any responsible constitutive model developer. Retaining the test problem in a repository where the problem can be run periodically is an excellent means of ensuring that the model continues to behave correctly. A second purpose of a test suite for constitutive models is that it gives application code developers confidence that the constitutive models work correctly. This is extremely important since any analyst that uses an application code for an engineering analysis will associate a constitutive model in LAME with the application code, not LAME. Therefore, ensuring the correct implementation of constitutive models is essential for application code teams. A third purpose of a constitutive model test suite is that it provides analysts with example problems that they can look at to understand the behavior of a specific model. Since the choice of a constitutive model, and the properties that are used in that model, have an enormous effect on the results of an
CONSTITUTIVE RELATIONSHIP OF TISSUE BEHAVIOR WITH DAMAGE ACCUMULATION OF HUMAN CORTICAL BONE
Luo, Qing; Leng, Huijie; Acuna, Rae; Dong, Xuanliang; Rong, Qiguo; Wang, Xiaodu
2010-01-01
Microdamage accumulation has been identified as a major conduit for bone tissues to absorb fracture energy. Due to the poor understanding of its underlying mechanism, however, an adequate constitutive relationship between damage accumulation and the mechanical behavior of bone has not yet been established. In this study, the constitutive relationship between the damage accumulation induced by overload and the evolution of mechanical properties of bone with incremental deformation was established based on the experimental results obtained from a novel progressive loading protocol developed in our laboratory. First, a decayed exponential model was proposed to capture the damage accumulation (modulus loss) with increasing applied strain. Next, a power law function was proposed to represent the progression of plastic deformation with damage accumulation. Finally, a linear combination of the Kohlrausch-Williams-Watts (KWW) function and Debye function was used to depict the viscoelastic behavior of bone associated with damage accumulation. The results of this study may help develop a constitutive model for predicting the mechanical behavior of cortical bone tissues. PMID:20472239
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Ramaswamy, V. G.; Vanstone, R. H.; Dame, L. T.; Laflen, J. H.
1985-01-01
The first year of progress on a NASA-Lewis contract with the General Electric Co is documented. The purpose of this contract (NAS3-23927) is to develop and evaluate unified constitutive equations for applications to hot-path components of aircraft gas turbine engines such as high pressure turbine blades and vanes. To accomplish this goal, uniaxial, notched, and multiaxial specimens made of conventionally cast Rene 80 are being tested under conditions that simulate engine operating conditions. To reduce the raw data, automated data reduction techniques are being developed that produce computer files containing the information needed to analyze proposed constitutive theories. Described are the analytical methods being developed to determine the parameters for these nonlinear unified theories by using the reduced data files. In another activity, a dedicated finite-element computer code is being developed to use unified theories in the structural analysis of hot-section components. This code was extensively verified for one such theory by successfully predicting the strain histories measured experimentally at the notch root of complex specimens taken from complex laboratory specimens.
Constitutive modeling of inelastic anisotropic material response
NASA Technical Reports Server (NTRS)
Stouffer, D. C.
1984-01-01
A constitutive equation was developed to predict the inelastic thermomechanical response of single crystal turbine blades. These equations are essential for developing accurate finite element models of hot section components and contribute significantly to the understanding and prediction of crack initiation and propagation. The method used was limited to unified state variable constitutive equations. Two approaches to developing an anisotropic constitutive equation were reviewed. One approach was to apply the Stouffer-Bodner representation for deformation induced anisotropy to materials with an initial anisotropy such as single crystals. The second approach was to determine the global inelastic strain rate from the contribution of the slip in each of the possible crystallographic slip systems. A three dimensional finite element is being developed with a variable constitutive equation link that can be used for constitutive equation development and to predict the response of an experiment using the actual specimen geometry and loading conditions.
Crushed-salt constitutive model update
Callahan, G.D.; Loken, M.C.; Mellegard, K.D.
1998-01-01
Modifications to the constitutive model used to describe the deformation of crushed salt are presented in this report. Two mechanisms--dislocation creep and grain boundary diffusional pressure solutioning--defined previously but used separately are combined to form the basis for the constitutive model governing the deformation of crushed salt. The constitutive model is generalized to represent three-dimensional states of stress. New creep consolidation tests are combined with an existing database that includes hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant and southeastern New Mexico salt to determine material parameters for the constitutive model. Nonlinear least-squares model fitting to data from the shear consolidation tests and a combination of the shear and hydrostatic consolidation tests produced two sets of material parameter values for the model. The change in material parameter values from test group to test group indicates the empirical nature of the model but demonstrates improvement over earlier work with the previous models. Key improvements are the ability to capture lateral strain reversal and better resolve parameter values. To demonstrate the predictive capability of the model, each parameter value set was used to predict each of the tests in the database. Based on the fitting statistics and the ability of the model to predict the test data, the model appears to capture the creep consolidation behavior of crushed salt quite well.
New Damage Remedies for Violations of Constitutional Rights.
ERIC Educational Resources Information Center
Russell, Billy W.
1979-01-01
Examines the concept of sovereign (governmental) immunity from prosecution for violating citizens' civil liberties. Attention is given to immunity under 42 U.S.C.A. Section 1983 and under the Constitution. Available from Baylor University Law School, Waco, Texas 76703; sc $4.00. (IRT)
A constitutive mechanical model for energetic materials
Hobbs, M.L.; Baer, M.R.; Gross, R.J.
1994-06-01
Cookoff modeling of energetic materials has traditionally addressed reactive heat flow with the goal of defining the onset of runaway combustion behavior. Current modeling efforts are now aimed toward predicting the violence of the event. Combined thermal, chemical, and mechanical response must be modeled, since confinement results in pressure buildup which can breach confinement or enhance gas-phase combustion rates leading to runaway combustion behavior. Thermally induced stresses can also cause gaps which inhibit heat flow. These mechanical effects must also be included in cookoff modeling. A new reactive elastic-plastic constitutive model for micromechanical response has been developed which represents a stress-strain relation for reacting materials such as explosives, propellants, pyrotechnics, or burning foams. This micromechanical model is based on bubble mechanics. A local force balance, with mass continuity constraints, forms the basis of the constitutive model requiring input of temperature and reacted fraction. This constitutive material model has been incorporated into a quasistatic mechanics code, SANTOS. To provide temperature and reacted gas fraction, the thermal-chemical solver, XCHEM, has been coupled to SANTOS. This paper summarizes the development of the micromechanical model with material property estimates for conventional energetic materials. This study shows that large pressures can arise from small reacted fractions which implies that cookoff modeling must consider the strong interaction between thermochemistry and mechanics.
Relationships among certain joint constitutive models.
Segalman, Daniel Joseph; Starr, Michael James
2004-09-01
In a recent paper, Starr and Segalman demonstrated that any Masing model can be represented as a parallel-series Iwan model. A preponderance of the constitutive models that have been suggested for simulating mechanical joints are Masing models, and the purpose of this discussion is to demonstrate how the Iwan representation of those models can yield insight into their character. In particular, this approach can facilitate a critical comparison among numerous plausible constitutive models. It is explicitly shown that three-parameter models such as Smallwood's (Ramberg-Osgood) calculate parameters in such a manner that macro-slip is not an independent parameter, yet the model admits macro-slip. The introduction of a fourth parameter is therefore required. It is shown that when a macro-slip force is specified for the Smallwood model the result is a special case of the Segalman four-parameter model. Both of these models admit a slope discontinuity at the inception of macro-slip. A five-parameter model that has the beneficial features of Segalman's four-parameter model is proposed. This model manifests a force-displacement curve having a continuous first derivative.
Cumulative fatigue damage models
NASA Technical Reports Server (NTRS)
Mcgaw, Michael A.
1988-01-01
The problem of calculating expected component life under fatigue loading conditions is complicated by the fact that component loading histories contain, in many cases, cyclic loads of widely varying amplitudes. In such a case a cumulative damage model is required, in addition to a fatigue damage criterion, or life relationship, in order to compute the expected fatigue life. The traditional cumulative damage model used in design is the linear damage rule. This model, while being simple to use, can yield grossly unconservative results under certain loading conditions. Research at the NASA Lewis Research Center has led to the development of a nonlinear cumulative damage model, named the double damage curve approach (DDCA), that has greatly improved predictive capability. This model, which considers the life (or loading) level dependence of damage evolution, was applied successfully to two polycrystalline materials, 316 stainless steel and Haynes 188. The cumulative fatigue behavior of the PWA 1480 single-crystal material is currently being measured to determine the applicability of the DDCA for this material.
Evaluation of constitutive models for crushed salt
Callahan, G.D.; Loken, M.C. [RE Hurtado, L.D.; Hansen, F.D.
1996-05-01
Three constitutive models are recommended as candidates for describing the deformation of crushed salt. These models are generalized to three-dimensional states of stress to include the effects of mean and deviatoric stress and modified to include effects of temperature, grain size, and moisture content. A database including hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant (WIPP) and southeastern New Mexico salt is used to determine material parameters for the models. To evaluate the capability of the models, parameter values obtained from fitting the complete database are used to predict the individual tests. Finite element calculations of a WIPP shaft with emplaced crushed salt demonstrate the model predictions.
Constitutive Modeling of Crosslinked Nanotube Materials
NASA Technical Reports Server (NTRS)
Odegard, G. M.; Frankland, S. J. V.; Herzog, M. N.; Gates, T. S.; Fay, C. C.
2004-01-01
A non-linear, continuum-based constitutive model is developed for carbon nanotube materials in which bundles of aligned carbon nanotubes have varying amounts of crosslinks between the nanotubes. The model accounts for the non-linear elastic constitutive behavior of the material in terms of strain, and is developed using a thermodynamic energy approach. The model is used to examine the effect of the crosslinking on the overall mechanical properties of variations of the crosslinked carbon nanotube material with varying degrees of crosslinking. It is shown that the presence of the crosslinks has significant effects on the mechanical properties of the carbon nanotube materials. An increase in the transverse shear properties is observed when the nanotubes are crosslinked. However, this increase is accompanied by a decrease in axial mechanical properties of the nanotube material upon crosslinking.
Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage
Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu
2007-05-17
Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix - WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material.
Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage
NASA Astrophysics Data System (ADS)
Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu
2007-05-01
Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix â€” WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material.
Constitutive modeling for isotropic materials (HOST)
NASA Technical Reports Server (NTRS)
Lindholm, Ulric S.; Chan, Kwai S.; Bodner, S. R.; Weber, R. M.; Walker, K. P.; Cassenti, B. N.
1984-01-01
The results of the first year of work on a program to validate unified constitutive models for isotropic materials utilized in high temperature regions of gas turbine engines and to demonstrate their usefulness in computing stress-strain-time-temperature histories in complex three-dimensional structural components. The unified theories combine all inelastic strain-rate components in a single term avoiding, for example, treating plasticity and creep as separate response phenomena. An extensive review of existing unified theories is given and numerical methods for integrating these stiff time-temperature-dependent constitutive equations are discussed. Two particular models, those developed by Bodner and Partom and by Walker, were selected for more detailed development and evaluation against experimental tensile, creep and cyclic strain tests on specimens of a cast nickel base alloy, B19000+Hf. Initial results comparing computed and test results for tensile and cyclic straining for temperature from ambient to 982 C and strain rates from 10(exp-7) 10(exp-3) s(exp-1) are given. Some preliminary date correlations are presented also for highly non-proportional biaxial loading which demonstrate an increase in biaxial cyclic hardening rate over uniaxial or proportional loading conditions. Initial work has begun on the implementation of both constitutive models in the MARC finite element computer code.
Constitutive modeling for isotropic materials (HOST)
NASA Technical Reports Server (NTRS)
Chan, Kwai S.; Lindholm, Ulric S.; Bodner, S. R.; Hill, Jeff T.; Weber, R. M.; Meyer, T. G.
1986-01-01
The results of the third year of work on a program which is part of the NASA Hot Section Technology program (HOST) are presented. The goals of this program are: (1) the development of unified constitutive models for rate dependent isotropic materials; and (2) the demonstration of the use of unified models in structural analyses of hot section components of gas turbine engines. The unified models selected for development and evaluation are those of Bodner-Partom and of Walker. A test procedure was developed for assisting the generation of a data base for the Bodner-Partom model using a relatively small number of specimens. This test procedure involved performing a tensile test at a temperature of interest that involves a succession of strain-rate changes. The results for B1900+Hf indicate that material constants related to hardening and thermal recovery can be obtained on the basis of such a procedure. Strain aging, thermal recovery, and unexpected material variations, however, preluded an accurate determination of the strain-rate sensitivity parameter is this exercise. The effects of casting grain size on the constitutive behavior of B1900+Hf were studied and no particular grain size effect was observed. A systematic procedure was also developed for determining the material constants in the Bodner-Partom model. Both the new test procedure and the method for determining material constants were applied to the alternate material, Mar-M247 . Test data including tensile, creep, cyclic and nonproportional biaxial (tension/torsion) loading were collected. Good correlations were obtained between the Bodner-Partom model and experiments. A literature survey was conducted to assess the effects of thermal history on the constitutive behavior of metals. Thermal history effects are expected to be present at temperature regimes where strain aging and change of microstructure are important. Possible modifications to the Bodner-Partom model to account for these effects are outlined
Constitutive modeling for isotropic materials (HOST)
NASA Technical Reports Server (NTRS)
Lindholm, U. S.; Chan, K. S.; Bodner, S. R.; Weber, R. M.; Walker, K. P.; Cassenti, B. N.
1985-01-01
This report presents the results of the second year of work on a problem which is part of the NASA HOST Program. Its goals are: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analyses of hot section components of gas turbine engines. The unified models selected for development and evaluation are that of Bodner-Partom and Walker. For model evaluation purposes, a large constitutive data base is generated for a B1900 + Hf alloy by performing uniaxial tensile, creep, cyclic, stress relation, and thermomechanical fatigue (TMF) tests as well as biaxial (tension/torsion) tests under proportional and nonproportional loading over a wide range of strain rates and temperatures. Systematic approaches for evaluating material constants from a small subset of the data base are developed. Correlations of the uniaxial and biaxial tests data with the theories of Bodner-Partom and Walker are performed to establish the accuracy, range of applicability, and integability of the models. Both models are implemented in the MARC finite element computer code and used for TMF analyses. Benchmark notch round experiments are conducted and the results compared with finite-element analyses using the MARC code and the Walker model.
NASA Astrophysics Data System (ADS)
Labergere, C.; Saanouni, K.; Benafia, S.; Galmiche, J.; Sulaiman, H.
2013-05-01
This paper presents the modelling and adaptive numerical simulation of the fine blanking process. Thermodynamically-consistent constitutive equations, strongly coupled with ductile damage, together with specific boundary conditions (particular command of forces on blank holder and counterpunch) are presented. This model is implemented into ABAQUS/EXPLICIT using the Vumat user subroutine and connected with an adaptive 2D remeshing procedure. The different material parameters are identified for the steel S600MC using experimental tensile tests conducted until the final fracture. A parametric study aiming to examine the sensitivity of the process parameters (die radius, clearance die/punch) to the punch force and fracture surfaces topology (convex zone, sheared zone, fracture zone and the burr).
Constitutive modelling of composite biopolymer networks.
Fallqvist, B; Kroon, M
2016-04-21
The mechanical behaviour of biopolymer networks is to a large extent determined at a microstructural level where the characteristics of individual filaments and the interactions between them determine the response at a macroscopic level. Phenomena such as viscoelasticity and strain-hardening followed by strain-softening are observed experimentally in these networks, often due to microstructural changes (such as filament sliding, rupture and cross-link debonding). Further, composite structures can also be formed with vastly different mechanical properties as compared to the individual networks. In this present paper, we present a constitutive model presented in a continuum framework aimed at capturing these effects. Special care is taken to formulate thermodynamically consistent evolution laws for dissipative effects. This model, incorporating possible anisotropic network properties, is based on a strain energy function, split into an isochoric and a volumetric part. Generalisation to three dimensions is performed by numerical integration over the unit sphere. Model predictions indicate that the constitutive model is well able to predict the elastic and viscoelastic response of biological networks, and to an extent also composite structures. PMID:26851172
Multiscale Constitutive Modeling of Asphalt Concrete
NASA Astrophysics Data System (ADS)
Underwood, Benjamin Shane
Multiscale modeling of asphalt concrete has become a popular technique for gaining improved insight into the physical mechanisms that affect the material's behavior and ultimately its performance. This type of modeling considers asphalt concrete, not as a homogeneous mass, but rather as an assemblage of materials at different characteristic length scales. For proper modeling these characteristic scales should be functionally definable and should have known properties. Thus far, research in this area has not focused significant attention on functionally defining what the characteristic scales within asphalt concrete should be. Instead, many have made assumptions on the characteristic scales and even the characteristic behaviors of these scales with little to no support. This research addresses these shortcomings by directly evaluating the microstructure of the material and uses these results to create materials of different characteristic length scales as they exist within the asphalt concrete mixture. The objectives of this work are to; 1) develop mechanistic models for the linear viscoelastic (LVE) and damage behaviors in asphalt concrete at different length scales and 2) develop a mechanistic, mechanistic/empirical, or phenomenological formulation to link the different length scales into a model capable of predicting the effects of microstructural changes on the linear viscoelastic behaviors of asphalt concrete mixture, e.g., a microstructure association model for asphalt concrete mixture. Through the microstructural study it is found that asphalt concrete mixture can be considered as a build-up of three different phases; asphalt mastic, fine aggregate matrix (FAM), and finally the coarse aggregate particles. The asphalt mastic is found to exist as a homogenous material throughout the mixture and FAM, and the filler content within this material is consistent with the volumetric averaged concentration, which can be calculated from the job mix formula. It is also
Improvements to constitutive material model for fabrics
NASA Astrophysics Data System (ADS)
Morea, Mihai I.
2011-12-01
The high strength to weight ratio of woven fabric offers a cost effective solution to be used in a containment system for aircraft propulsion engines. Currently, Kevlar is the only Federal Aviation Administration (FAA) approved fabric for usage in systems intended to mitigate fan blade-out events. This research builds on an earlier constitutive model of Kevlar 49 fabric developed at Arizona State University (ASU) with the addition of new and improved modeling details. Latest stress strain experiments provided new and valuable data used to modify the material model post peak behavior. These changes reveal an overall improvement of the Finite Element (FE) model's ability to predict experimental results. First, the steel projectile is modeled using Johnson-Cook material model and provides a more realistic behavior in the FE ballistic models. This is particularly noticeable when comparing FE models with laboratory tests where large deformations in projectiles are observed. Second, follow-up analysis of the results obtained through the new picture frame tests conducted at ASU provides new values for the shear moduli and corresponding strains. The new approach for analysis of data from picture frame tests combines digital image analysis and a two-level factorial optimization formulation. Finally, an additional improvement in the material model for Kevlar involves checking the convergence at variation of mesh density of fabrics. The study performed and described herein shows the converging trend, therefore validating the FE model.
A constitutive model for predicting rock fragmentation by blasting
NASA Astrophysics Data System (ADS)
Liu, Liqing; Katsabanis, P. D.
1996-05-01
This paper describes the development of a constitutive model for predicting rock damage and fragment size distribution due to explosive loading. The model is based on continuum mechanics and statistical fracture mechanics, assuming the rock medium is an isotropic, continuous and homogeneous material with pre-existing microcracks. In the model, damage to the rock medium is defined as the probability of fracture at a given crack density which is obtained by integrating a crack density function over time. The material constants used in the crack density function are determined according to their physical meaning. The minimum damage value at which the fragments may be formed is set by assuming that there is at least one crack per unit volume. Fragment size distribution is achieved considering the equilibrium between kinetic energy and surface energy. The simulation results are in good accordance with the theory of explosive energy partitioning in a rock medium. As a result, the damage zone induced by the shock wave and stress waves, once established, remains stable. The model has been calibrated by field crater blasting and small scale bench blasting tests.
Constitutive Models for Shape Memory Alloy Polycrystals
NASA Technical Reports Server (NTRS)
Comstock, R. J., Jr.; Somerday, M.; Wert, J. A.
1996-01-01
Shape memory alloys (SMA) exhibiting the superelastic or one-way effects can produce large recoverable strains upon application of a stress. In single crystals this stress and resulting strain are very orientation dependent. We show experimental stress/strain curves for a Ni-Al single crystal for various loading orientations. Also shown are model predictions; the open and closed circles indicate recoverable strains obtained at various stages in the transformation process. Because of the strong orientation dependence of shape memory properties, crystallographic texture can be expected to play an important role in the mechanical behavior of polycrystalline SMA. It is desirable to formulate a constitutive model to better understand and exploit the unique properties of SMA.
Lee, H.K.; Simunovic, S.
1999-09-01
A micromechanical damage constitutive model is presented to predict the overall elastoplastic behavior and damage evolution in random carbon fiber polymer matrix composites (RFPCs).To estimate the overall elastoplastic damage responses,an effective yield criterion is derived based on the ensemble-volume averaging process and first-order effects of eigenstrains due to the existence of spheroidal (prolate) fibers.The proposed effective yield criterion,to ether with the assumed overall associative plastic flow rule and hardening law, constitutes the analytical foundation for the estimation of effective elastoplastic behavior of ductile matrix composites.First,an effective elastoplastic constitutive dama e model for aligned fiber-reinforced composites is proposed.A micromechanical damage constitutive model for RFPCs is then developed.The average process over all orientations upon overning constitutive field equations and overall yield function for aligned fiber-reinforced composites i s performed to obtain the constitutive relations and effective yield function of RFPCs.The discrete numerical integration algorithms and the continuum tan ent operator are also presented to implement the proposed dama e constitutive model.The dama e constitutive model forms the basis for the pro ressive crushing in composite structures under impact loading.
Mesoscale constitutive modeling of magnetic dispersions.
Bhandar, Anand S; Wiest, John M
2003-01-15
A constitutive model for dispersions of acicular magnetic particles has been developed by modeling the particles as rigid dumbbells dispersed in a solvent. The effects of Brownian motion, anisotropic hydrodynamic drag, a steric force in the form of the Maier-Saupe potential, and, most importantly, a mean-field magnetic potential are included in the model. The development is similar to previous models for liquid-crystalline polymers. The model predicts multiple orientational states for the dispersion, and this phase behavior is described in terms of an orientational order parameter S and an average alignment parameter J; the latter is introduced because the magnetic particles have distinguishable direction due to polarity. A transition from isotropic to nematic phases at equilibrium is predicted. Multiple nematic phases-both prolate and oblate-are predicted in the presence of steady shear flow and external magnetic field parallel to the flow. The effect of increasing magnetic interparticle interactions and particle concentration is also presented. Comparisons with experimental data for the steady shear viscosity show very good agreement. PMID:16256493
Constitutive modeling for single crystal superalloys
NASA Technical Reports Server (NTRS)
Stouffer, D. C.; Jayaraman, N.; Sheh, M.; Alden, D.
1986-01-01
The inelastic response of single crystal gamma/gamma prime superalloys is quite different from the behavior of polycrystalline nickel base superalloys. Upto a critical temperature the yield stress of single crystal alloys is a function of the material orientation relative to the direction of the applied stress and the material exhibits significant tension/compression asymmetry. This behavior is primarily due to slip on the octahedral slip system. Above the critical temperature there is a sharp drop in the yield stress, cube slip becomes more predominant and the tension/compression asymmetry is reduced. Similar orientation and tension/compression asymmetry is observed in creep and secondary creep above the critical temperature is inferred to occur by octahedral slip. There are two exceptions to this behavior. First, loading near the (111) orientation exhibits cube slip at all temperatures, and; second, loading near the (001) orientation produces only octahedral slip at all temperatures. The constitutive model is based on separating the total global strain into elastic and inelastic components. This model is developed and briefly discussed.
Failure Behavior and Constitutive Model of Weakly Consolidated Soft Rock
Wang, Wei-ming; Zhao, Zeng-hui; Wang, Yong-ji; Gao, Xin
2013-01-01
Mining areas in western China are mainly located in soft rock strata with poor bearing capacity. In order to make the deformation failure mechanism and strength behavior of weakly consolidated soft mudstone and coal rock hosted in Ili No. 4 mine of Xinjiang area clear, some uniaxial and triaxial compression tests were carried out according to the samples of rocks gathered in the studied area, respectively. Meanwhile, a damage constitutive model which considered the initial damage was established by introducing a damage variable and a correction coefficient. A linearization process method was introduced according to the characteristics of the fitting curve and experimental data. The results showed that samples under different moisture contents and confining pressures presented completely different failure mechanism. The given model could accurately describe the elastic and plastic yield characteristics as well as the strain softening behavior of collected samples at postpeak stage. Moreover, the model could precisely reflect the relationship between the elastic modulus and confining pressure at prepeak stage. PMID:24489511
Constitutive model development for lightly cemented scrap rubber tire chips
NASA Astrophysics Data System (ADS)
Tsoi, Wa Yeung
2005-11-01
Rubber-soil (lightly cemented scrap rubber tire chips) is a promising solution for the global scrap tire problem. It is also a promising material for various geotechnical engineering applications because of its advantageous properties such as lightweight, high permeability, high ductility and ease to cast. Intensive laboratory studies, mostly under triaxial testing, are conducted and a constitutive model is proposed. Firstly, the effective stress principle is proven applicable for Rubber-soil under normal engineering stress level although the inter-particle contact area is large. Secondly, because of the gravel-sized surface voids on the testing samples, membrane penetration is serious so an integrated remedy method is proposed, where the surface voids are patched up first and then a lubricated reinforced membrane is dressed on. It is found that the volumetric deformation of Rubber-soil is very recoverable even after 20% volume contraction but the over consolidation results illustrate a decreasing stiffness, which is believed due to volumetric damage. Shearing on the sample gives typical results as sands where clear phase transformation is observed, but the strains involved are higher and more recoverable. Besides, shear stiffness is observed decreasing with deformation, which is believed due to shear damage. There are other observations such as the difference in the curvatures of unloading and reloading curves in CD tests, which might be a frictional phenomenon. Based on the laboratory observations and on the analogy of a continuum spring-block system, a constitutive model termed as Analogical Model is proposed. Fifteen model parameters are involved but most of them are typical soil parameters. The remaining ones have clear physical meanings and can be easily calibrated. It is found that the model can satisfactorily capture many features observed from the experiments, such as hardening, softening, apparent permanent deformations, stiffness decay due to damage
Constitutive modeling of shock response of polytetrafluoroethylene
NASA Astrophysics Data System (ADS)
Resnyansky, A. D.; Bourne, N. K.; Millett, J. C. F.; Brown, E. N.
2011-08-01
Polytetrafluoroethylene (PTFE) is a polymer with a simple atomic structure that shows complex behavior under pressure and demonstrates a highly variable metastable phase structure in shock waves with amorphous and crystalline components. In turn, the crystalline component has four known phases with the high-pressure transition of the crystalline domain from crystalline phase IV at ambient through phase II to III. At the same time, as has been recently studied using spectrometry, the crystalline region nucleates from the amorphous one with load. Stress and velocity shock-wave profiles acquired recently with embedded gauges demonstrate features that may be related to the impedance mismatch between the phase domains subjected to such transitions resulting in variations of mechanical and thermophysical characteristics. We consider the inter-phase non-equilibrium and the amorphous-to-crystalline and inter-crystalline transitions that are associated with the high pressure and temperature transformations under shock wave loading as possible candidates for the analysis. The present work utilizes a multi-phase constitutive model that considers strength effects to describe the observed response under shock loading of the PTFE material. Experimental plate impact shock-wave histories are compared with calculated profiles using kinetics describing the transitions. The study demonstrates that the inter-phase pressure non-equilibrium of the state parameters plays the key role in the delay of the shock wave attenuation. At the same time, the forward transition associated with the crystallization might be responsible for the velocity spike in the experimental velocity profiles at high impact velocity and the modulus variation at low impact velocity. On the other hand, an accelerated attenuation of the velocity in the rarefaction wave is associated with another transition resulting in the residual crystallinity change during unloading.
Life prediction and constitutive models for anisotropic materials
NASA Technical Reports Server (NTRS)
Bill, R. C.
1982-01-01
The intent of this program is to develop a basic understanding of cyclic creep-fatigue deformation mechanisms and damage accumulation, a capability for reliable life prediction, and the ability to model the constitutive behavior of anisotropic single crystal (SC) and directionally solidified or recrystallized (DSR) comprise the program, and the work breakdown for each option reflects a distinct concern for two classes of anisotropic materials, SC and DSR materials, at temperatures encountered in the primary gas path (airfoil temperatures), and at temperatures typical of the blade root attachment and shank area. Work directed toward the higher temperature area of concern in the primary gas path includes effects of coatings on the behavior and properties of the materials of interest. The blade root attachment work areas will address the effects of stress concentrations associated with attachment features.
Material modeling and structural analysis with the microplane constitutive model
NASA Astrophysics Data System (ADS)
Brocca, Michele
The microplane model is a versatile and powerful approach to constitutive modeling in which the stress-strain relations are defined in terms of vectors rather than tensors on planes of all possible orientations. Such planes are called the microplanes and are representative of the microstructure of the material. The microplane model with kinematic constraint has been successfully employed in the past in the modeling of concrete, soils, ice, rocks, fiber composites and other quasibrittle materials. The microplane model provides a powerful and efficient numerical and theoretical framework for the development and implementation of constitutive models for any kind of material. The dissertation presents a review of the background from which the microplane model stems, highlighting differences and similarities with other approaches. The basic structure of the microplane model is then presented, together with its extension to finite strain deformation. To show the effectiveness of the microplane model approach, some examples are given demonstrating applications of microplane models in structural analysis with the finite element method. Some new constitutive models are also introduced for materials characterized by very different properties and microstructures, showing that the approach is indeed very versatile and provides a robust basis for the study of a broad range of problems. New models are introduced for metal plasticity, shape memory alloys and cellular materials. The new models are compared quantitatively with the existing models and experimental data. In particular, the newly introduced microplane models for metal plasticity are compared with the classical J2-flow theory for incremental plasticity. An existing microplane model for concrete is employed in finite element analysis of the 'tube-squash' test, in which concrete undergoes very large deviatoric deformation, and of the size effect in compressive failure of concrete columns. The microplane model for shape
Towards a Simple Constitutive Model for Bread Dough
NASA Astrophysics Data System (ADS)
Tanner, Roger I.
2008-07-01
Wheat flour dough is an example of a soft solid material consisting of a gluten (rubbery) network with starch particles as a filler. The volume fraction of the starch filler is high-typically 60%. A computer-friendly constitutive model has been lacking for this type of material and here we report on progress towards finding such a model. The model must describe the response to small strains, simple shearing starting from rest, simple elongation, biaxial straining, recoil and various other transient flows. A viscoelastic Lodge-type model involving a damage function. which depends on strain from an initial reference state fits the given data well, and it is also able to predict the thickness at exit from dough sheeting, which has been a long-standing unsolved puzzle. The model also shows an apparent rate-dependent yield stress, although no explicit yield stress is built into the model. This behaviour agrees with the early (1934) observations of Schofield and Scott Blair on dough recoil after unloading.
Constitutive Modeling and Numerical Simulation of Frp Confined Concrete Specimens
NASA Astrophysics Data System (ADS)
Smitha, Gopinath; Ramachandramurthy, Avadhanam; Nagesh, Ranganatha Iyer; Shahulhameed, Eduvammal Kunhimoideen
2014-09-01
Fiber-reinforced polymer (FRP) composites are generally used for the seismic retrofit of concrete members to enhance their strength and ductility. In the present work, the confining effect of Carbon Fiber-Reinforced Polymer (CFRP) composite layers has been investigated by numerical simulation. The numerical simulation has been carried out using nonlinear finite element analysis (FEA) to predict the response behaviour of CFRP-wrapped concrete cylinders. The nonlinear behaviour of concrete in compression and the linear elastic behaviour of CFRP has been modeled using an appropriate constitutive relationship. A cohesive model has been developed for modeling the interface between the concrete and CFRP. The interaction and damage failure criteria between the concrete to the cohesive element and the cohesive element to the CFRP has also been accounted for in the modeling. The response behaviour of the wrapped concrete specimen has been compared with the proposed interface model and with a perfectly bonded condition. The results obtained from the present study showed good agreement with the experimental load-displacement response and the failure pattern in the literature. Further, a sensitivity analysis has been carried out to study the effect of the number of layers of CFRP on the concrete specimens. It has been observed that wrapping with two layers was found to be the optimum, beyond which the response becomes flexible but with a higher load-carrying capacity
Salajegheh, Nima; Abedrabbo, Nader; Pourboghrat, Farhang
2005-08-05
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 is 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.
NASA Astrophysics Data System (ADS)
Salajegheh, Nima; Abedrabbo, Nader; Pourboghrat, Farhang
2005-08-01
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 is 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.
NASA Astrophysics Data System (ADS)
Gray, G. T., III; Livescu, V.; Rigg, P. A.; Trujillo, C. P.; Cady, C. M.; Chen, S. R.; Carpenter, J. S.; Lienert, T. J.; Fensin, S.
2015-09-01
For additive manufacturing (AM), the certification and qualification paradigm needs to evolve as there exists no "ASTM-type" additive manufacturing certified process or AM-material produced specifications. Accordingly, utilization of AM materials to meet engineering applications requires quantification of the constitutive properties of these evolving materials in comparison to conventionally-manufactured metals and alloys. Cylinders of 316L SS were produced using a LENS MR-7 laser additive manufacturing system from Optomec (Albuquerque, NM) equipped with a 1kW Yb-fiber laser. The microstructure of the AM-316L SS is detailed in both the as-built condition and following heat-treatments designed to obtain full recrystallization. The constitutive behavior as a function of strain rate and temperature is presented and compared to that of nominal annealed wrought 316L SS plate. The dynamic damage evolution and failure response of all three materials was probed using flyer-plate impact driven spallation experiments at a peak stress of 4.5 GPa to examine incipient spallation response. The spall strength of AM-produced 316L SS was found to be very similar for the peak shock stress studied to that of annealed wrought or AM-316L SS following recrystallization. The damage evolution as a function of microstructure was characterized using optical metallography.
Multivariate pluvial flood damage models
Van Ootegem, Luc; Verhofstadt, Elsy; Van Herck, Kristine; Creten, Tom
2015-09-15
Depthâ€“damage-functions, relating the monetary flood damage to the depth of the inundation, are commonly used in the case of fluvial floods (floods caused by a river overflowing). We construct four multivariate damage models for pluvial floods (caused by extreme rainfall) by differentiating on the one hand between ground floor floods and basement floods and on the other hand between damage to residential buildings and damage to housing contents. We do not only take into account the effect of flood-depth on damage, but also incorporate the effects of non-hazard indicators (building characteristics, behavioural indicators and socio-economic variables). By using a Tobit-estimation technique on identified victims of pluvial floods in Flanders (Belgium), we take into account the effect of cases of reported zero damage. Our results show that the flood depth is an important predictor of damage, but with a diverging impact between ground floor floods and basement floods. Also non-hazard indicators are important. For example being aware of the risk just before the water enters the building reduces content damage considerably, underlining the importance of warning systems and policy in this case of pluvial floods. - Highlights: â€¢ Prediction of damage of pluvial floods using also non-hazard information â€¢ We include â€˜no damage casesâ€™ using a Tobit model. â€¢ The damage of flood depth is stronger for ground floor than for basement floods. â€¢ Non-hazard indicators are especially important for content damage. â€¢ Potential gain of policies that increase awareness of flood risks.
Modeling of glass fracture damage using continuum damage mechanics - Static spherical indentation
Sun, Xin; Khaleel, Mohammad A.
2004-07-01
Continuum damage mechanics based constitutive model is used to study the stone-impact resistance of automotive windshields. An axisymmetric finite element model is created to simulate the transient dynamic response and impact induced damge tensors for laminated glass layers subject to stone-impact loading. The windshield glass consists of two glass outer layers laminated by a thin poly-vinyl butyral (PVB) layer. The constitutive behavior of the glass layers is simulated suing continuum damage mechanics model with linear damage evolution. The PVB layer is modeled with linear viscoelastic solid. The model is used to predict and examine damage patterns on different glass surfaces for different windshield designs including variations in ply thickness and curvatures.
Constitutive modeling of fiber-reinforced cement composites
NASA Astrophysics Data System (ADS)
Boulfiza, Mohamed
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}â‰¥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.
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 New Uncoupled Viscoplastic Constitutive Model
NASA Technical Reports Server (NTRS)
Bradley, W. L.; Yuen, S.
1983-01-01
A new uncoupled viscoplastic model has been proposed along with experiments and analysis to define the various material constraints. Distinguishing between rate sensitive and rate insensitive strain allows the rate sensitive strain to be modelled over a wide range of temperatures with very little variation in the stress component 'n'. Furthermore, it allows the rounded corners on stress-strain hysteresis loops to be achieved very naturally.
A phenomenological constitutive model for low density polyurethane foams
Neilsen, M.K.; Morgan, H.S.; Krieg, R.D.
1987-04-01
Results from a series of hydrostatic and triaxial compression tests which were performed on polyurethane foams are presented in this report. These tests indicate that the volumetric and deviatoric parts of the foam behavior are strongly coupled. This coupling behavior could not be captured with any of several commonly used plasticity models. Thus, a new constitutive model was developed. This new model was based on a decomposition of the foam response into two parts: (1) response of the polymer skeleton, and (2) response of the air inside the cells. The air contribution was completely volumetric. The new constitutive model was implemented in two finite element codes, SANCHO and PRONTO. Results from a series of analyses completed with these codes indicated that the new constitutive model captured all of the foam behaviors that had been observed in the experiments. Finally, a typical dynamic problem was analyzed using the new constitutive model and other constitutive models to demonstrate differences between the models. Results from this series of analyses indicated that the new constitutive model generated displacement and acceleration predictions that were between predictions obtained using the other models. This result was expected. 9 refs., 45 figs., 4 tabs.
Study on the Constitutive Model for Jointed Rock Mass
Xu, Qiang; Chen, Jianyun; Li, Jing; Zhao, Chunfeng; Yuan, Chenyang
2015-01-01
A new elasto-plastic constitutive model for jointed rock mass, which can consider the persistence ratio in different visual angle and anisotropic increase of plastic strain, is proposed. The proposed the yield strength criterion, which is anisotropic, is not only related to friction angle and cohesion of jointed rock masses at the visual angle but also related to the intersection angle between the visual angle and the directions of the principal stresses. Some numerical examples are given to analyze and verify the proposed constitutive model. The results show the proposed constitutive model has high precision to calculate displacement, stress and plastic strain and can be applied in engineering analysis. PMID:25885695
Constitutive Modeling of Piezoelectric Polymer Composites
NASA Technical Reports Server (NTRS)
Odegard, Gregory M.; Gates, Tom (Technical Monitor)
2003-01-01
A new modeling approach is proposed for predicting the bulk electromechanical properties of piezoelectric composites. The proposed model offers the same level of convenience as the well-known Mori-Tanaka method. In addition, it is shown to yield predicted properties that are, in most cases, more accurate or equally as accurate as the Mori-Tanaka scheme. In particular, the proposed method is used to determine the electromechanical properties of four piezoelectric polymer composite materials as a function of inclusion volume fraction. The predicted properties are compared to those calculated using the Mori-Tanaka and finite element methods.
Evaluation of potential crushed-salt constitutive models
Callahan, G.D.; Loken, M.C.; Sambeek, L.L. Van; Chen, R.; Pfeifle, T.W.; Nieland, J.D.
1995-12-01
Constitutive models describing the deformation of crushed salt are presented in this report. Ten constitutive models with potential to describe the phenomenological and micromechanical processes for crushed salt were selected from a literature search. Three of these ten constitutive models, termed Sjaardema-Krieg, Zeuch, and Spiers models, were adopted as candidate constitutive models. The candidate constitutive models were generalized in a consistent manner to three-dimensional states of stress and modified to include the effects of temperature, grain size, and moisture content. A database including hydrostatic consolidation and shear consolidation tests conducted on Waste Isolation Pilot Plant and southeastern New Mexico salt was used to determine material parameters for the candidate constitutive models. Nonlinear least-squares model fitting to data from the hydrostatic consolidation tests, the shear consolidation tests, and a combination of the shear and hydrostatic tests produces three sets of material parameter values for the candidate models. The change in material parameter values from test group to test group indicates the empirical nature of the models. To evaluate the predictive capability of the candidate models, each parameter value set was used to predict each of the tests in the database. Based on the fitting statistics and the ability of the models to predict the test data, the Spiers model appeared to perform slightly better than the other two candidate models. The work reported here is a first-of-its kind evaluation of constitutive models for reconsolidation of crushed salt. Questions remain to be answered. Deficiencies in models and databases are identified and recommendations for future work are made. 85 refs.
Remarks on ConstitutiveModeling of Nanofluids
Massoudi, Mehrdad; Tran X. Phuoc
2012-01-01
Nanofluids are made by adding nanoscale particles in low volumetric fractions to a fluid in order to enhance or improve their rheological, mechanical, optical, and thermal properties. The base fluid can be any liquid such as oil, water, ethylene glycol, or conventional fluid mixtures. Limited available studies on nanofluid viscosity have been reported [1-19]. In most of these studies, the behavior of the viscosity and the shear stress of nanofluids have been interpreted using the widely used empirical model developed by Casson [20].
The courthouse doors do not close: constitutional challenges to non-economic damage caps.
Bashshur, Ramona
2011-01-01
Following efforts at addressing health care reform that spanned decades, the US Congress passed massive health reform legislation in 2010, with key provisions to be implemented over the next few years. This legislation has been heralded as the ultimate legislative response to the spiraling cost of care and inequity of access to care. Yet, these reforms have left many unanswered questions about the perennial issue of tort reform, in particular, caps on non-economic damages. This article begins with a broad perspective on tort reform and the debate surrounding the issue, and ends with a search for common ground where the threat of litigation may be reduced while the constitutional rights of citizens remain safeguarded. PMID:21812354
Acute MUS81 depletion leads to replication fork slowing and a constitutive DNA damage response
Xing, Meichun; Wang, Xiaohui; Palmai-Pallag, Timea; Shen, Huahao; Helleday, Thomas; Hickson, Ian D.; Ying, Songmin
2015-01-01
The MUS81 protein belongs to a conserved family of DNA structure-specific nucleases that play important roles in DNA replication and repair. Inactivation of the Mus81 gene in mice has no major deleterious consequences for embryonic development, although cancer susceptibility has been reported. We have investigated the role of MUS81 in human cells by acutely depleting the protein using shRNAs. We found that MUS81 depletion from human fibroblasts leads to accumulation of ssDNA and a constitutive DNA damage response that ultimately activates cellular senescence. Moreover, we show that MUS81 is required for efficient replication fork progression during an unperturbed S-phase, and for recovery of productive replication following replication stalling. These results demonstrate essential roles for the MUS81 nuclease in maintenance of replication fork integrity. PMID:26415217
Constitutive modeling of shock response of PTFE
Brown, Eric N; Reanyansky, Anatoly D; Bourne, Neil K; Millett, Jeremy C F
2009-01-01
The PTFE (polytetrafluoroethylene) material is complex and attracts attention of the shock physics researchers because it has amorphous and crystalline components. In turn, the crystalline component has four known phases with the high pressure transition to phase III. At the same time, as has been recently studied using spectrometry, the crystalline region is growing with load. Stress and velocity shock-wave profiles acquired recently with embedded gauges demonstrate feature that may be related to impedance mismatches between the regions subjected to some transitions resulting in density and modulus variations. We consider the above mentioned amorphous-to-crystalline transition and the high pressure Phase II-to-III transitions as possible candidates for the analysis. The present work utilizes a multi-phase rate sensitive model to describe shock response of the PTFE material. One-dimensional experimental shock wave profiles are compared with calculated profiles with the kinetics describing the transitions. The objective of this study is to understand the role of the various transitions in the shock response of PTFE.
Analysis of a microcrack model and constitutive equations for time-dependent dilatancy of rocks
NASA Astrophysics Data System (ADS)
Chen, Zuan
2003-11-01
Based on experimental observations and theoretical analyses, the author introduces an ideal microcrack model in which an array of cracks with the same shape and initial size is distributed evenly in rocks. The mechanism of creep dilatancy for rocks is analysed theoretically. Initiation, propagation and linkage of pre-existing microcracks during creep are well described. Also, the relationship between the velocity of microcrack growth and the duration of the creep process is derived numerically. The relationship agrees well with the character of typical experimental creep curves, and includes three stages of creep. Then the damage constitutive equations and damage evolution equations, which describe the dilatant behaviour of rocks, are presented. Because the dilatant estimated value is taken as the damage variable, the relationship between the microscopic model and the macroscopic constitutive equations is established. In this way the mechanical behaviour of rocks can be predicted.
Asymmetric Damage Segregation Constitutes an Emergent Population-Level Stress Response.
Vedel, SÃ¸ren; Nunns, Harry; KoÅ¡mrlj, Andrej; Semsey, Szabolcs; Trusina, Ala
2016-08-01
Asymmetric damage segregation (ADS) is a mechanism for increasing population fitness through non-random, asymmetric partitioning of damaged macromolecules at cell division. ADS has been reported across multiple organisms, though the measured effects on fitness of individuals are often small. Here, we introduce a cell-lineage-based framework that quantifies the population-wide effects of ADS and then verify our results experimentally in E.Â coli under heat and antibiotic stress. Using an experimentally validated mathematical model, we find that the beneficial effect of ADS increases with stress. In effect, low-damage subpopulations divide faster and amplify within the population acting like a positive feedback loop whose strength scales with stress. Analysis of protein aggregates shows that the degree of asymmetric inheritance is damage dependent in single cells. Together our results indicate that, despite small effects in single cell, ADS exerts a strong beneficial effect on the population level and arises from the redistribution of damage within aÂ population, through both single-cell and population-level feedback. PMID:27426983
Constitutive models for rubber networks undergoing simultaneous crosslinking and scission.
Thompson, Aidan Patrick; Curro, John G.; Rottach, Dana R.; Grest, Gary Stephen; Budzien, Joanne L.; Lo, David Chi S.
2006-01-01
Constitutive models for chemically reacting networks are formulated based on a generalization of the independent network hypothesis. These models account for the coupling between chemical reaction and strain histories, and have been tested by comparison with microscopic molecular dynamics simulations. An essential feature of these models is the introduction of stress transfer functions that describe the interdependence between crosslinks formed and broken at various strains. Efforts are underway to implement these constitutive models into the finite element code Adagio. Preliminary results are shown that illustrate the effects of changing crosslinking and scission rates and history.
Xu, Yidong; Qian, Chunxiang
2013-01-01
Based on meso-damage mechanics and finite element analysis, the aim of this paper is to describe the feasibility of the Gursonâ€“Tvergaardâ€“Needleman (GTN) constitutive model in describing the tensile behavior of corroded reinforcing bars. The orthogonal test results showed that different fracture pattern and the related damage evolution process can be simulated by choosing different material parameters of GTN constitutive model. Compared with failure parameters, the two constitutive parameters are significant factors affecting the tensile strength. Both the nominal yield and ultimate tensile strength decrease markedly with the increase of constitutive parameters. Combining with the latest data and trial-and-error method, the suitable material parameters of GTN constitutive model were adopted to simulate the tensile behavior of corroded reinforcing bars in concrete under carbonation environment attack. The numerical predictions can not only agree very well with experimental measurements, but also simplify the finite element modeling process. PMID:23342140
Damage modeling for Taylor impact simulations
NASA Astrophysics Data System (ADS)
Anderson, C. E., Jr.; Chocron, I. S.; Nicholls, A. E.
2006-08-01
G. I. Taylor showed that dynamic material properties could be deduced from the impact of a projectile against a rigid boundary. The Taylor anvil test became very useful with the advent of numerical simulations and has been used to infer and/or to validate material constitutive constants. A new experimental facility has been developed to conduct Taylor anvil impacts to support validation of constitutive constants used in simulations. Typically, numerical simulations are conducted assuming 2-D cylindrical symmetry, but such computations cannot hope to capture the damage observed in higher velocity experiments. A computational study was initiated to examine the ability to simulate damage and subsequent deformation of the Taylor specimens. Three-dimensional simulations, using the Johnson-Cook damage model, were conducted with the nonlinear Eulerian wavecode CTH. The results of the simulations are compared to experimental deformations of 6061-T6 aluminum specimens as a function of impact velocity, and conclusions regarding the ability to simulate fracture and reproduce the observed deformations are summarized.
Requirements for energy based constitutive modeling in tire mechanics
NASA Astrophysics Data System (ADS)
Luchini, John R.; Peters, Jim M.; Mars, Will V.
1995-08-01
The history, requirements, and theoretical basis of a new energy based constitutive model for (rubber) material elasticity, hysteresis, and failure are presented. Energy based elasticity is handled by many constitutive models, both in one dimension and in three dimensions. Conversion of mechanical energy to heat can be modeled with viscoelasticity or as structural hysteresis. We are seeking unification of elasticity, hysteresis, and failure mechanisms such as fatigue and wear. An energy state characterization for failure criteria of (rubber) materials may provide this unification and also help explain the interaction of temperature effects with failure mechanisms which are described as creation of growth of internal crack surface. Improved structural modeling of tires with FEM should result from such a unified constitutive theory. The theory will also guide experimental work and should enable better interpretation of the results of computational stress analyses.
Requirements for energy based constitutive modeling in tire mechanics
NASA Technical Reports Server (NTRS)
Luchini, John R.; Peters, Jim M.; Mars, Will V.
1995-01-01
The history, requirements, and theoretical basis of a new energy based constitutive model for (rubber) material elasticity, hysteresis, and failure are presented. Energy based elasticity is handled by many constitutive models, both in one dimension and in three dimensions. Conversion of mechanical energy to heat can be modeled with viscoelasticity or as structural hysteresis. We are seeking unification of elasticity, hysteresis, and failure mechanisms such as fatigue and wear. An energy state characterization for failure criteria of (rubber) materials may provide this unification and also help explain the interaction of temperature effects with failure mechanisms which are described as creation of growth of internal crack surface. Improved structural modeling of tires with FEM should result from such a unified constitutive theory. The theory will also guide experimental work and should enable better interpretation of the results of computational stress analyses.
Deformation modeling and constitutive modeling for anisotropic superalloys
NASA Technical Reports Server (NTRS)
Milligan, Walter W.; Antolovich, Stephen D.
1989-01-01
A study of deformation mechanisms in the single crystal superalloy PWA 1480 was conducted. Monotonic and cyclic tests were conducted from 20 to 1093 C. Both (001) and near-(123) crystals were tested, at strain rates of 0.5 and 50 percent/minute. The deformation behavior could be grouped into two temperature regimes: low temperatures, below 760 C; and high temperatures, above 820 to 950 C depending on the strain rate. At low temperatures, the mechanical behavior was very anisotropic. An orientation dependent CRSS, a tension-compression asymmetry, and anisotropic strain hardening were all observed. The material was deformed by planar octahedral slip. The anisotropic properties were correlated with the ease of cube cross-slip, as well as the number of active slip systems. At high temperatures, the material was isotropic, and deformed by homogeneous gamma by-pass. It was found that the temperature dependence of the formation of superlattice-intrinsic stacking faults was responsible for the local minimum in the CRSS of this alloy at 400 C. It was proposed that the cube cross-slip process must be reversible. This was used to explain the reversible tension-compression asymmetry, and was used to study models of cross-slip. As a result, the cross-slip model proposed by Paidar, Pope and Vitek was found to be consistent with the proposed slip reversibility. The results were related to anisotropic viscoplastic constitutive models. The model proposed by Walter and Jordan was found to be capable of modeling all aspects of the material anisotropy. Temperature and strain rate boundaries for the model were proposed, and guidelines for numerical experiments were proposed.
The anisotropic material constitutive models for the human cornea.
Li, Long-yuan; Tighe, Brian
2006-03-01
This paper presents an anisotropic analysis model for the human cornea. The model is based on the assumption that the fibrils in the cornea are organised into lamellae, which may have preferential orientation along the superior-inferior and nasal-temporal directions, while the alignment of lamellae with different orientations is assumed to be random. Hence, the cornea can be regarded as a laminated composite shell. The constitutive equation describing the relationships between membrane forces, bending moments, and membrane strains, bending curvatures are derived. The influences of lamella orientations and the random alignment of lamellae on the stiffness coefficients of the constitutive equation are discussed. PMID:16426861
Unified constitutive model for single crystal deformation behavior with applications
NASA Technical Reports Server (NTRS)
Walker, K. P.; Meyer, T. G.; Jordan, E. H.
1988-01-01
Single crystal materials are being used in gas turbine airfoils and are candidates for other hot section components because of their increased temperature capabilities and resistance to thermal fatigue. Development of a constitutive model which assesses the inelastic behavior of these materials has been studied in 2 NASA programs: Life Prediction and Constitutive Models for Engine Hot Section Anisotropic Materials and Biaxial Constitutive Equation Development for Single Crystals. The model has been fit to a large body of constitutive data for single crystal PWA 1480 material. The model uses a unified approach for computing total inelastic strains (creep plus plasticity) on crystallographic slip systems reproducing observed directional and strain rate effects as a natural consequence of the summed slip system quantities. The model includes several of the effects that have been reported to influence deformation in single crystal materials, such as shear stress, latent hardening, and cross slip. The model is operational in a commercial Finite Element code and is being installed in a Boundary Element Method code.
Constitutive modeling of human liver based on in vivo measurements.
Mazza, Edoardo; Grau, Patrick; Hollenstein, Marc; Bajka, Michael
2008-01-01
In vivo aspiration experiments on human livers are analyzed and material parameters for a non-linear-viscoelastic constitutive model are determined. A novel procedure is applied for the inverse analysis that accounts for the initial tissue deformation in the experiment and for the non-homogeneity of liver tissue. A numerical model is used consisting of a surface layer (capsule) and an underlying non-linear-viscoelastic solid (parenchyma). The capsule is modeled as hyperelastic membrane using data from measurements on bovine and human tissue. In a two step optimization procedure the set of constitutive model parameters for the "average" response of liver parenchyma is obtained. The proposed model is in line with literature values of high strain rate elastic modulus obtained from dynamic elastography. The model can be used to predict the nonlinear, time dependent behavior of human liver in computer simulations related to surgery training and planning. PMID:18982669
Probabilistic constitutive relationships for cyclic material strength models
NASA Technical Reports Server (NTRS)
Boyce, L.; Chamis, C. C.
1988-01-01
A methodology is developed that provides a probabilistic treatment for the lifetime of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs.
The Constitutive Modeling of Thin Films with Randon Material Wrinkles
NASA Technical Reports Server (NTRS)
Murphey, Thomas W.; Mikulas, Martin M.
2001-01-01
Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%
Rate dependent constitutive models for fiber reinforced polymer composites
NASA Technical Reports Server (NTRS)
Gates, Thomas S.
1990-01-01
A literature survey was conducted to assess the state-of-the-art in rate dependent constitutive models for continuous fiber reinforced polymer matrix composite (PMC) materials. Several recent models which include formulations for describing plasticity, viscoelasticity, viscoplasticity, and rate-dependent phenomenon such as creep and stress relaxation are outlined and compared. When appropriate, these comparisons include brief descriptions of the mathematical formulations, the test procedures required for generating material constants, and details of available data comparing test results to analytical predictions.
Numerical considerations in the development and implementation of constitutive models
NASA Technical Reports Server (NTRS)
Haisler, W. E.; Imbrie, P. K.
1985-01-01
Several unified constitutive models were tested in uniaxial form by specifying input strain histories and comparing output stress histories. The purpose of the tests was to evaluate several time integration methods with regard to accuracy, stability, and computational economy. The sensitivity of the models to slight changes in input constants was also investigated. Results are presented for In100 at 1350 F and Hastelloy-X at 1800 F.
Hyperelastic anisotropic microplane constitutive model for annulus fibrosus.
Caner, Ferhun C; Guo, Zaoyang; Moran, Brian; Bazant, Zdenek P; Carol, Ignacio
2007-10-01
In a recent paper, Peng et al. (2006, "An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis," ASME J. Appl. Mech., 73(5), pp. 815-824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, "A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis," J. Mech. Phys. Solids, 54(9), pp. 1952-1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, "Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue," ASME J. Biomech. Eng., 128(3), pp. 419-427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two
Unified constitutive modeling for proportional and nonproportional cyclic plasticity responses
NASA Astrophysics Data System (ADS)
Krishna, Shree
Several features of cyclic plasticity, e.g. cyclic hardening/softening, ratcheting, relaxation, and their dependence on strain range, nonproportionality of loading, time, and temperature determine the stress-strain responses of materials under cyclic loading. Numerous efforts have been made in the past decades to characterize and model these responses. Many of these responses can be simulated reasonably by the existing constitutive models, but the same models would fail in simulating the structural responses, local stress-strain or global deformation. One of the reasons for this deficiency is that the constitutive models are not robust enough to simulate the cyclic plasticity responses when they interact with each other. This deficiency can be understood better or resolved by developing and validating constitutive models against a broad set of experimental responses and two or more of the responses interacting with each other. This dissertation develops a unified constitutive model by studying the cyclic plasticity features in an integrated manner and validating the model by simulating a broad set of proportional and nonproportional cyclic plasticity responses. The study demonstrates the drawbacks of the existing nonlinear kinematic hardening model originally developed by Chaboche and then develop and incorporate novel ideas into the model for improving its cyclic response simulations. The Chaboche model is modified by incorporating strain-range dependent cyclic hardening/softening through the kinematic hardening rule parameters, in addition to the conventional method of using only the isotropic hardening parameters. The nonproportional loading memory parameters of Tanaka and of Benallal and Marquis are incorporated to study the influence of nonproportionality. The model is assessed by simulating hysteresis loop shape, cyclic hardening-softening, cross-effect, cyclic relaxation, subsequent cyclic softening, and finally a series of ratcheting responses under
Modeling Fatigue Damage in Long-Fiber Thermoplastics
Nguyen, Ba Nghiep; Kunc, Vlastimil; Bapanapalli, Satish K.
2009-10-30
This paper applies a fatigue damage model recently developed for injection-molded long-fiber thermoplastics (LFTs) to predict the modulus reduction and fatigue lifetime of glass/polyamide 6,6 (PA6,6) specimens. The fatigue model uses a multiscale mechanistic approach to describe fatigue damage accumulation in these materials subjected to cyclic loading. Micromechanical modeling using a modified Eshelby-Mori-Tanaka approach combined with averaging techniques for fiber length and orientation distributions is performed to establish the stiffness reduction relation for the composite as a function of the microcrack volume fraction. Next, continuum damage mechanics and a thermodynamic formulation are used to derive the constitutive relations and the damage evolution law. The fatigue damage model has been implemented in the ABAQUS finite element code and has been applied to analyze fatigue of the studied glass/PA6,6 specimens. The predictions agree well with the experimental results.
Development of a viscoelastic continuum damage model for cyclic loading
NASA Astrophysics Data System (ADS)
Sullivan, R. W.
2008-12-01
A previously developed spectrum model for linear viscoelastic behavior of solids is used to describe the rate-dependent damage growth of a time dependent material under cyclic loading. Through the use of the iterative solution of a special Volterra integral equation, the cyclic strain history is described. The spectrum-based model is generalized for any strain rate and any uniaxial load history to formulate the damage function. Damage evolution in the body is described through the use of a rate-type evolution law which uses a pseudo strain to express the viscoelastic constitutive equation with damage. The resulting damage function is used to formulate a residual strength model. The methodology presented is demonstrated by comparing the peak values of the computed cyclic strain history as well as the residual strength model predictions to the experimental data of a polymer matrix composite.
Temperature Dependent Constitutive Modeling for Magnesium Alloy Sheet
Lee, Jong K.; Lee, June K.; Kim, Hyung S.; Kim, Heon Y.
2010-06-15
Magnesium alloys have been increasingly used in automotive and electronic industries because of their excellent strength to weight ratio and EMI shielding properties. However, magnesium alloys have low formability at room temperature due to their unique mechanical behavior (twinning and untwining), prompting for forming at an elevated temperature. In this study, a temperature dependent constitutive model for magnesium alloy (AZ31B) sheet is developed. A hardening law based on non linear kinematic hardening model is used to consider Bauschinger effect properly. Material parameters are determined from a series of uni-axial cyclic experiments (T-C-T or C-T-C) with the temperature ranging 150-250 deg. C. The influence of temperature on the constitutive equation is introduced by the material parameters assumed to be functions of temperature. Fitting process of the assumed model to measured data is presented and the results are compared.
Unified constitutive models for high-temperature structural applications
NASA Technical Reports Server (NTRS)
Lindholm, U. S.; Chan, K. S.; Bodner, S. R.; Weber, R. M.; Walker, K. P.
1988-01-01
Unified constitutive models are characterized by the use of a single inelastic strain rate term for treating all aspects of inelastic deformation, including plasticity, creep, and stress relaxation under monotonic or cyclic loading. The structure of this class of constitutive theory pertinent for high temperature structural applications is first outlined and discussed. The effectiveness of the unified approach for representing high temperature deformation of Ni-base alloys is then evaluated by extensive comparison of experimental data and predictions of the Bodner-Partom and the Walker models. The use of the unified approach for hot section structural component analyses is demonstrated by applying the Walker model in finite element analyses of a benchmark notch problem and a turbine blade problem.
Temperature Dependent Constitutive Modeling for Magnesium Alloy Sheet
NASA Astrophysics Data System (ADS)
Lee, Jong K.; Lee, June K.; Kim, Hyung S.; Kim, Heon Y.
2010-06-01
Magnesium alloys have been increasingly used in automotive and electronic industries because of their excellent strength to weight ratio and EMI shielding properties. However, magnesium alloys have low formability at room temperature due to their unique mechanical behavior (twinning and untwining), prompting for forming at an elevated temperature. In this study, a temperature dependent constitutive model for magnesium alloy (AZ31B) sheet is developed. A hardening law based on non linear kinematic hardening model is used to consider Bauschinger effect properly. Material parameters are determined from a series of uni-axial cyclic experiments (T-C-T or C-T-C) with the temperature ranging 150-250Â° C. The influence of temperature on the constitutive equation is introduced by the material parameters assumed to be functions of temperature. Fitting process of the assumed model to measured data is presented and the results are compared.
Comparison of two laryngeal tissue fiber constitutive models
NASA Astrophysics Data System (ADS)
Hunter, Eric J.; Palaparthi, Anil Kumar Reddy; Siegmund, Thomas; Chan, Roger W.
2014-02-01
Biological tissues are complex time-dependent materials, and the best choice of the appropriate time-dependent constitutive description is not evident. This report reviews two constitutive models (a modified Kelvin model and a two-network Ogden-Boyce model) in the characterization of the passive stress-strain properties of laryngeal tissue under tensile deformation. The two models are compared, as are the automated methods for parameterization of tissue stress-strain data (a brute force vs. a common optimization method). Sensitivity (error curves) of parameters from both models and the optimized parameter set are calculated and contrast by optimizing to the same tissue stress-strain data. Both models adequately characterized empirical stress-strain datasets and could be used to recreate a good likeness of the data. Nevertheless, parameters in both models were sensitive to measurement errors or uncertainties in stress-strain, which would greatly hinder the confidence in those parameters. The modified Kelvin model emerges as a potential better choice for phonation models which use a tissue model as one component, or for general comparisons of the mechanical properties of one type of tissue to another (e.g., axial stress nonlinearity). In contrast, the Ogden-Boyce model would be more appropriate to provide a basic understanding of the tissue's mechanical response with better insights into the tissue's physical characteristics in terms of standard engineering metrics such as shear modulus and viscosity.
A review of nonlinear constitutive models for metals
NASA Technical Reports Server (NTRS)
Allen, David H.; Harris, Charles E.
1990-01-01
Over the past two decades a number of thermomechanical constitutive theories have been proposed for viscoplastic metals. These models are in most cases similar in that they utilize a set of internal state variables which provide locally averaged representations of microphysical phenomena such as dislocation rearrangement and grain boundary sliding. The state of development of several of these models is now at the point where accurate theoretical solutions can be obtained for a wide variety of structural problems at elevated temperatures. The fundamentals of viscoplasticity are briefly reviewed and a general framework is outlined. Several of the more prominent models are reviewed, and predictions from models are compared to experimental results.
Fault models and constitutive laws across the lithosphere
NASA Astrophysics Data System (ADS)
Shimamoto, T.
2011-12-01
Establishment of fault model is important not only for modeling earthquake cycles (stress accumulation, earthquake generation and afterslip), but also for analyzing tectonics of lithosphere. Since Sibson (1977, J. Geol. Soc. London) proposed a famous fault model, several fault models have been proposed (Scholz, 1988, Geol. Rundschau; Shimamoto, 1989, J. Struct. Geol.; Kawamoto and Shimamoto, 1998, Tectonophy). There has not been much progress in fault models since then, and even those fault models had limited applications in the modeling earthquakes and tectonics because no constitutive laws describing brittle to high-temperature ductile deformation across the lithosphere have been proposed. Moreover there was no additional experimental data reported to cover the brittle-ductile transition under large shearing deformation. However, the situation has been changing since Shimamoto (2004, JpGU) and Shimamoto and Noda, 2010, AGU) proposed an empirical friction to flow law which describes the transition from friction to fully plastic flow under shear for halite. Only frictional constitutive parameters and parameters in flow law are used and properties in the transitional regime can be predicted once those parameters are known. Thus this law provides a working model for reanalyzing diverse fault properties such as clay-bearing faults, for planning experimental researches to produce friction to flow behavior for realistic rocks, and for modeling fault and plate-boundary behaviors including generation of large earthquakes. I will summarize the current status on fault models and friction to flow constitutive laws across the lithosphere focusing the following aspects. (1) Friction to flow transition for important rocks. Existing friction and flows laws will be combined to propose constitutive property across the lithosphere (e.g., rate and state friction law combined with flow law for diabase). I will show how such a law can be used in the modeling using 2D modeling of
Mesoscale constitutive modeling of non-crystallizing filled elastomers
NASA Astrophysics Data System (ADS)
Harish, Ajay B.; Wriggers, Peter; Jungk, Juliane; Hojdis, Nils; Recker, Carla
2016-04-01
Elastomers are exceptional materials owing to their ability to undergo large deformations before failure. However, due to their very low stiffness, they are not always suitable for industrial applications. Addition of filler particles provides reinforcing effects and thus enhances the material properties that render them more versatile for applications like tyres etc. However, deformation behavior of filled polymers is accompanied by several nonlinear effects like Mullins and Payne effect. To this day, the physical and chemical changes resulting in such nonlinear effect remain an active area of research. In this work, we develop a heterogeneous (or multiphase) constitutive model at the mesoscale explicitly considering filler particle aggregates, elastomeric matrix and their mechanical interaction through an approximate interface layer. The developed constitutive model is used to demonstrate cluster breakage, also, as one of the possible sources for Mullins effect observed in non-crystallizing filled elastomers.
A variational constitutive model for porous metal plasticity
NASA Astrophysics Data System (ADS)
Weinberg, K.; Mota, A.; Ortiz, M.
2006-01-01
This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.
Dynamic mechanical behavior and the constitutive model of concrete subjected to impact loadings
NASA Astrophysics Data System (ADS)
Ning, Jianguo; Liu, Haifeng; Shang, Lin
2008-11-01
Based on the theory of consecutive damage mechanics, micro-mechanics, statistics and the visco-plastic constitutive equation of Perzyna, a coupled model of damage and plasticity is developed to describe the complex behavior of concrete subjected to impact loadings. In this model, some suppositions about deformation of the material and evolution of the damage are made. First, concrete is macroscopically assumed to be homogeneous and consecutive, while it is microscopically filled with large amounts of micro-crack and micro-void defects. Second, the damage evolution of the micro-cracks is caused by the nucleation, growth and coalescence of the micro-cracks due to the interior tensile stress in concrete, which leads to a degradation in the strength and stiffness of concrete. Third, compaction of concrete is physically a collapse of the material micro-void. It produces irreversible plastic strains in the material and, at the same time, an increase in the bulk modulus. Fourth, there is no interaction between the micro-crack and the micro-void. Last, when the damage reaches a critical value, the concrete may fail totally. The model parameters for concrete are determined by plate impact experiments. The model predictions fit the experimental results well. So the model can be used to simulate the dynamic mechanical behavior of concrete under impact loadings.
A constitutive model of nanocomposite hydrogels with nanoparticle crosslinkers
NASA Astrophysics Data System (ADS)
Wang, Qiming; Gao, Zheming
2016-09-01
Nanocomposite hydrogels with only nanoparticle crosslinkers exhibit extraordinarily higher stretchability and toughness than the conventional organically crosslinked hydrogels, thus showing great potential in the applications of artificial muscles and cartilages. Despite their potential, the microscopic mechanics details underlying their mechanical performance have remained largely elusive. Here, we develop a constitutive model of the nanoparticle hydrogels to elucidate the microscopic mechanics behaviors, including the microarchitecture and evolution of the nanoparticle crosslinked polymer chains during the mechanical deformation. The constitutive model enables us to understand the Mullins effect of the nanocomposite hydrogels, and the effects of nanoparticle concentrations and sizes on their cyclic stress-strain behaviors. The theory is quantitatively validated by the tensile tests on a nanocomposite hydrogel with nanosilica crosslinkers. The theory can also be extended to explain the mechanical behaviors of existing hydrogels with nanoclay crosslinkers, and the necking instability of the composite hydrogels with both nanoparticle crosslinkers and organic crosslinkers. We expect that this constitutive model can be further exploited to reveal mechanics behaviors of novel particle-polymer chain interactions, and to design unprecedented hydrogels with both high stretchability and toughness.
Slag Behavior in Gasifiers. Part II: Constitutive Modeling of Slag
Massoudi, Mehrdad; Wang, Ping
2013-02-07
The viscosity of slag and the thermal conductivity of ash deposits are among two of the most important constitutive parameters that need to be studied. The accurate formulation or representations of the (transport) properties of coal present a special challenge of modeling efforts in computational fluid dynamics applications. Studies have indicated that slag viscosity must be within a certain range of temperatures for tapping and the membrane wall to be accessible, for example, between 1,300 Â°C and 1,500 Â°C, the viscosity is approximately 25 PaÂ·s. As the operating temperature decreases, the slag cools and solid crystals begin to form. Since slag behaves as a non-linear fluid, we discuss the constitutive modeling of slag and the important parameters that must be studied. We propose a new constitutive model, where the stress tensor not only has a yield stress part, but it also has a viscous part with a shear rate dependency of the viscosity, along with temperature and concentration dependency, while allowing for the possibility of the normal stress effects. In Part I, we reviewed, identify and discuss the key coal ash properties and the operating conditions impacting slag behavior.
Bayesian calibration of hyperelastic constitutive models of soft tissue.
Madireddy, Sandeep; Sista, Bhargava; Vemaganti, Kumar
2016-06-01
There is inherent variability in the experimental response used to characterize the hyperelastic mechanical response of soft tissues. This has to be accounted for while estimating the parameters in the constitutive models to obtain reliable estimates of the quantities of interest. The traditional least squares method of parameter estimation does not give due importance to this variability. We use a Bayesian calibration framework based on nested Monte Carlo sampling to account for the variability in the experimental data and its effect on the estimated parameters through a systematic probability-based treatment. We consider three different constitutive models to represent the hyperelastic nature of soft tissue: Mooney-Rivlin model, exponential model, and Ogden model. Three stress-strain data sets corresponding to the deformation of agarose gel, bovine liver tissue, and porcine brain tissue are considered. Bayesian fits and parameter estimates are compared with the corresponding least squares values. Finally, we propagate the uncertainty in the parameters to a quantity of interest (QoI), namely the force-indentation response, to study the effect of model form on the values of the QoI. Our results show that the quality of the fit alone is insufficient to determine the adequacy of the model, and due importance has to be given to the maximum likelihood value, the landscape of the likelihood distribution, and model complexity. PMID:26751706
Constitutive modeling of crimped collagen fibrils in soft tissues.
Grytz, Rafael; Meschke, GÃ¼nther
2009-10-01
A microstructurally oriented constitutive formulation for the hyperelastic response of crimped collagen fibrils existing in soft connective tissues is proposed. The model is based on observations that collagen fibrils embedded in a soft matrix crimp into a smooth three-dimensional pattern when unloaded. Following ideas presented by Beskos and Jenkins [Beskos, D., Jenkins, J., 1975. A mechanical model for mammalian tendon. ASME Journal of Applied Mechanics 42, 755-758] and Freed and Doehring [Freed, A., Doehring, T., 2005. Elastic model for crimped collagen fibrils. Journal of Biomechanical Engineering 127, 587-593] the collagen fibril crimp is approximated by a cylindrical helix to represent the constitutive behavior of the hierarchical organized substructure of biological tissues at the fibrillar level. The model is derived from the nonlinear axial force-stretch relationship of an extensible helical spring, including the full extension of the spring as a limit case. The geometrically nonlinear solution of the extensible helical spring is carried out by an iterative procedure. The model only requires one material parameter and two geometrical parameters to be determined from experiments. The ability of the proposed model to reproduce the biomechanical response of fibrous tissues is demonstrated for fascicles from rat tail tendons, for porcine cornea strips, and for bovine Achilles tendons. PMID:19627859
A constitutive model for magnetostriction based on thermodynamic framework
NASA Astrophysics Data System (ADS)
Ho, Kwangsoo
2016-08-01
This work presents a general framework for the continuum-based formulation of dissipative materials with magneto-mechanical coupling in the viewpoint of irreversible thermodynamics. The thermodynamically consistent model developed for the magnetic hysteresis is extended to include the magnetostrictive effect. The dissipative and hysteretic response of magnetostrictive materials is captured through the introduction of internal state variables. The evolution rate of magnetostrictive strain as well as magnetization is derived from thermodynamic and dissipative potentials in accordance with the general principles of thermodynamics. It is then demonstrated that the constitutive model is competent to describe the magneto-mechanical behavior by comparing simulation results with the experimental data reported in the literature.
Life prediction and constitutive models for engine hot section
NASA Technical Reports Server (NTRS)
Swanson, G. A.; Meyer, T. G.; Nissley, D. M.
1986-01-01
The purpose of this program is to develop life prediction models for coated anisotropic materials used in gas turbine airfoils. In the program, two single crystal alloys and two coatings are being tested. These include PWA 1480, Alloy 185, overlay coating (PWA 286), and aluminide coating (PWA 273). Constitutive models are also being developed for these materials to predict the time independent (plastic) and time dependent (creep) strain histories of the materials in the lab tests and for actual design conditions. This nonlinear material behavior is particularly important for high temperature gas turbine applications and is basic to any life prediction system. Some of the accomplishments of the program are highlighted.
Image guided constitutive modeling of the silicone brain phantom
NASA Astrophysics Data System (ADS)
Puzrin, Alexander; Skrinjar, Oskar; Ozan, Cem; Kim, Sihyun; Mukundan, Srinivasan
2005-04-01
The goal of this work is to develop reliable constitutive models of the mechanical behavior of the in-vivo human brain tissue for applications in neurosurgery. We propose to define the mechanical properties of the brain tissue in-vivo, by taking the global MR or CT images of a brain response to ventriculostomy - the relief of the elevated intracranial pressure. 3D image analysis translates these images into displacement fields, which by using inverse analysis allow for the constitutive models of the brain tissue to be developed. We term this approach Image Guided Constitutive Modeling (IGCM). The presented paper demonstrates performance of the IGCM in the controlled environment: on the silicone brain phantoms closely simulating the in-vivo brain geometry, mechanical properties and boundary conditions. The phantom of the left hemisphere of human brain was cast using silicon gel. An inflatable rubber membrane was placed inside the phantom to model the lateral ventricle. The experiments were carried out in a specially designed setup in a CT scanner with submillimeter isotropic voxels. The non-communicative hydrocephalus and ventriculostomy were simulated by consequently inflating and deflating the internal rubber membrane. The obtained images were analyzed to derive displacement fields, meshed, and incorporated into ABAQUS. The subsequent Inverse Finite Element Analysis (based on Levenberg-Marquardt algorithm) allowed for optimization of the parameters of the Mooney-Rivlin non-linear elastic model for the phantom material. The calculated mechanical properties were consistent with those obtained from the element tests, providing justification for the future application of the IGCM to in-vivo brain tissue.
A new constitutive model for nitrogen austenitic stainless steel
NASA Astrophysics Data System (ADS)
FrÃ©chard, S.; Lichtenberger, A.; Rondot, F.; Faderl, N.; RedjaÃ¯mia, A.; Adoum, M.
2003-09-01
Quasi-static, quasi-dynamic and dynamic compression tests have been performed on a nitrogen alloyed austenitic stainless steel. For all strain rates, a high strain hardening rate and a good ductility have been achieved. In addition, this steel owns a great strain rate sensitivity. The temperature sensitivity bas been determined between 20Â°C and 400Â°C. Microstructural analysis has been performed after different loading conditions in relation to the behaviour of the material. Johnson-Cook and Zerilli-Armstrong models have been selected to fit the experimental data into constitutive equations. These models do not reproduce properly the behaviour of this type of steel over the complete range. A new constitutive model that fits very well all the experimental data at different strain, strain rate and temperature has been determined. The model is based on empirical considerations on the separated influence of the main parameters. Single Taylor tests have been realized to validate the models. Live observations of the specimen during impact have been achieved using a special CCD camera set-up. The overall profile at different times are compared to numerical predictions using LS-DYNA code.
Micromechanics and constitutive modeling of connective soft tissues.
Fallah, A; Ahmadian, M T; Firozbakhsh, K; Aghdam, M M
2016-07-01
In this paper, a micromechanical model for connective soft tissues based on the available histological evidences is developed. The proposed model constituents i.e. collagen fibers and ground matrix are considered as hyperelastic materials. The matrix material is assumed to be isotropic Neo-Hookean while the collagen fibers are considered to be transversely isotropic hyperelastic. In order to take into account the effects of tissue structure in lower scales on the macroscopic behavior of tissue, a strain energy density function (SEDF) is developed for collagen fibers based on tissue hierarchical structure. Macroscopic response and properties of tissue are obtained using the numerical homogenization method with the help of ABAQUS software. The periodic boundary conditions and the proposed constitutive models are implemented into ABAQUS using the DISP and the UMAT subroutines, respectively. The existence of the solution and stable material behavior of proposed constitutive model for collagen fibers are investigated based on the poly-convexity condition. Results of the presented micromechanics model for connective tissues are compared and validated with available experimental data. Effects of geometrical and material parameters variation at microscale on macroscopic mechanical behavior of tissues are investigated. The results show that decrease in collagen content of the connective tissues like the tendon due to diseases leads 20% more stretch than healthy tissue under the same load which can results in connective tissue malfunction and hypermobility in joints. PMID:26807767
A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues.
Comellas, Ester; Gasser, T Christian; Bellomo, Facundo J; Oller, Sergio
2016-03-01
Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data. PMID:27009177
Damage modeling and damage detection for structures using a perturbation method
NASA Astrophysics Data System (ADS)
Dixit, Akash
This thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage. Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following: 1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity. 2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it. 3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and
Constitutive Modeling of Nanotube-Reinforced Polymer Composites
NASA Technical Reports Server (NTRS)
Odegard, G. M.; Gates, T. S.; Wise, K. E.
2002-01-01
In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube shapes, sizes, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/LaRC-SI (with a PmPV interface) composite systems, one with aligned SWNTs and the other with three-dimensionally randomly oriented SWNTs. The Young's modulus and shear modulus have been calculated for the two systems for various nanotube lengths and volume fractions.
Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems
NASA Technical Reports Server (NTRS)
Odegard, Gregory M.; Harik, Vasyl M.; Wise, Kristopher E.; Gates, Thomas S.
2001-01-01
In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.
Constitutive Modeling of Nanotube-Reinforced Polymer Composites
NASA Technical Reports Server (NTRS)
Odegard, G. M.; Gates, T. S.; Wise, K. E.; Park, C.; Siochi, E. J.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube lengths, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyimide composite systems.
Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems
NASA Technical Reports Server (NTRS)
Odegard, Gregory M.; Harik, Vasyl M.; Wise, Kristopher E.; Gates, Thomas S.
2004-01-01
In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.
Anisotropic effects on constitutive model parameters of aluminum alloys
NASA Astrophysics Data System (ADS)
Brar, Nachhatter S.; Joshi, Vasant S.
2012-03-01
Simulation of low velocity impact on structures or high velocity penetration in armor materials heavily rely on constitutive material models. Model constants are determined from tension, compression or torsion stress-strain at low and high strain rates at different temperatures. These model constants are required input to computer codes (LS-DYNA, DYNA3D or SPH) to accurately simulate fragment impact on structural components made of high strength 7075-T651 aluminum alloy. Johnson- Cook model constants determined for Al7075-T651 alloy bar material failed to simulate correctly the penetration into 1' thick Al-7075-T651plates. When simulation go well beyond minor parameter tweaking and experimental results show drastically different behavior it becomes important to determine constitutive parameters from the actual material used in impact/penetration experiments. To investigate anisotropic effects on the yield/flow stress of this alloy quasi-static and high strain rate tensile tests were performed on specimens fabricated in the longitudinal "L", transverse "T", and thickness "TH" directions of 1' thick Al7075 Plate. While flow stress at a strain rate of ~1/s as well as ~1100/s in the thickness and transverse directions are lower than the longitudinal direction. The flow stress in the bar was comparable to flow stress in the longitudinal direction of the plate. Fracture strain data from notched tensile specimens fabricated in the L, T, and Thickness directions of 1' thick plate are used to derive fracture constants.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
NASA Technical Reports Server (NTRS)
Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.
1989-01-01
The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.
Constitutive modelling of evolving flow anisotropy including distortional hardening
Pietryga, Michael P.; Vladimirov, Ivaylo N.; Reese, Stefanie
2011-05-04
The paper presents a new constitutive model for anisotropic metal plasticity that takes into account the expansion or contraction (isotropic hardening), translation (kinematic hardening) and change of shape (distortional hardening) of the yield surface. The experimentally observed region of high curvature ('nose') on the yield surface in the loading direction and flattened shape in the reverse loading direction are modelled here by means of the concept of directional distortional hardening. The modelling of directional distortional hardening is accomplished by means of an evolving fourth-order tensor. The applicability of the model is illustrated by fitting experimental subsequent yield surfaces at finite plastic deformation. Comparisons with test data for aluminium low and high work hardening alloys display a good agreement between the simulation results and the experimental data.
Constitutive modeling and computational implementation for finite strain plasticity
NASA Technical Reports Server (NTRS)
Reed, K. W.; Atluri, S. N.
1985-01-01
This paper describes a simple alternate approach to the difficult problem of modeling material behavior. Starting from a general representation for a rate-tpe constitutive equation, it is shown by example how sets of test data may be used to derive restrictions on the scalar functions appearing in the representation. It is not possible to determine these functions from experimental data, but the aforementioned restrictions serve as a guide in their eventual definition. The implications are examined for hypo-elastic, isotropically hardening plastic, and kinematically hardening plastic materials. A simple model for the evolution of the 'back-stress,' in a kinematic-hardening plasticity theory, that is entirely analogous to a hypoelastic stress-strain relation is postulated and examined in detail in modeling finitely plastic tension-torsion test. The implementation of rate-type material models in finite element algorithms is also discussed.
A constitutive model for ballistic gelatin at surgical strain rates.
Ravikumar, Nishant; Noble, Christopher; Cramphorn, Edward; Taylor, Zeike A
2015-07-01
This paper describes a constitutive model for ballistic gelatin at the low strain rates experienced, for example, by soft tissues during surgery. While this material is most commonly associated with high speed projectile penetration and impact investigations, it has also been used extensively as a soft tissue simulant in validation studies for surgical technologies (e.g. surgical simulation and guidance systems), for which loading speeds and the corresponding mechanical response of the material are quite different. We conducted mechanical compression experiments on gelatin specimens at strain rates spanning two orders of magnitude (~0.001-0.1s(-1)) and observed a nonlinear load-displacement history and strong strain rate-dependence. A compact and efficient visco-hyperelastic constitutive model was then formulated and found to fit the experimental data well. An Ogden type strain energy density function was employed for the elastic component. A single Prony exponential term was found to be adequate to capture the observed rate-dependence of the response over multiple strain rates. The model lends itself to immediate use within many commercial finite element packages. PMID:25863009
Anisotropic Effects on Constitutive Model Parameters of Aluminum Alloys
NASA Astrophysics Data System (ADS)
Brar, Nachhatter; Joshi, Vasant
2011-06-01
Simulation of low velocity impact on structures or high velocity penetration in armor materials heavily rely on constitutive material models. The model constants are required input to computer codes (LS-DYNA, DYNA3D or SPH) to accurately simulate fragment impact on structural components made of high strength 7075-T651 aluminum alloys. Johnson-Cook model constants determined for Al7075-T651 alloy bar material failed to simulate correctly the penetration into 1' thick Al-7075-T651plates. When simulations go well beyond minor parameter tweaking and experimental results are drastically different it is important to determine constitutive parameters from the actual material used in impact/penetration experiments. To investigate anisotropic effects on the yield/flow stress of this alloy we performed quasi-static and high strain rate tensile tests on specimens fabricated in the longitudinal, transverse, and thickness directions of 1' thick Al7075-T651 plate. Flow stresses at a strain rate of ~1100/s in the longitudinal and transverse direction are similar around 670MPa and decreases to 620 MPa in the thickness direction. These data are lower than the flow stress of 760 MPa measured in Al7075-T651 bar stock.
Ductile damage model with void coalescence
Tonks, D.L.
1995-03-01
A general model for ductile damage in metals is presented. It includes damage induced by shear stress as well as damage caused by volumetric tension. Spallation is included as a special case. Strain induced damage is also treated. Void nucleation and growth are included and give rise to strain rate effects. Strain rate effects also arise in the model through elastic release wave propagation between damage centers. Underlying physics of the model is the nucleation, growth, and coalescence of voids in a plastically flowing solid. Implementation of the model in hydrocodes is discussed.
Materials constitutive models for nonlinear analysis of thermally cycled structures
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hunt, L. E.
1982-01-01
Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.
An Experimental Study and Constitutive Modeling of Saturated Porous Rocks
NASA Astrophysics Data System (ADS)
Xie, S. Y.; Shao, J. F.
2015-01-01
This paper is devoted to the experimental characterization and constitutive modeling of saturated porous rocks. A typical porous chalk is investigated. Drained hydrostatic and triaxial compression tests are first performed to characterize the basic mechanical behavior of chalk. Drained triaxial tests with constant interstitial pressure are then carried out to study the effects of interstitial pressure on the plastic deformation and failure criterion. Finally, undrained triaxial compression tests are performed to investigate poromechanical coupling in saturated conditions. Based on the experimental data and some relevant micromechanical considerations, a micromechanics-based plastic model is proposed and extended to poroplastic coupling using the effective stress concept. The proposed model is verified through comparisons between the numerical results and experimental data for both drained and undrained tests.
NASA Technical Reports Server (NTRS)
Allen, David H.; Groves, Scott E.; Harris, Charles E.
1988-01-01
The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.
A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.
English, Shawn Allen
2014-09-01
A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.
A Micromechanics Based Constitutive Model For Brittle Failure at High Strain Rates
NASA Astrophysics Data System (ADS)
Bhat, H. S.; Rosakis, A.; Sammis, C. G.
2011-12-01
The micromechanical damage mechanics formulated by Ashby and Sammis [1] and generalized by Desh- pande and Evans [2] has been extended to allow for a more generalized stress state and to incorporate an ex- perimentally motivated new crack growth (damage evo- lution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces strain-rate sensitivity in the constitutive re- sponse. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from Ëœ 10-6 to 103 s-1. Model parameters determined from from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.
Constitutive modeling of ascending thoracic aortic aneurysms using microstructural parameters.
Pasta, Salvatore; Phillippi, Julie A; Tsamis, Alkiviadis; D'Amore, Antonio; Raffa, Giuseppe M; Pilato, Michele; Scardulla, Cesare; Watkins, Simon C; Wagner, William R; Gleason, Thomas G; Vorp, David A
2016-02-01
Ascending thoracic aortic aneurysm (ATAA) has been associated with diminished biomechanical strength and disruption in the collagen fiber microarchitecture. Additionally, the congenital bicuspid aortic valve (BAV) leads to a distinct extracellular matrix structure that may be related to ATAA development at an earlier age than degenerative aneurysms arising in patients with the morphological normal tricuspid aortic valve (TAV). The purpose of this study was to model the fiber-reinforced mechanical response of ATAA specimens from patients with either BAV or TAV. This was achieved by combining image-analysis derived parameters of collagen fiber dispersion and alignment with tensile testing data. Then, numerical simulations were performed to assess the role of anisotropic constitutive formulation on the wall stress distribution of aneurysmal aorta. Results indicate that both BAV ATAA and TAV ATAA have altered collagen fiber architecture in the medial plane of experimentally-dissected aortic tissues when compared to normal ascending aortic specimens. The study findings highlight that differences in the collagen fiber distribution mostly influences the resulting wall stress distribution rather than the peak stress. We conclude that fiber-reinforced constitutive modeling that takes into account the collagen fiber defect inherent to the aneurysmal ascending aorta is paramount for accurate finite element predictions and ultimately for biomechanical-based indicators to reliably distinguish the more from the less 'malignant' ATAAs. PMID:26669606
High rate constitutive modeling of aluminium alloy tube
NASA Astrophysics Data System (ADS)
Salisbury, C. P.; Worswick, M. J.; Mayer, R.
2006-08-01
As the need for fuel efficient automobiles increases, car designers are investigating light-weight materials for automotive bodies that will reduce the overall automobile weight. Aluminium alloy tube is a desirable material to use in automotive bodies due to its light weight. However, aluminium suffers from lower formability than steel and its energy absorption ability in a crash event after a forming operation is largely unknown. As part of a larger study on the relationship between crashworthiness and forming processes, constitutive models for 3mm AA5754 aluminium tube were developed. A nominal strain rate of 100/s is often used to characterize overall automobile crash events, whereas strain rates on the order of 1000/s can occur locally. Therefore, tests were performed at quasi-static rates using an Instron test fixture and at strain rates of 500/s to 1500/s using a tensile split Hopkinson bar. High rate testing was then conducted at rates of 500/s, 1000/s and 1500/s at 21circC, 150circC and 300circC. The generated data was then used to determine the constitutive parameters for the Johnson-Cook and Zerilli-Armstrong material models.
Mechanistic Constitutive Models for Rubber Elasticity and Viscoelasticity
Puso, M
2003-01-21
Physically based models which describe the finite strain behavior of vulcanized rubber are developed. Constitutive laws for elasticity and viscoelasticity are derived by integrating over orientation space the forces due to each individual polymer chain. A novel scheme is presented which effectively approximates these integrals in terms of strain and strain invariants. In addition, the details involving the implementation of such models into a quasi-static large strain finite element formulation are provided. In order to account for the finite extensibility of a molecular chain, Langevin statistics is used to model the chain response. The classical statistical model of rubber assumes that polymer chains interact only at the chemical crosslinks. It is shown that such model when fitted for uniaxial tension data cannot fit compression or equibiaxial data. A model which incorporates the entanglement interactions of surrounding chains, in addition to the finite extensibility of the chains, is shown to give better predictions than the classical model. The technique used for approximating the orientation space integral was applied to both the classical and entanglement models. A viscoelasticity model based on the force equilibration process as described by Doi and Edwards is developed. An assumed form for the transient force in the chain is postulated. The resulting stress tensor is composed of an elastic and a viscoelastic portion with the elastic stress given by the proposed entanglement model. In order to improve the simulation of experimental data, it was found necessary to include the effect of unattached or dangling polymer chains in the viscoelasticity model. The viscoelastic effect of such chains is the manifestation of a disengagement process. This disengagement model for unattached polymer chains motivated an empirical model which was very successful in simulating the experimental results considered.
NASA Astrophysics Data System (ADS)
Nagel, T.; BÃ¶ttcher, N.; GÃ¶rke, U. J.; Kolditz, O.
2014-12-01
The design process of geotechnical installations includes the application of numerical simulation tools for safety assessment, dimensioning and long term effectiveness estimations. Underground salt caverns can be used for the storage of natural gas, hydrogen, oil, waste or compressed air. For their design one has to take into account fluctuating internal pressures due to different levels of filling, the stresses imposed by the surrounding rock mass, irregular geometries and possibly heterogeneous material properties [3] in order to estimate long term cavern convergence as well as locally critical wall stresses. Constitutive models applied to rock salt are usually viscoplastic in nature and most often based on a Burgers-type rheological model extended by non-linear viscosity functions and/or plastic friction elements. Besides plastic dilatation, healing and damage are sometimes accounted for as well [2]. The scales of the geotechnical system to be simulated and the laboratory tests from which material parameters are determined are vastly different. The most common material testing modalities to determine material parameters in geoengineering are the uniaxial and the triaxial compression tests. Some constitutive formulations in widespread use are formulated based on equivalent rather than tensorial quantities valid under these specific test conditions and are subsequently applied to heterogeneous underground systems and complex 3D load cases. We show here that this procedure is inappropriate and can lead to erroneous results. We further propose alternative formulations of the constitutive models in question that restore their validity under arbitrary loading conditions. For an efficient numerical simulation, the discussed constitutive models are integrated locally with a Newton-Raphson algorithm that directly provides the algorithmically consistent tangent matrix for the global Newton iteration of the displacement based finite element formulation. Finally, the finite
Derenzini, Enrico; Agostinelli, Claudio; Imbrogno, Enrica; Iacobucci, Ilaria; Casadei, Beatrice; Brighenti, Elisa; Righi, Simona; Fuligni, Fabio; Ghelli Luserna Di RorÃ , Andrea; Ferrari, Anna; Martinelli, Giovanni; Pileri, Stefano; Zinzani, Pier Luigi
2015-03-30
The recent finding that MYC-driven cancers are sensitive to inhibition of the DNA damage response (DDR) pathway, prompted us to investigate the role of DDR pathway as therapeutic target in diffuse large B-cell lymphoma (DLBCL), which frequently overexpresses the MYC oncogene. In a preliminary immunohistochemical study conducted on 99 consecutive DLBCL patients, we found that about half of DLBCLs showed constitutive expression of the phosphorylated forms of checkpoint kinases (CHK) and CDC25c, markers of DDR activation, and of phosphorylated histone H2AX (Î³H2AX), marker of DNA damage and genomic instability. Constitutive Î³H2AX expression correlated with c-MYC levels and DDR activation, and defined a subset of tumors characterised by poor outcome. Next, we used the CHK inhibitor PF-0477736 as a tool to investigate whether the inhibition of the DDR pathway might represent a novel therapeutic approach in DLBCL. Submicromolar concentrations of PF-0477736 hindered proliferation in DLBCL cell lines with activated DDR pathway. These results were fully recapitulated with a different CHK inhibitor (AZD-7762). Inhibition of checkpoint kinases induced rapid DNA damage accumulation and apoptosis in DLBCL cell lines and primary cells. These data suggest that pharmacologic inhibition of DDR through targeting of CHK kinases may represent a novel therapeutic strategy in DLBCL. PMID:25544753
Derenzini, Enrico; Agostinelli, Claudio; Imbrogno, Enrica; Iacobucci, Ilaria; Casadei, Beatrice; Brighenti, Elisa; Righi, Simona; Fuligni, Fabio; Di RorÃ , Andrea Ghelli Luserna; Ferrari, Anna; Martinelli, Giovanni; Pileri, Stefano; Zinzani, Pier Luigi
2015-01-01
The recent finding that MYC-driven cancers are sensitive to inhibition of the DNA damage response (DDR) pathway, prompted us to investigate the role of DDR pathway as therapeutic target in diffuse large B-cell lymphoma (DLBCL), which frequently overexpresses the MYC oncogene. In a preliminary immunohistochemical study conducted on 99 consecutive DLBCL patients, we found that about half of DLBCLs showed constitutive expression of the phosphorylated forms of checkpoint kinases (CHK) and CDC25c, markers of DDR activation, and of phosphorylated histone H2AX (Î³H2AX), marker of DNA damage and genomic instability. Constitutive Î³H2AX expression correlated with c-MYC levels and DDR activation, and defined a subset of tumors characterised by poor outcome. Next, we used the CHK inhibitor PF-0477736 as a tool to investigate whether the inhibition of the DDR pathway might represent a novel therapeutic approach in DLBCL. Submicromolar concentrations of PF-0477736 hindered proliferation in DLBCL cell lines with activated DDR pathway. These results were fully recapitulated with a different CHK inhibitor (AZD-7762). Inhibition of checkpoint kinases induced rapid DNA damage accumulation and apoptosis in DLBCL cell lines and primary cells. These data suggest that pharmacologic inhibition of DDR through targeting of CHK kinases may represent a novel therapeutic strategy in DLBCL. PMID:25544753
Constitutive modelling of dual phase steel sheet and tube
NASA Astrophysics Data System (ADS)
Thompson, A. C.; Salisbury, C. P.; Worswick, M. J.; Mayer, R.
2006-08-01
Automobile manufacturers are currently striving to improve vehicle fuel efficiency through reduction of vehicle weight. Dual phase steels are good candidates for automotive bodies due to their high strength-to-weight ratio, and good formablity and weldability. As part of a project on the interaction between forming and crashworthiness, constitutive parameters of a dual phase steel were determined for both sheet and tube stock in order to support analysis of the tube response throughout forming processes and in crash simulations. Stress - strain data was collected at a quasi-static rate as well as rates from 0.1 to 1500 s - 1. The intermediate strain rate response was captured using an instrumented falling weight tensile tester (35 100 s - 1), while a tensile split Hopkinson bar (500 1500 s - 1) was used to capture the high-rate response. This range of strain rates is typical of the rates seen in a crash simulation. Tests were also performed at higher temperatures (150Â°C and 300Â°C) at rates of 500 and 1500 s - 1 to capture the thermal softening response. The dual phase steel sheet and tube show an appreciable amount of strain rate sensitivity throughout the complete range of strain rates. It also exhibited a large amount of thermal softening. The thermal sensitivity is identical for the sheet and tube. Fits to the Johnson-Cook constitutive model were obtained from the experimental results.
Constitutive modeling of calcium carbonate supersaturated seawater mixtures
NASA Astrophysics Data System (ADS)
Reis, Martina; Sousa, Maria De FÃ¡tima; Bertran, Celso; Bassi, Adalberto
2014-11-01
Calcium carbonate supersaturated seawater mixtures have attracted attention of many researchers since the deposition of CaCO3(s) from such solutions can lead to scaling problems in oil fields. However, despite their evident practical importance in petroleum engineering, the hydro and thermodynamic behaviors of these mixtures have not been well-understood yet. In this work, a constitutive model based on the foundations of the constitutive theory of continuum mechanics, and the MÃ¼ller-Liu entropy principle is proposed. The calcium carbonate supersaturated seawater mixture is regarded as a reactive viscous fluid with heat and electrical conductions. The obtained results indicate that the thermodynamic behavior of CaCO3 supersaturated seawater mixtures is closely related to the individual dynamics of each constituent of the mixture, particularly to the linear momentum, and mass exchanges. Furthermore, the results show that, unlike classical continuum mixtures, the extra entropy flux is not null, and higher-order gradients of deformation contribute to the residual entropy production of the class of mixtures under study. The results of this work may be relevant for the prevention of the mineral scale formation in oil fields. The first author acknowledges the SÃ£o Paulo Research Foundation (Grant 2013/ 20872-2) for its funding.
Constitutive models for static and dynamic response of geotechnical materials
NASA Astrophysics Data System (ADS)
Nemat-Nasser, S.
1983-11-01
The objective of this research program has been to develop realistic macroscopic constitutive relations which describe static and dynamic properties of geotechnical materials (soils and rocks). To this end a coordinated theoretical and experimental activity has been followed. The theoretical work includes a balanced combination of statistical microscopic (at the grain size level) modeling and a nonclassical elasto-plastic macroscopic formulation. The latter includes the effects of internal friction, plastic compressibility, and pressure sensitivity, as well as anisotropy which is commonly observed in geotechnical materials. The following specific goals have been sought: (1) to develop three-dimensional constitutive relations under ordinary or high pressures (such as those induced by blasting or tectonic forces which may cause a large amount of densification by relative motion and possible crushing of grains); and (2) to examine and characterize the behavior of saturated granular materials under dynamic loading. The latter item includes characterization of possible liquefaction and subsidence which may be induced in granular materials under confining pressure by ground vibration or passage of waves. The theoretical work has been carefully coordinated with key experiments in order to: (1) understand the basic physics of the process, both at macroscopic and microscopic levels; (2) to verify the corresponding theoretical predictions; and (3) to establish relevant material parameters.
An uncoupled viscoplastic constitutive model for metals at elevated temperature
NASA Technical Reports Server (NTRS)
Haisler, W. E.; Cronenworth, J.
1983-01-01
An uncoupled constitutive model for predicting the transient response of thermal and rate dependent, inelastic material behavior is presented. The uncoupled model assumes that there is a temperature below which the total strain consists essentially of elastic and rate insensitive inelastic strains only. Above this temperature, the rate dependent inelastic strain (creep) dominates. The rate insensitive inelastic strain component is modeled in an incremental form with a yield function, flow rule and hardening law. Revisions to the hardening rule permit the model to predict temperature-dependent kinematic-isotropic hardening behavior, cyclic saturation, asymmetric stress-strain response upon stress reversal, and variable Bauschinger effect. The rate dependent inelastic strain component is modeled using a rate equation in terms of back stress, drag stress and exponent n as functions of temperature and strain. A sequence of hysteresis loops and relaxation tests are utilized to define the rate dependent inelastic strain rate. Evaluation of the model is performed by comparison with experiments involving various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy-X.
Modeling the Constitutive Behaviour of PET for Stretch Blow Moulding
NASA Astrophysics Data System (ADS)
Yan, S. Y.; Menary, G.
2011-05-01
There are a substantial amount of constitutive models that have been developed to capture the finite deformation behavior of polymers for forming simulations. Most of these models have been used to capture the behavior in uniaxial and simultaneous biaxial modes of deformation. However, very few have attempted to model the sequential biaxial deformation behavior which is more appropriate for the stretch blow moulding process. The aim of this work is to develop a model for PET to successfully capture the sequential stress-strain behavior as a function of temperature and strain rate, thus making it suitable for use in simulations of stretch blow moulding. Biaxial test data has been generated at temperatures and strain rates appropriate for stretch blow moulding and a model developed by Buckley et al. has been implemented within the commercial finite element package Abaqus/Explicit. In parallel, an efficient automatic curve fitting procedure has been developed to enable the material parameters to be easily found from biaxial test data. The results show that the Buckley model can predict the stress response of equibiaxial deformation well, but cannot predict the sequential biaxial deformation.
NASA Astrophysics Data System (ADS)
Vidal-SallÃ©, Emmanuelle; Chassagne, Pierre
2007-06-01
This paper presents a nonlinear viscoelastic orthotropic constitutive equation applied to wood material. The proposed model takes into account mechanical and mechanosorptive creep via a 3D stress ratio and moisture change rate for a cylindrical orthotropic material. Orthotropic frame is based on the grain direction (L), radial (R) and hoop (T) directions, which are natural wood directions. Particular attention is taken to ensure the model to fulfill the necessary dissipation conditions. It is based on a rheological generalized Maxwell model with two elements in parallel in addition with a single linear spring taking into account the long term response. The proposed model is implemented in the finite element code ABAQUS/StandardÂ® via a user subroutine UMAT and simple example is shown to demonstrate the capability of the proposed model. Future works would deal with damage and fracture prediction for wooden structures submitted to climate variations and mechanical loading.
A microstructurally inspired damage model for early venous thrombus.
Rausch, Manuel K; Humphrey, Jay D
2015-03-01
Accumulative damage may be an important contributor to many cases of thrombotic disease progression. Thus, a complete understanding of the pathological role of thrombus requires an understanding of its mechanics and in particular mechanical consequences of damage. In the current study, we introduce a novel microstructurally inspired constitutive model for thrombus that considers a non-uniform distribution of microstructural fibers at various crimp levels and employs one of the distribution parameters to incorporate stretch-driven damage on the microscopic level. To demonstrate its ability to represent the mechanical behavior of thrombus, including a recently reported Mullins type damage phenomenon, we fit our model to uniaxial tensile test data of early venous thrombus. Our model shows an agreement with these data comparable to previous models for damage in elastomers with the added advantages of a microstructural basis and fewer model parameters. We submit that our novel approach marks another important step toward modeling the evolving mechanics of intraluminal thrombus, specifically its damage, and hope it will aid in the study of physiological and pathological thrombotic events. PMID:26523784
Some advances in experimentation supporting development of viscoplastic constitutive models
NASA Technical Reports Server (NTRS)
Ellis, J. R.; Robinson, D. N.
1985-01-01
The development of a biaxial extensometer capable of measuring axial, torsion, and diametral strains to near-microstrain resolution at elevated temperatures is discussed. An instrument with this capability was needed to provide experimental support to the development of viscoplastic constitutive models. The advantages gained when torsional loading is used to investigate inelastic material response at elevated temperatures are highlighted. The development of the biaxial extensometer was conducted in two stages. The first involved a series of bench calibration experiments performed at room temperature. The second stage involved a series of in-place calibration experiments conducted at room and elevated temperature. A review of the calibration data indicated that all performance requirements regarding resolution, range, stability, and crosstalk had been met by the subject instrument over the temperature range of interest, 21 C to 651 C. The scope of the in-place calibration experiments was expanded to investigate the feasibility of generating stress relaxation data under torsional loading.
Some advances in experimentation supporting development of viscoplastic constitutive models
NASA Technical Reports Server (NTRS)
Ellis, J. R.; Robinson, D. N.
1985-01-01
The development of a biaxial extensometer capable of measuring axial, torsion, and diametral strains to near-microstrain resolution at elevated temperatures is discussed. An instrument with this capability was needed to provide experimental support to the development of viscoplastic constitutive models. The advantages gained when torsional loading is used to investigate inelastic material response at elevated temperatures are highlighted. The development of the biaxial extensometer was conducted in two stages. The first involved a series of bench calibration experiments performed at room temperature. The second stage involved a series of in-place calibration experiments performed at room temperature. A review of the calibration data indicated that all performance requirements regarding resolution, range, stability, and crosstalk had been met by the subject instrument over the temperature range of interest, 21 C to 651 C. The scope of the in-placed calibration experiments was expanded to investigate the feasibility of generating stress relaxation data under torsional loading.
A Micromechanics Finite-Strain Constitutive Model of Fibrous Tissue
Chen, Huan; Liu, Yi; Zhao, Xuefeng; Lanir, Yoram; Kassab, Ghassan S.
2011-01-01
Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation; i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) strain energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations, and spatial distribution of the fibers, as well as the material nonlinearity at finite-strain deformation. In an illustrative simulation, the predictions of the macroscopic stress-strain relation, and the statistical deformation of the fibers are compared to the UF model, as well as finite-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-strain relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials. PMID:21927506
A micromechanics finite-strain constitutive model of fibrous tissue
NASA Astrophysics Data System (ADS)
Chen, Huan; Liu, Yi; Zhao, Xuefeng; Lanir, Yoram; Kassab, Ghassan S.
2011-09-01
Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation, i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) strain energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations and spatial distribution of the fibers, as well as the material nonlinearity at finite-strain deformation. In an illustrative simulation, the predictions of the macroscopic stress-strain relation and the statistical deformation of the fibers are compared to the UF model, as well as finite-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-strain relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials.
Imanishi, Satoshi; Umezu, Tomohiro; Ohtsuki, Kazushige; Kobayashi, Chiaki; Ohyashiki, Kazuma; Ohyashiki, Junko H
2014-06-01
5-Azacytidine (AZA) exerts its anti-tumor effects by exerting cytotoxicity via its incorporation into RNA and DNA, which causes the reactivation of aberrantly silenced growth-regulatory genes by promoter demethylation, as well as DNA damage. AZA is used for patients with myelodysplastic syndrome and acute myeloid leukemia. However, some patients demonstrate resistance to AZA, the mechanisms of which are not fully elucidated. We therefore sought to better characterize the molecular mechanism of AZA resistance using an in vitro model of AZA resistance. We established AZA-resistant cell lines by exposing the human leukemia cell lines U937 and HL-60 to clinical concentrations of AZA, and characterized these cells. AZA-resistant cells showed a down-regulation of the DNMT3A protein, in correlation with their marked genome-wide DNA hypomethylation. Furthermore, genes involved in pyrimidine metabolism were down-regulated in both AZA-resistant cell lines; AZA sensitivity was restored by inhibition of CTP synthase. Of note is that the DNA damage response pathway is constitutively activated in the AZA-resistant cell lines, but not in the parental cell lines. Inhibition of the DNA damage response pathway canceled the AZA resistance, in association with an increase in apoptotic cells. We found that the molecular mechanism underlying AZA resistance involves pyrimidine metabolism and the DNA damage response through ATM kinase. This study therefore sheds light on the mechanisms underlying AZA resistance, and will enable better understanding of AZA resistance in patients undergoing AZA treatment. PMID:24680865
Nonlinear ultrasound modelling and validation of fatigue damage
NASA Astrophysics Data System (ADS)
Fierro, G. P. Malfense; Ciampa, F.; Ginzburg, D.; Onder, E.; Meo, M.
2015-05-01
Nonlinear ultrasound techniques have shown greater sensitivity to microcracks and they can be used to detect structural damages at their early stages. However, there is still a lack of numerical models available in commercial finite element analysis (FEA) tools that are able to simulate the interaction of elastic waves with the materials nonlinear behaviour. In this study, a nonlinear constitutive material model was developed to predict the structural response under continuous harmonic excitation of a fatigued isotropic sample that showed anharmonic effects. Particularly, by means of Landau's theory and Kelvin tensorial representation, this model provided an understanding of the elastic nonlinear phenomena such as the second harmonic generation in three-dimensional solid media. The numerical scheme was implemented and evaluated using a commercially available FEA software LS-DYNA, and it showed a good numerical characterisation of the second harmonic amplitude generated by the damaged region known as the nonlinear response area (NRA). Since this process requires only the experimental second-order nonlinear parameter and rough damage size estimation as an input, it does not need any baseline testing with the undamaged structure or any dynamic modelling of the fatigue crack growth. To validate this numerical model, the second-order nonlinear parameter was experimentally evaluated at various points over the fatigue life of an aluminium (AA6082-T6) coupon and the crack propagation was measured using an optical microscope. A good correlation was achieved between the experimental set-up and the nonlinear constitutive model.
Constitutive Modeling of Superalloy Single Crystals and Directionally Solidified Materials
NASA Technical Reports Server (NTRS)
Walker, K. P.; Jordan, E. H.
1985-01-01
A unified viscoplastic constitutive relation based on crystallographic slip theory was developed for the deformation analysis of nickel base face centered cubic superalloy single crystals at elevated temperature. The single crystal theory is embedded in a self consistent method to derive a constitutive relation for a directionally solidified material comprised of a polycrystalline aggregate of columnar cylindrical grains. One of the crystallographic axes of the cylindrical crystals points in the columnar direction while the remaining crystallographic axes are oriented at random in the basal plane perpendicular to the columnar direction. These constitutive formulations are coded in FORTRAN for use in nonlinear finite element and boundary element programs.
A constitutive model for Sn-Pb solder.
Neilsen, Michael K.; Vianco, Paul Thomas; Boyce, Brad Lee
2010-10-01
A unified creep plasticity damage (UCPD) model for Sn-Pb solder is developed in this paper. Stephens and Frear (1999) studied the creep behavior of near-eutectic 60Sn-40Pb solder subjected to low strain rates and found that the inelastic (creep and plastic) strain rate could be accurately described using a hyperbolic Sine function of the applied effective stress. A recently developed high-rate servo-hydraulic method was employed to characterize the temperature and strain-rate dependent stress-strain behavior of eutectic Sn-Pb solder over a wide range of strain rates (10{sup -4} to 10{sup 2} per second). The steady state inelastic strain rate data from these latest experiments were also accurately captured by the hyperbolic Sine equation developed by Stephens and Frear. Thus, this equation was used as the basis for the UCPD model for Sn-Pb solder developed in this paper. Stephens, J.J., and Frear, D.R., Metallurgical and Materials Transactions A, Volume 30A, pp. 1301-1313, May 1999.
Intelligent-based Structural Damage Detection Model
Lee, Eric Wai Ming; Yu, K.F.
2010-05-21
This paper presents the application of a novel Artificial Neural Network (ANN) model for the diagnosis of structural damage. The ANN model, denoted as the GRNNFA, is a hybrid model combining the General Regression Neural Network Model (GRNN) and the Fuzzy ART (FA) model. It not only retains the important features of the GRNN and FA models (i.e. fast and stable network training and incremental growth of network structure) but also facilitates the removal of the noise embedded in the training samples. Structural damage alters the stiffness distribution of the structure and so as to change the natural frequencies and mode shapes of the system. The measured modal parameter changes due to a particular damage are treated as patterns for that damage. The proposed GRNNFA model was trained to learn those patterns in order to detect the possible damage location of the structure. Simulated data is employed to verify and illustrate the procedures of the proposed ANN-based damage diagnosis methodology. The results of this study have demonstrated the feasibility of applying the GRNNFA model to structural damage diagnosis even when the training samples were noise contaminated.
Downs, J. Crawford; Burgoyne, Claude F.; Suh, J-K. Francis
2009-01-01
Background The sclera is the white outer shell and principal load-bearing tissue of the eye as it sustains the intraocular pressure. We have hypothesized that the mechanical properties of the posterior sclera play a significant role in, and are altered by the development of glaucoma â€“ an ocular disease manifested by structural damage to the optic nerve head. Method of Approach An anisotropic hyperelastic constitutive model is presented to simulate the mechanical behavior of the posterior sclera under acute elevations of intraocular pressure. The constitutive model is derived from fiber-reinforced composite theory, and incorporates stretch-induced stiffening of the reinforcing collagen fibers. Collagen fiber alignment was assumed to be multi-directional at local material points, confined within the plane tangent to the scleral surface, and described by the semi-circular von-Mises distribution. The introduction of a model parameter, namely the fiber concentration factor, was used to control collagen fiber alignment along a preferred fiber orientation. To investigate the effects of scleral collagen fiber alignment on the overall behaviors of the posterior sclera and optic nerve head, finite element simulations of an idealized eye were performed. The four output quantities analyzed were the scleral canal expansion, the scleral canal twist, the posterior scleral canal deformation and the posterior laminar deformation. Results A circumferential fiber organization in the sclera restrained scleral canal expansion but created posterior laminar deformation, whereas the opposite was observed with a meridional fiber organization. Additionally, the fiber concentration factor acted as an amplifying parameter on the considered outputs. Conclusions The present model simulation suggests that the posterior sclera has a large impact on the overall behavior of the optic nerve head. It is therefore primordial to provide accurate mechanical properties for this tissue. In a companion
How useful are complex flood damage models?
NASA Astrophysics Data System (ADS)
SchrÃ¶ter, Kai; Kreibich, Heidi; Vogel, Kristin; Riggelsen, Carsten; Scherbaum, Frank; Merz, Bruno
2014-04-01
We investigate the usefulness of complex flood damage models for predicting relative damage to residential buildings in a spatial and temporal transfer context. We apply eight different flood damage models to predict relative building damage for five historic flood events in two different regions of Germany. Model complexity is measured in terms of the number of explanatory variables which varies from 1 variable up to 10 variables which are singled out from 28 candidate variables. Model validation is based on empirical damage data, whereas observation uncertainty is taken into consideration. The comparison of model predictive performance shows that additional explanatory variables besides the water depth improve the predictive capability in a spatial and temporal transfer context, i.e., when the models are transferred to different regions and different flood events. Concerning the trade-off between predictive capability and reliability the model structure seem more important than the number of explanatory variables. Among the models considered, the reliability of Bayesian network-based predictions in space-time transfer is larger than for the remaining models, and the uncertainties associated with damage predictions are reflected more completely.
NASA Astrophysics Data System (ADS)
Andrews, Benjamin J.
The phenomena of creep and fatigue have each been thoroughly studied. More recently, attempts have been made to predict the damage evolution in engineering materials due to combined creep and fatigue loading, but these formulations have been strictly empirical and have not been used successfully outside of a narrow set of conditions. This work proposes a new creep-fatigue crack growth model based on constitutive creep equations (adjusted to experimental data) and Paris law fatigue crack growth. Predictions from this model are compared to experimental data in two steels: modified 9Cr-1Mo steel and AISI 316L stainless steel. Modified 9Cr-1Mo steel is a high-strength steel used in the construction of pressure vessels and piping for nuclear and conventional power plants, especially for high temperature applications. Creep-fatigue and pure creep experimental data from the literature are compared to model predictions, and they show good agreement. Material constants for the constitutive creep model are obtained for AISI 316L stainless steel, an alloy steel widely used for temperature and corrosion resistance for such components as exhaust manifolds, furnace parts, heat exchangers and jet engine parts. Model predictions are compared to pure creep experimental data, with satisfactory results. Assumptions and constraints inherent in the implementation of the present model are examined. They include: spatial discretization, similitude, plane stress constraint and linear elasticity. It is shown that the implementation of the present model had a non-trivial impact on the model solutions in 316L stainless steel, especially the spatial discretization. Based on these studies, the following conclusions are drawn: 1. The constitutive creep model consistently performs better than the Nikbin, Smith and Webster (NSW) model for predicting creep and creep-fatigue crack extension. 2. Given a database of uniaxial creep test data, a constitutive material model such as the one developed for
Probabilistic constitutive relationships for material strength degradation models
NASA Technical Reports Server (NTRS)
Boyce, L.; Chamis, C. C.
1989-01-01
In the present probabilistic methodology for the strength of aerospace propulsion system structural components subjected to such environmentally-induced primitive variables as loading stresses, high temperature, chemical corrosion, and radiation, time is encompassed as an interacting element, allowing the projection of creep and fatigue effects. A probabilistic constitutive equation is postulated to account for the degradation of strength due to these primitive variables which may be calibrated by an appropriately curve-fitted least-squares multiple regression of experimental data. The resulting probabilistic constitutive equation is embodied in the PROMISS code for aerospace propulsion component random strength determination.
NASA Technical Reports Server (NTRS)
Allen Phillip A.; Wilson, Christopher D.
2003-01-01
The development of a pressure-dependent constitutive model with combined multilinear kinematic and isotropic hardening is presented. The constitutive model is developed using the ABAQUS user material subroutine (UMAT). First the pressure-dependent plasticity model is derived. Following this, the combined bilinear and combined multilinear hardening equations are developed for von Mises plasticity theory. The hardening rule equations are then modified to include pressure dependency. The method for implementing the new constitutive model into ABAQUS is given.
Application of damage models in metal forming
Zhu, Y.Y.; Zacharia, T.
1995-06-01
The development of damage models in the analysis of metal forming processes, to characterize the formability limits, is an important area of ongoing research. In this paper, two energy-based damage models for the simulation of crack initiation in metal forming processes are presented. The first one is an isotropic damage model with two damage variables. The second one is an anisotropic model with a damage characteristic tensor. The damage models are developed within the general framework of continuum thermodynamics for irreversible processes by identifying a proper set of internal variables together with their associated generalized forces. An approach is proposed to account for microcrack opening and closing. A viscoplastic regularization algorithm is used to take into account the strain rate effect and to improve numerical stability. Both models have been incorporated into the finite element code, LAGAMINE. The models were applied to simulations of upsetting of collar cylinders and nonisothermal hemispherical punch stretching. The results of the analyses were validated by comparing the finite element simulations with experimentally obtained data.
Modeling laser damage to the retina
NASA Astrophysics Data System (ADS)
Clark, Clifton D.
This dissertation presents recent progress in several areas related to modeling laser damage to the retina. In Chapter 3, we consider the consequences of using the Arrhenius damage model to predict the damage thresholds of multiple pulse, or repetitive pulse, exposures. We have identified a few fundamental trends associated with the multiple pulse damage predictions made by the Arrhenius model. These trends differ from what would be expected by non-thermal mechanisms, and could prove useful in differentiating thermal and non-thermal damage. Chapter 4 presents a new rate equation damage model hypothesized to describe photochemical damage. The model adds a temperature dependent term to the simple rate equation implied by the principle of reciprocity that is characteristic of photochemical damage thresholds. A recent damage threshold study, conducted in-vitro, has revealed a very sharp transition between thermal and photochemical damage threshold trends. For the wavelength used in the experiment (413 nm), thermal damage thresholds were observed at exposure levels that were twice the expected photochemical damage threshold, based on the traditional understanding of photochemical damage. Our model accounts for this observed trend by introducing a temperature dependent quenching, or repair, rate to the photochemical damage rate. For long exposures that give a very small temperature rise, the model reduces to the principle of reciprocity. Near the transition region between thermal and photochemical damage, the model allows the damage threshold to be set by thermal mechanisms, even at exposure above the reciprocity exposure. In Chapter 5, we describe a retina damage model that includes thermal lensing in the eye by coupling beam propagation and heat transfer models together. Thermal lensing has recently been suggested as a contributing factor to the large increase in measured retinal damage thresholds in the near infrared. The transmission of the vitreous decreases
Improving Flood Damage Assessment Models in Italy
NASA Astrophysics Data System (ADS)
Amadio, M.; Mysiak, J.; Carrera, L.; Koks, E.
2015-12-01
The use of Stage-Damage Curve (SDC) models is prevalent in ex-ante assessments of flood risk. To assess the potential damage of a flood event, SDCs describe a relation between water depth and the associated potential economic damage over land use. This relation is normally developed and calibrated through site-specific analysis based on ex-post damage observations. In some cases (e.g. Italy) SDCs are transferred from other countries, undermining the accuracy and reliability of simulation results. Against this background, we developed a refined SDC model for Northern Italy, underpinned by damage compensation records from a recent flood event. Our analysis considers both damage to physical assets and production losses from business interruptions. While the first is calculated based on land use information, production losses are measured through the spatial distribution of Gross Value Added (GVA). An additional component of the model assesses crop-specific agricultural losses as a function of flood seasonality. Our results show an overestimation of asset damage from non-calibrated SDC values up to a factor of 4.5 for tested land use categories. Furthermore, we estimate that production losses amount to around 6 per cent of the annual GVA. Also, maximum yield losses are less than a half of the amount predicted by the standard SDC methods.
NASA Technical Reports Server (NTRS)
Koharchik, Michael; Murphy, Lindsay; Parker, Paul
2012-01-01
An impact model was developed to predict how three specific foam types would damage the Space Shuttle Orbiter insulating tiles. The inputs needed for the model are the foam type, the foam mass, the foam impact velocity, the foam impact incident angle, the type being impacted, and whether the tile is new or aged (has flown at least one mission). The model will determine if the foam impact will cause damage to the tile. If it can cause damage, the model will output the damage cavity dimensions (length, depth, entry angle, exit angle, and sidewall angles). It makes the calculations as soon as the inputs are entered (less than 1 second). The model allows for the rapid calculation of numerous scenarios in a short time. The model was developed from engineering principles coupled with significant impact testing (over 800 foam impact tests). This model is applicable to masses ranging from 0.0002 up to 0.4 pound (0.09 up to 181 g). A prior tool performed a similar function, but was limited to the assessment of a small range of masses and did not have the large test database for verification. In addition, the prior model did not provide outputs of the cavity damage length, entry angle, exit angle, or sidewall angles.
Dislocation Density-Based Constitutive Model for the Mechanical Behavior of Irradiated Cu
Arsenlis, A; Wirth, B D; Rhee, M
2003-04-10
Performance degradation of structural steels in nuclear environments results from the development of a high number density of nanometer scale defects. The defects observed in copper-based alloys are composed of vacancy clusters in the form of stacking fault tetrahedra and/or prismatic dislocation loops, which impede dislocation glide and are evidenced in macroscopic uniaxial stress-strain curves as increased yield strengths, decreased total strain to failure, decreased work hardening and the appearance of a distinct upper yield point above a critical defect concentration (neutron dose). In this paper, we describe the development of an internal state variable model for the mechanical behavior of materials subject to these environments. This model has been developed within an information-passing multiscale materials modeling framework, in which molecular dynamics simulations of dislocation--radiation defect interactions, inform the final coarse-grained continuum model. The plasticity model includes mechanisms for dislocation density growth and multiplication and for radiation defect density evolution with dislocation interaction. The general behavior of the constitutive (single material point) model shows that as the defect density increases, the initial yield point increases and the initial strain hardening decreases. The final coarse-grained model is implemented into a finite element framework and used to simulate the behavior of tensile specimens with varying levels of irradiation induced material damage. The simulation results compare favorably with the experimentally observed mechanical properties of irradiated materials in terms of their increased strength, decreased hardening, and decreased ductility with increasing irradiation dose.
An Irreversible Constitutive Law for Modeling the Delamination Process using Interface Elements
NASA Technical Reports Server (NTRS)
Goyal, Vinay K.; Johnson, Eric R.; Davila, Carlos G.; Jaunky, Navin; Ambur, Damodar (Technical Monitor)
2002-01-01
An irreversible constitutive law is postulated for the formulation of interface elements to predict initiation and progression of delamination in composite structures. An exponential function is used for the constitutive law such that it satisfies a multi-axial stress criterion for the onset of delamination, and satisfies a mixed mode fracture criterion for the progression of delamination. A damage parameter is included to prevent the restoration of the previous cohesive state between the interfacial surfaces. To demonstrate the irreversibility capability of the constitutive law, steady-state crack growth is simulated for quasi-static loading-unloading cycle of various fracture test specimens.
An Irreversible Constitutive Law for Modeling the Delamination Process Using Interface Elements
NASA Technical Reports Server (NTRS)
Goyal, Vinay K.; Johnson, Eric R.; Davila, Carlos G.; Jaunky, Navin; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
An irreversible constitutive law is postulated for the formulation of interface elements to predict initiation and progression of delamination in composite structures. An exponential function is used for the constitutive law such that it satisfies a multi-axial stress criterion for the onset of delamination, and satisfies a mixed mode fracture criterion for the progression of delamination. A damage parameter is included to prevent the restoration of the previous cohesive state between the interfacial surfaces. To demonstrate the irreversibility capability of the constitutive law, steady-state crack growth is simulated for quasi-static loading-unloading cycle of various fracture test specimens.
Nucleation in models of damage mechanics
NASA Astrophysics Data System (ADS)
Gran, J. D.; Rundle, J. B.; Klein, W.; Turcotte, D. L.
2010-12-01
A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study two cellular automaton models of damage mechanics which. The first model is a modified slider-block model with failure threshold weakening. A block is considered partially damaged after its first slip, and any subsequent failure of that block will occur at reduced failure threshold. Damage here is defined as the fraction of blocks that have a reduced failure threshold. The threshold weakening parameter is viewed as a scaling field similar to the occupation probability in site percolation. The second model is time-dependent fiber-bundle model, where the time to failure for each element is specified from a Poissonian distribution and the hazard rate is assumed to have a power-law dependence on stress. Damage here is defined to be the fraction of blocks or fibers that have failed. Because there is no healing, catastrophic failure occurs. The transient behavior prior to rupture propagation is studied and scaling laws are obtained. We compare both models to mean-field percolation which has been shown to be representative of spinodal nucleation and to laboratory experiments that display power-law behavior.
Prediction Of Formability In Sheet Metal Forming Processes Using A Local Damage Model
Teixeira, P.; Santos, Abel; Cesar Sa, J.; Andrade Pires, F.; Barata da Rocha, A.
2007-05-17
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.
Modeling of rock friction 1. Experimental results and constitutive equations
Dieterich, J.H.
1979-01-01
Direct shear experiments on ground surfaces of a granodiorite from Raymond, California, at normal stresses of ??6 MPa demonstrate that competing time, displacement, and velocity effects control rock friction. It is proposed that the strength of the population of points of contacts between sliding surfaces determines frictional strength and that the population of contacts changes continuously with displacements. Previous experiments demonstrate that the strength of the contacts increases with the age of the contacts. The present experiments establish that a characteristic displacement, proportional to surface roughness, is required to change the population of contacts. Hence during slip the average age of the points of contact and therefore frictional strength decrease as slip velocity increases. Displacement weakening and consequently the potential for unstable slip occur whenever displacement reduces the average age of the contacts. In addition to this velocity dependency, which arises from displacement dependency and time dependency, the experiments also show a competing but transient increase in friction whenever slip velocity increases. Creep of the sliding surface at stresses below that for steady state slip is also observed. Constitutive relationships are developed that permit quantitative simulation of the friction versus displacement data as a function of surface roughness and for different time and velocity histories. Unstable slip in experiments is controlled by these constitutive effects and by the stiffness of the experimental system. It is argued that analogous properties control earthquake instability. Copyright ?? 1979 by the American Geophysical Union.
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.
Integrated research in constitutive modelling at elevated temperatures, part 2
NASA Technical Reports Server (NTRS)
Haisler, W. E.; Allen, D. H.
1986-01-01
Four current viscoplastic models are compared experimentally with Inconel 718 at 1100 F. A series of tests were performed to create a sufficient data base from which to evaluate material constants. The models used include Bodner's anisotropic model; Krieg, Swearengen, and Rhode's model; Schmidt and Miller's model; and Walker's exponential model.
NASA Astrophysics Data System (ADS)
Iseri, Y.; Iwasaki, A.; Miyazaki, C.; Kanae, S.
2014-12-01
Tropical cyclones (TCs) sometimes cause serious damages to human society and thus possible changes of TC properties in the future have been concerned. In fact, the Fifth Assessment Report (AR5) by IPCC (Intergovernmental Panel on Climate Change) mentions likely increasing in intensity and rain rate of TCs. In addition, future change of socioeconomic condition (e.g. population growth) might worsen TC impacts in the future. Thereby, in this study, we developed regression models to estimate economic damages by TCs (hereafter TC damage model), and employed those models to project TC economic damages under several future climate and socioeconomic scenarios. We developed the TC damage models for each of 4 regions; western North Pacific, North American, North Indian, and Southern Hemisphere. The inputs for TC damage model are tropical cyclone central pressure, populations in the area exposed by tropical cyclone wind, and GDP (Gross Domestic Product) per capita. The TC damage models we firstly developed tended to overestimate very low damages and also underestimate very high damages. Thereby we modified structure of TC damage models to improve model performance, and then executed extensive validation of the model. The modified model presented better performance in estimating very low and high TC damages. After the modification and validation of the model, we determined the structure of TC damage models and projected TC economic damages. The result indicated increase in TC economic damage in global scale, while TC economic damage against world GDP would decrease in the future, which result is consistent with previous study.
Modeling of nonlinear constitutive relations of woven ceramic composites
Kuo, Wen-Shyong; Chou, Tsu-Wei
1991-08-01
The linear and nonlinear tensile behavior of SiC/SiC composites is examined. This analysis is based on the observed stress-strain behavior and damage evolution from a series of loading and unloading tensile tests. Stress distribution of the composite with transverse cracks in the transverse yarns is examined, and the nonlinearity of the composite stress-strain relation due to the presence of transverse cracks is predicted by application of a maximum failure strain criterion for the transverse yarn. 7 refs.
A Constitutive Model for Long Time Duration Mechanical Behavior in Insensitive High Explosives
Darnell, I M; Oh, S; Hrousis, C A; Cunningham, B J; Gagliardi, F J
2010-03-09
An anisotropic constitutive model for the long term dimensional stability of insensitive high explosives is proposed. Elastic, creep, thermal, and ratchet growth strains are developed. Pressure and temperature effects are considered. The constitutive model is implemented in an implicit finite element code and compared to a variety of experimental data.
Girard, MichaÃ«l J A; Downs, J Crawford; Burgoyne, Claude F; Suh, J-K Francis
2009-05-01
The sclera is the white outer shell and principal load-bearing tissue of the eye as it sustains the intraocular pressure. We have hypothesized that the mechanical properties of the posterior sclera play a significant role in and are altered by the development of glaucoma-an ocular disease manifested by structural damage to the optic nerve head. An anisotropic hyperelastic constitutive model is presented to simulate the mechanical behavior of the posterior sclera under acute elevations of intraocular pressure. The constitutive model is derived from fiber-reinforced composite theory, and incorporates stretch-induced stiffening of the reinforcing collagen fibers. Collagen fiber alignment was assumed to be multidirectional at local material points, confined within the plane tangent to the scleral surface, and described by the semicircular von Mises distribution. The introduction of a model parameter, namely, the fiber concentration factor, was used to control collagen fiber alignment along a preferred fiber orientation. To investigate the effects of scleral collagen fiber alignment on the overall behaviors of the posterior sclera and optic nerve head, finite element simulations of an idealized eye were performed. The four output quantities analyzed were the scleral canal expansion, the scleral canal twist, the posterior scleral canal deformation, and the posterior laminar deformation. A circumferential fiber organization in the sclera restrained scleral canal expansion but created posterior laminar deformation, whereas the opposite was observed with a meridional fiber organization. Additionally, the fiber concentration factor acted as an amplifying parameter on the considered outputs. The present model simulation suggests that the posterior sclera has a large impact on the overall behavior of the optic nerve head. It is therefore primordial to provide accurate mechanical properties for this tissue. In a companion paper (Girard, Downs, Bottlang, Burgoyne, and Suh, 2009
Mathematical modeling of damage in unidirectional composites
NASA Technical Reports Server (NTRS)
Goree, J. G.; Dharani, L. R.; Jones, W. F.
1981-01-01
A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.
Constitutive modeling for blast-induced wave propagation
NASA Astrophysics Data System (ADS)
Drumm, E. C.
1985-03-01
The description of stress-time history acting on a buried structure is a major source of error in the analysis of underground structures to weapons loadings. The stress wave propagating spherically from the weapon is attenuated as it travels from the source. This attenuation is a function of the inelastic response of the soil, and results in an increase in the loading rise time or decrease in the loading rate. Since the inelastic soil response is a function of the loading rate, a wave propagation analysis should be conducted to determine the stresses on the structure. At the interface between the soil and structure, the stress is modified further by soil-structure interaction effects. Thus, the stress on the structure is a function of both the structural and soil properties as well as the distance traveled by the stress wave. These related phenomena can be included in a numerical analysis, but the accuracy depends on the constitutive representation of the materials. One-dimensional wave propagation experiments and impact tests with various soils are reviewed, and the attenuation as a function of the soil stress-strain response is discussed.
Integrated research in constitutive modelling at elevated temperatures, part 1
NASA Technical Reports Server (NTRS)
Haisler, W. E.; Allen, D. H.
1986-01-01
Topics covered include: numerical integration techniques; thermodynamics and internal state variables; experimental lab development; comparison of models at room temperature; comparison of models at elevated temperature; and integrated software development.
A micro to macro approach to polymer matrix composites damage modeling : final LDRD report.
English, Shawn Allen; Brown, Arthur A.; Briggs, Timothy M.
2013-12-01
Capabilities are developed, verified and validated to generate constitutive responses using material and geometric measurements with representative volume elements (RVE). The geometrically accurate RVEs are used for determining elastic properties and damage initiation and propagation analysis. Finite element modeling of the meso-structure over the distribution of characterizing measurements is automated and various boundary conditions are applied. Plain and harness weave composites are investigated. Continuum yarn damage, softening behavior and an elastic-plastic matrix are combined with known materials and geometries in order to estimate the macroscopic response as characterized by a set of orthotropic material parameters. Damage mechanics and coupling effects are investigated and macroscopic material models are demonstrated and discussed. Prediction of the elastic, damage, and failure behavior of woven composites will aid in macroscopic constitutive characterization for modeling and optimizing advanced composite systems.
Survey of four damage models for concrete.
Leelavanichkul, Seubpong; Brannon, Rebecca Moss
2009-08-01
Four conventional damage plasticity models for concrete, the Karagozian and Case model (K&C), the Riedel-Hiermaier-Thoma model (RHT), the Brannon-Fossum model (BF1), and the Continuous Surface Cap Model (CSCM) are compared. The K&C and RHT models have been used in commercial finite element programs many years, whereas the BF1 and CSCM models are relatively new. All four models are essentially isotropic plasticity models for which 'plasticity' is regarded as any form of inelasticity. All of the models support nonlinear elasticity, but with different formulations. All four models employ three shear strength surfaces. The 'yield surface' bounds an evolving set of elastically obtainable stress states. The 'limit surface' bounds stress states that can be reached by any means (elastic or plastic). To model softening, it is recognized that some stress states might be reached once, but, because of irreversible damage, might not be achievable again. In other words, softening is the process of collapse of the limit surface, ultimately down to a final 'residual surface' for fully failed material. The four models being compared differ in their softening evolution equations, as well as in their equations used to degrade the elastic stiffness. For all four models, the strength surfaces are cast in stress space. For all four models, it is recognized that scale effects are important for softening, but the models differ significantly in their approaches. The K&C documentation, for example, mentions that a particular material parameter affecting the damage evolution rate must be set by the user according to the mesh size to preserve energy to failure. Similarly, the BF1 model presumes that all material parameters are set to values appropriate to the scale of the element, and automated assignment of scale-appropriate values is available only through an enhanced implementation of BF1 (called BFS) that regards scale effects to be coupled to statistical variability of material
Constitutive Modeling of the Mechanical Properties of Optical Fibers
NASA Technical Reports Server (NTRS)
Moeti, L.; Moghazy, S.; Veazie, D.; Cuddihy, E.
1998-01-01
Micromechanical modeling of the composite mechanical properties of optical fibers was conducted. Good agreement was obtained between the values of Young's modulus obtained by micromechanics modeling and those determined experimentally for a single mode optical fiber where the wave guide and the jacket are physically coupled. The modeling was also attempted on a polarization-maintaining optical fiber (PANDA) where the wave guide and the jacket are physically decoupled, and found not to applicable since the modeling required perfect bonding at the interface. The modeling utilized constituent physical properties such as the Young's modulus, Poisson's ratio, and shear modulus to establish bounds on the macroscopic behavior of the fiber.
A constitutive model of polyether-ether-ketone (PEEK).
Chen, Fei; Ou, Hengan; Lu, Bin; Long, Hui
2016-01-01
A modified Johnson-Cook (JC) model was proposed to describe the flow behaviour of polyether-ether-ketone (PEEK) with the consideration of coupled effects of strain, strain rate and temperature. As compared to traditional JC model, the modified one has better ability to predict the flow behaviour at elevated temperature conditions. In particular, the yield stress was found to be inversely proportional to temperature from the predictions of the proposed model. PMID:26409233
Constitutive models used to simulate penetration and perforation of concrete targets
Akers, S.A.; Adley, M.D.
1996-12-31
Only a limited number of nonlinear constitutive models are available in wave propagation codes to simulate geologic materials, and these models often do not capture the fundamental and often complex mechanical behavior of these materials. Researchers at the WES have recently implemented two models, which were specifically designed for geologic materials, into the large-strain Lagrangian wave-propagation code EPIC. These models are currently being used in finite-element simulations of penetration and ground-shock problems. In this paper, the formulation of the constitutive models is examined and the implementation of the models into EPIC is briefly described. Results from a series of calculations are presented to illustrate the effect of the constitutive models on penetration and perforation problems. Three models are compared, one of the new WES models, the EPIC crushable-solids model, which is often employed to model geologic materials, and EPIC`s Holmquist-Johnson-Cook model for concrete.
Modeling and Algorithmic Approaches to Constitutively-Complex, Microstructured Fluids
Miller, Gregory H.; Forest, Gregory
2011-12-22
We present a new multiscale model for complex uids based on three scales: microscopic, kinetic, and continuum. We choose the microscopic level as Kramers' bead-rod model for polymers, which we describe as a system of stochastic di erential equations with an implicit constraint formulation. The associated Fokker-Planck equation is then derived, and adiabatic elimination removes the fast momentum coordinates. Approached in this way, the kinetic level reduces to a dispersive drift equation. The continuum level is modeled with a nite volume Godunov-projection algorithm. We demonstrate computation of viscoelastic stress divergence using this multiscale approach.
Evaluation of Inelastic Constitutive Models for Nonlinear Structural Analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1983-01-01
The influence of inelastic material models on computed stress-strain states, and therefore predicted lives, was studied for thermomechanically loaded structures. Nonlinear structural analyses were performed on a fatigue specimen which was subjected to thermal cycling in fluidized beds and on a mechanically load cycled benchmark notch specimen. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic-kinematic, combined plus transient creep) were exercised. Of the plasticity models, kinematic hardening gave results most consistent with experimental observations. Life predictions using the computed strain histories at the critical location with a Strainrange Partitioning approach considerably overpredicted the crack initiation life of the thermal fatigue specimen.
Experience in calibrating the double-hardening constitutive model Monot
NASA Astrophysics Data System (ADS)
Hicks, M. A.
2003-11-01
The Monot double-hardening soil model has previously been implemented within a general purpose finite element algorithm, and used in the analysis of numerous practical problems. This paper reviews experience gained in calibrating Monot to laboratory data and demonstrates how the calibration process may be simplified without detriment to the range of behaviours modelled. It describes Monot's principal features, important governing equations and various calibration methods, including strategies for overconsolidated, cemented and cohesive soils. Based on a critical review of over 30 previous Monot calibrations, for sands and other geomaterials, trends in parameter values have been identified, enabling parameters to be categorized according to their relative importance. It is shown that, for most practical purposes, a maximum of only 5 parameters is needed; for the remaining parameters, standard default values are suggested. Hence, the advanced stress-strain modelling offered by Monot is attainable with a similar number of parameters as would be needed for some simpler, less versatile, models. Copyright
Vianco, P.T.; Burchett, S.N.; Neilsen, M.K.; Rejent, J.A.; Frear, D.R.
1999-04-12
Thermal mechanical fatigue (TMF) is an important damage mechanism for solder joints exposed to cyclic temperature environments. Predicting the service reliability of solder joints exposed to such conditions requires two knowledge bases: first, the extent of fatigue damage incurred by the solder microstructure leading up to fatigue crack initiation, must be quantified in both time and space domains. Secondly, fatigue crack initiation and growth must be predicted since this metric determines, explicitly, the loss of solder joint functionality as it pertains to its mechanical fastening as well as electrical continuity roles. This paper will describe recent progress in a research effort to establish a microstructurally-based, constitutive model that predicts TMF deformation to 63Sn-37Pb solder in electronic solder joints up to the crack initiation step. The model is implemented using a finite element setting; therefore, the effects of both global and local thermal expansion mismatch conditions in the joint that would arise from temperature cycling.
What Constitutes a Relevant Animal Model of the Ketogenic Diet?
Holmes, Gregory L.
2009-01-01
Summary Animal models of human disease have been enormously important in improving our understanding of the pathophysiological basis and the development of novel therapies. In epilepsy, modeling using both in vivo and in vitro preparations has provided insight into fundamental neuronal mechanisms. Indeed, much of our understanding of seizure mechanisms comes from animal studies. The conceptual advances in understanding basic mechanisms of epilepsies have been largely validated in humans, attesting to the validity of the rationale and providing a basis for bridging the gaps between experimental and human data. While the ketogenic diet is clearly efficacious in a wide variety of seizure types and syndromes, the mechanism of action of the diet has not been established. Animal models will continue to be enormously important in furthering our understanding of how dietary therapy can help individuals with epilepsy. PMID:19049589
A kinematically driven anisotropic viscoelastic constitutive model applied to tires
NASA Astrophysics Data System (ADS)
Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.
1995-08-01
Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.
A kinematically driven anisotropic viscoelastic constitutive model applied to tires
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.
1995-01-01
Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.
Density Functional Theory Models for Radiation Damage
NASA Astrophysics Data System (ADS)
Dudarev, S. L.
2013-07-01
Density functional theory models developed over the past decade provide unique information about the structure of nanoscale defects produced by irradiation and about the nature of short-range interaction between radiation defects, clustering of defects, and their migration pathways. These ab initio models, involving no experimental input parameters, appear to be as quantitatively accurate and informative as the most advanced experimental techniques developed for the observation of radiation damage phenomena. Density functional theory models have effectively created a new paradigm for the scientific investigation and assessment of radiation damage effects, offering new insight into the origin of temperature- and dose-dependent response of materials to irradiation, a problem of pivotal significance for applications.
Formation of algae growth constitutive relations for improved algae modeling.
Gharagozloo, Patricia E.; Drewry, Jessica L.
2013-01-01
This SAND report summarizes research conducted as a part of a two year Laboratory Directed Research and Development (LDRD) project to improve our abilities to model algal cultivation. Algae-based biofuels have generated much excitement due to their potentially large oil yield from relatively small land use and without interfering with the food or water supply. Algae mitigate atmospheric CO2 through metabolism. Efficient production of algal biofuels could reduce dependence on foreign oil by providing a domestic renewable energy source. Important factors controlling algal productivity include temperature, nutrient concentrations, salinity, pH, and the light-to-biomass conversion rate. Computational models allow for inexpensive predictions of algae growth kinetics in these non-ideal conditions for various bioreactor sizes and geometries without the need for multiple expensive measurement setups. However, these models need to be calibrated for each algal strain. In this work, we conduct a parametric study of key marine algae strains and apply the findings to a computational model.
A Robust Damage Assessment Model for Corrupted Database Systems
NASA Astrophysics Data System (ADS)
Fu, Ge; Zhu, Hong; Li, Yingjiu
An intrusion tolerant database uses damage assessment techniques to detect damage propagation scales in a corrupted database system. Traditional damage assessment approaches in a intrusion tolerant database system can only locate damages which are caused by reading corrupted data. In fact, there are many other damage spreading patterns that have not been considered in traditional damage assessment model. In this paper, we systematically analyze inter-transaction dependency relationships that have been neglected in the previous research and propose four different dependency relationships between transactions which may cause damage propagation. We extend existing damage assessment model based on the four novel dependency relationships. The essential properties of our model is also discussed.
Constitutive Models for Debris-bearing Ice Layers
NASA Astrophysics Data System (ADS)
Moore, P. L.
2013-12-01
Rock debris is incorporated within many glaciers and ice sheets, particularly in basal ice layers and englacial debris bands. Field observations and laboratory experiments have shown that debris inclusions can both strengthen and weaken ice by as much as two orders of magnitude compared to debris-free ice under the same conditions. Nevertheless, models of glacier flow usually neglect any effect of debris-bearing layers. Where debris-bearing ice is present, proper treatment of its deformation could profoundly impact model results. A three-phase mechanical model is presented that reproduces many of the key observations of debris-bearing ice rheology. First order variables in the model are limited to debris concentration, particle size, solute concentration and temperature. At low debris concentrations (less than about 40% by volume), the mixture is treated under the framework of a dispersion-strengthened metal alloy but with a fluidity that is enhanced by premelted water at ice-debris interfaces. While debris strengthens the ice by interfering with the motion of dislocations, thermally-activated detachment can reduce the effect at temperatures close to melting. At these warm temperatures, recovery aided by unfrozen interfacial water acts to weaken the mixture, an effect that is further ehnanced by the presence of solutes at particle surfaces. Whether the debris-bearing ice is stronger or weaker than debris-free ice in the model depends strongly on the specific surface area of the debris and on a parameter that describes the thermal detachment of dislocations. As debris concentrations exceed about 40%, dispersion-strengthened ice flow still governs bulk deformation but the effective viscosity is further increased by enhanced strain rates in the ice "matrix" as the average inter-particle distance declines. At still higher concentrations (greater than about 52% by volume for sand), deformation is primarily frictional. The mixture is thus treated as a dilatant Coulomb
A continuous damage model based on stepwise-stress creep rupture tests
NASA Technical Reports Server (NTRS)
Robinson, D. N.
1985-01-01
A creep damage accumulation model is presented that makes use of the Kachanov damage rate concept with a provision accounting for damage that results from a variable stress history. This is accomplished through the introduction of an additional term in the Kachanov rate equation that is linear in the stress rate. Specification of the material functions and parameters in the model requires two types of constituting a data base: (1) standard constant-stress creep rupture tests, and (2) a sequence of two-step creep rupture tests.
Constitutive Relationships and Models in Continuum Theories of Multiphase Flows. [conferences
NASA Technical Reports Server (NTRS)
Decker, Rand (Editor)
1989-01-01
In April, 1989, a workshop on constitutive relationships and models in continuum theories of multiphase flows was held at NASA's Marshall Space Flight Center. Topics of constitutive relationships for the partial or per phase stresses, including the concept of solid phase pressure are discussed. Models used for the exchange of mass, momentum, and energy between the phases in a multiphase flow are also discussed. The program, abstracts, and texts of the presentations from the workshop are included.
Non-linear approach in visco-hyperelastic constitutive modelling of polyurethane nanocomposite
NASA Astrophysics Data System (ADS)
Pawlikowski, Marek
2014-02-01
The constitutive modelling of the polyurethane nanocomposite presented in the paper is done in the context of its possible application as one of the components of the intervertebral disc prosthesis. The constitutive study is a part of the researches aiming at creation of the new prosthetic device. The material is considered as incompressible, isotropic and visco-hyperelastic one. The focus of the work lies on the formulation of a constitutive equation for its further implementation in finite element analyses. The equation is formulated on the basis of uniaxial monotonic compression tests and relaxation tests performed at room temperature. The constants of the constitutive model are determined from the experimental data by means of the curve-fitting approach employing least-squares optimisation method. The constitutive modelling consisted of two steps. In the first one pure hyperelastic model was determined. The Mooney-Rivlin model proved to be the best one to describe hyperelastic behaviour of the material. In the second step non-linear visco-hyperelastic model was derived. Relaxation times, characteristic amplitudes and Mooney-Rivlin hyperelastic constants were calibrated on the basis of strain-stress curves (hysteresis loops) obtained experimentally at three strain rates, i.e. and . The constitutive law is validated on the basis of relaxation test. The paper concludes with summary and plans for further investigations in the area.
A continuum damage model of fatigue-induced damage in laminated composites
NASA Technical Reports Server (NTRS)
Harris, Charles E.; Allen, David H.
1988-01-01
A model is presented which predicts the stress-strain behavior of continuous fiber reinforced laminated composites in the presence of microstructural damage. The model is based on the concept of continuum damage mechanics and uses internal state variables to characterize the various damage modes. The associated internal state variable growth laws are mathematical models of the loading history induced development of microstructural damage. The model is demonstrated by using it to predict the response of damaged AS-4/3502 graphite/epoxy laminate panels.
NASA Astrophysics Data System (ADS)
Grelot, FrÃ©dÃ©ric; Agenais, Anne-Laurence; BrÃ©mond, Pauline
2014-05-01
In France, since 2011, it is mandatory for local communities to conduct cost-benefit analysis (CBA) of their flood management projects, to make them eligible for financial support from the State. Meanwhile, as a support, the French Ministry in charge of Environment proposed a methodology to fulfill CBA. Like for many other countries, this methodology is based on the estimation of flood damage. Howerver, existing models to estimate flood damage were judged not convenient for a national-wide use. As a consequence, the French Ministry in charge of Environment launched studies to develop damage models for different sectors, such as: residential sector, public infrastructures, agricultural sector, and commercial and industrial sector. In this presentation, we aim at presenting and discussing methodological choices of those damage models. They all share the same principle: no sufficient data from past events were available to build damage models on a statistical analysis, so modeling was based on expert knowledge. We will focus on the model built for agricultural activities and more precisely for agricultural lands. This model was based on feedback from 30 agricultural experts who experienced floods in their geographical areas. They were selected to have a representative experience of crops and flood conditions in France. The model is composed of: (i) damaging functions, which reveal physiological vulnerability of crops, (ii) action functions, which correspond to farmers' decision rules for carrying on crops after a flood, and (iii) economic agricultural data, which correspond to featured characteristics of crops in the geographical area where the flood management project studied takes place. The two first components are generic and the third one is specific to the area studied. It is, thus, possible to produce flood damage functions adapted to different agronomic and geographical contexts. In the end, the model was applied to obtain a pool of damage functions giving
NASA Astrophysics Data System (ADS)
Grelot, FrÃ©dÃ©ric; Agenais, Anne-Laurence; BrÃ©mond, Pauline
2015-04-01
In France, since 2011, it is mandatory for local communities to conduct cost-benefit analysis (CBA) of their flood management projects, to make them eligible for financial support from the State. Meanwhile, as a support, the French Ministry in charge of Environment proposed a methodology to fulfill CBA. Like for many other countries, this methodology is based on the estimation of flood damage. However, existing models to estimate flood damage were judged not convenient for a national-wide use. As a consequence, the French Ministry in charge of Environment launched studies to develop damage models for different sectors, such as: residential sector, public infrastructures, agricultural sector, and commercial and industrial sector. In this presentation, we aim at presenting and discussing methodological choices of those damage models. They all share the same principle: no sufficient data from past events were available to build damage models on a statistical analysis, so modeling was based on expert knowledge. We will focus on the model built for agricultural activities and more precisely for agricultural lands. This model was based on feedback from 30 agricultural experts who experienced floods in their geographical areas. They were selected to have a representative experience of crops and flood conditions in France. The model is composed of: (i) damaging functions, which reveal physiological vulnerability of crops, (ii) action functions, which correspond to farmers' decision rules for carrying on crops after a flood, and (iii) economic agricultural data, which correspond to featured characteristics of crops in the geographical area where the flood management project studied takes place. The two first components are generic and the third one is specific to the area studied. It is, thus, possible to produce flood damage functions adapted to different agronomic and geographical contexts. In the end, the model was applied to obtain a pool of damage functions giving
Modeling Coal Seam Damage in Cast Blasting
Chung, S.H.; Preece, D.S.
1998-11-23
A discrete element computer program named DMC_BLAST (Distinct Motion Code) has been under development since 1987 for modeling rock blasting (Preece & Taylor, 1989). This program employs explicit time integration and uses spherical or cylindrical elements that are represented as circles in two dimensions. DMC_BLAST calculations compare favorably with data from actual bench blasts (Preece et al, 1993). Coal seam chilling refers to the shattering of a significant portion of the coal leaving unusable fines. It is also refereed to as coal damage. Chilling is caused during a blast by a combination of explosive shock energy and movement of the adjacent rock. Chilling can be minimized by leaving a buffer zone between the bottom of the blastholes and the coal seam or by changing the blast design to decrease the powder factor or by a combination of both. Blast design in coal mine cast blasting is usually a compromise between coal damage and rock fragmentation and movement (heave). In this paper the damage to coal seams from rock movement is examined using the discrete element computer code DMC_BLAST. A rock material strength option has been incorporated into DMC_BLAST by placing bonds/links between the spherical particles used to model the rock. These bonds tie the particles together but can be broken when the tensile, compressive or shear stress in the bond exceeds the defined strength. This capability has been applied to predict coal seam damage, particularly at the toe of a cast blast where drag forces exerted by movement of the overlying rock can adversely effect the top of the coal at the bench face. A simulation of coal mine cast blasting has been performed with special attention being paid to the strength of the coal and its behavior at t he bench face during movement of the overlying material.
NASA Astrophysics Data System (ADS)
Haberman, Keith
2001-07-01
A micromechanically based constitutive model for the dynamic inelastic behavior of brittle materials, specifically "Dionysus-Pentelicon marble" with distributed microcracking is presented. Dionysus-Pentelicon marble was used in the construction of the Parthenon, in Athens, Greece. The constitutive model is a key component in the ability to simulate this historic explosion and the preceding bombardment form cannon fire that occurred at the Parthenon in 1678. Experiments were performed by Rosakis (1999) that characterized the static and dynamic response of this unique material. A micromechanical constitutive model that was previously successfully used to model the dynamic response of granular brittle materials is presented. The constitutive model was fitted to the experimental data for marble and reproduced the experimentally observed basic uniaxial dynamic behavior quite well. This micromechanical constitutive model was then implemented into the three dimensional nonlinear lagrangain finite element code Dyna3d(1998). Implementing this methodology into the three dimensional nonlinear dynamic finite element code allowed the model to be exercised on several preliminary impact experiments. During future simulations, the model is to be used in conjunction with other numerical techniques to simulate projectile impact and blast loading on the Dionysus-Pentelicon marble and on the structure of the Parthenon.
Life prediction and constitutive models for engine hot section anisotropic materials
NASA Technical Reports Server (NTRS)
Swanson, G. A.; Linask, I.; Nissley, D. M.; Norris, P. P.; Meyer, T. G.; Walker, K. P.
1987-01-01
The results are presented of a program designed to develop life prediction and constitutive models for two coated single crystal alloys used in gas turbine airfoils. The two alloys are PWA 1480 and Alloy 185. The two oxidation resistant coatings are PWA 273, an aluminide coating, and PWA 286, an overlay NiCoCrAlY coating. To obtain constitutive and fatigue data, tests were conducted on uncoated and coated specimens loaded in the CH76 100 CH110 , CH76 110 CH110 , CH76 111 CH110 and CH76 123 CH110 crystallographic directions. Two constitutive models are being developed and evaluated for the single crystal materials: a micromechanic model based on crystallographic slip systems, and a macroscopic model which employs anisotropic tensors to model inelastic deformation anisotropy. Based on tests conducted on the overlay coating material, constitutive models for coatings also appear feasible and two initial models were selected. A life prediction approach was proposed for coated single crystal materials, including crack initiation either in the coating or in the substrate. The coating initiated failures dominated in the tests at load levels typical of gas turbine operation. Coating life was related to coating stress/strain history which was determined from specimen data using the constitutive models.
An investigation of the material and model parameters for a constitutive model for MSMAs
NASA Astrophysics Data System (ADS)
Dikes, Jason; Feigenbaum, Heidi; Ciocanel, Constantin
2015-04-01
A two dimensional constitutive model capable of predicting the magneto-mechanical response of a magnetic shape memory alloy (MSMA) has been developed and calibrated using a zero field-variable stress test1. This calibration approach is easy to perform and facilitates a faster evaluation of the three calibration constants required by the model (vs. five calibration constants required by previous models2,3). The calibration constants generated with this approach facilitate good model predictions of constant field-variable stress tests, for a wide range of loading conditions1. However, the same calibration constants yield less accurate model predictions for constant stress-variable field tests. Deployment of a separate calibration method for this type of loading, using a varying field-zero stress calibration test, also didn't lead to improved model predictions of this loading case. As a result, a sensitivity analysis was performed on most model and material parameters to identify which of them may influence model predictions the most, in both types of loading conditions. The sensitivity analysis revealed that changing most of these parameters did not improve model predictions for all loading types. Only the anisotropy coefficient was found to improve significantly field controlled model predictions and slightly worsen model predictions for stress controlled cases. This suggests that either the value of the anisotropy coefficient (which is provided by the manufacturer) is not accurate, or that the model is missing features associated with the magnetic energy of the material.
Modeling neural activity with cumulative damage distributions.
Leiva, VÃctor; Tejo, Mauricio; Guiraud, Pierre; Schmachtenberg, Oliver; Orio, Patricio; Marmolejo-Ramos, Fernando
2015-10-01
Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data. PMID:25998210
Interacting damage models mapped onto ising and percolation models
Toussaint, Renaud; Pride, Steven R.
2004-03-23
The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model
Interacting damage models mapped onto Ising and percolation models.
Toussaint, Renaud; Pride, Steven R
2005-04-01
We introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasi-static fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, we show that damage models with global load sharing are isomorphic to standard percolation theory and that damage models with a local load sharing rule are isomorphic to the standard Ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. We also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, we also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard
Development of a unified constitutive model for an isotropic nickel base superalloy Rene 80
NASA Technical Reports Server (NTRS)
Ramaswamy, V. G.; Vanstone, R. H.; Laflen, J. H.; Stouffer, D. C.
1988-01-01
Accurate analysis of stress-strain behavior is of critical importance in the evaluation of life capabilities of hot section turbine engine components such as turbine blades and vanes. The constitutive equations used in the finite element analysis of such components must be capable of modeling a variety of complex behavior exhibited at high temperatures by cast superalloys. The classical separation of plasticity and creep employed in most of the finite element codes in use today is known to be deficient in modeling elevated temperature time dependent phenomena. Rate dependent, unified constitutive theories can overcome many of these difficulties. A new unified constitutive theory was developed to model the high temperature, time dependent behavior of Rene' 80 which is a cast turbine blade and vane nickel base superalloy. Considerations in model development included the cyclic softening behavior of Rene' 80, rate independence at lower temperatures and the development of a new model for static recovery.
Damage Propagation Modeling for Aircraft Engine Prognostics
NASA Technical Reports Server (NTRS)
Saxena, Abhinav; Goebel, Kai; Simon, Don; Eklund, Neil
2008-01-01
This paper describes how damage propagation can be modeled within the modules of aircraft gas turbine engines. To that end, response surfaces of all sensors are generated via a thermo-dynamical simulation model for the engine as a function of variations of flow and efficiency of the modules of interest. An exponential rate of change for flow and efficiency loss was imposed for each data set, starting at a randomly chosen initial deterioration set point. The rate of change of the flow and efficiency denotes an otherwise unspecified fault with increasingly worsening effect. The rates of change of the faults were constrained to an upper threshold but were otherwise chosen randomly. Damage propagation was allowed to continue until a failure criterion was reached. A health index was defined as the minimum of several superimposed operational margins at any given time instant and the failure criterion is reached when health index reaches zero. Output of the model was the time series (cycles) of sensed measurements typically available from aircraft gas turbine engines. The data generated were used as challenge data for the Prognostics and Health Management (PHM) data competition at PHM 08.
NASA Technical Reports Server (NTRS)
Walker, K. P.
1981-01-01
Results of a 20-month research and development program for nonlinear structural modeling with advanced time-temperature constitutive relationships are reported. The program included: (1) the evaluation of a number of viscoplastic constitutive models in the published literature; (2) incorporation of three of the most appropriate constitutive models into the MARC nonlinear finite element program; (3) calibration of the three constitutive models against experimental data using Hastelloy-X material; and (4) application of the most appropriate constitutive model to a three dimensional finite element analysis of a cylindrical combustor liner louver test specimen to establish the capability of the viscoplastic model to predict component structural response.
NASA Astrophysics Data System (ADS)
Gu, Sendong; Zhang, Liwen; Zhang, Chi; Shen, Wenfei
2016-03-01
The hot deformation characteristics of nickel-based alloy Nimonic 80A were investigated by isothermal compression tests conducted in the temperature range of 1,000-1,200Â°C and the strain rate range of 0.01â€”5 s-1 on a Gleeble-1500 thermomechanical simulator. In order to establish the constitutive models for dynamic recrystallization (DRX) behavior and flow stress of Nimonic 80A, the material constants Î±, n and DRX activation energy Q in the constitutive models were calculated by the regression analysis of the experimental data. The dependences of initial stress, saturation stress, steady-state stress, dynamic recovery (DRV) parameter, peak strain, critical strain and DRX grain size on deformation parameters were obtained. Then, the Avrami equation including the critical strain for DRX and the peak strain as a function of strain was established to describe the DRX volume fraction. Finally, the constitutive model for flow stress of Nimonic 80A was developed in DRV region and DRX region, respectively. The flow stress values predicted by the constitutive model are in good agreement with the experimental ones, which indicates that the constitutive model can give an accurate estimate for the flow stress of Nimonic 80A under the deformation conditions.
Life prediction and constitutive models for engine hot section anisotropic materials program
NASA Technical Reports Server (NTRS)
Swanson, G. A.; Linask, I.; Nissley, D. M.; Norris, P. P.; Meyer, T. G.; Walker, K. P.
1986-01-01
This report presents the results of the first year of a program designed to develop life prediction and constitutive models for two coated single crystal alloys used in gas turbine airfoils. The two alloys are PWA 1480 and Alloy 185. The two oxidation resistant coatings are PWA 273, an aluminide coating, and PWA 286, an overlay NiCoCrAlY coating. To obtain constitutive and/or fatigue data, tests were conducted on coated and uncoated PWA 1480 specimens tensilely loaded in the 100 , 110 , 111 , and 123 directions. A literature survey of constitutive models was completed for both single crystal alloys and metallic coating materials; candidate models were selected. One constitutive model under consideration for single crystal alloys applies Walker's micromechanical viscoplastic formulation to all slip systems participating in the single crystal deformation. The constitutive models for the overlay coating correlate the viscoplastic data well. For the aluminide coating, a unique test method is under development. LCF and TMF tests are underway. The two coatings caused a significant drop in fatigue life, and each produced a much different failure mechanism.
NASA Astrophysics Data System (ADS)
Misra, Anil; Singh, Viraj
2015-09-01
Thermomechanics and granular micromechanics approaches are combined to derive constitutive equations for modeling rate-dependent granular materials with damage and plasticity. The derivation is motivated by the recognition that the effect of micro-scale mechanisms upon the macro-scale behavior is known to be significant for granular materials. A general thermomechanical framework applicable to rate-dependent granular materials with damage and plasticity is developed. Based upon this framework, an expression for macro-scale Cauchy stress tensor is obtained in terms of the micro-scale grain interaction forces and the relationship between micro- and macro-scale kinematics. In addition, a Clausius-Duhem type inequality applicable to inter-granular interaction is derived, which is used to establish micro-scale constitutive relations for particular type of inter-granular interactions. The expression for Cauchy stress tensor and the micro-scale constitutive relations is then combined under a mean field kinematic assumption to obtain evolution-type macro-scale constitutive equations. The advantage of the granular micromechanics approach is that the damage and plasticity are defined using simple 1d functions at micro-scale, and complicated plastic potentials, damage functions and rules for their evolution are not required. The resultant model is applied to investigate primary, secondary and tertiary creep, creep-recovery as well as rate-dependent response under uniaxial compressive loading. Model applicability is also demonstrated for asymmetric tensile-compressive response under creep-recovery loading. The model is used to evaluate the evolution of elastic energy, and viscous, plastic and damage dissipation at the macro- and micro-scale with respect to creep time and loading level. The results show the development of loading-induced anisotropy due to damage and plasticity in these materials.
Christian Gasser, T
2011-06-01
Understanding the failure and damage mechanisms of soft biological tissue is critical to a sensitive and specific characterization of tissue injury tolerance and its relation to biological responses. Despite increasing experimental and analytical efforts, failure-related irreversible effects of soft biological tissue are still poorly understood. There is still no clear definition of what "damage" of a soft biological material is, and conventional macroscopic indicators, as known from damage of engineering materials for example, may not identify the tissue's tolerance to injury appropriately. To account for the complex three-dimensional arrangement of collagen, a microfiber model approach is applied, where constitutive relations for collagen fibers are integrated over the unit sphere, which in turn defines the tissue's macroscopic properties. A collagen fiber is represented by a bundle of proteoglycan cross-linked collagen fibrils that undergoes irreversible deformations when exceeding its elastic tensile limit. The proposed constitutive model is able to predict strain stiffening at physiological strain levels and does not exhibit a clear macroscopic elastic limit, two typical features known from soft biological tissue testing. An elastic-predictor/plastic-corrector implementation of the model is followed and constitutive parameters are estimated from in vitro test data from a particular abdominal aortic aneurysm (AAA). Damage-based structural instabilities of the AAA under different inflation conditions are investigated, where the collagen orientation density has been estimated from its in vivo stress state. PMID:21338718
NASA Astrophysics Data System (ADS)
Yin, Yajun; Xue, Mingde; Yu, Shouwen
A lower bound rigid plastic constitutive model for porous materials has been published recently, but its reliability and accuracy is still kept unknown. Therefore, this paper is confined to examine this model by comparing it with other ones such as the upper bound one and experimental-based one. Under three loading states (i.e. uniaxial stress condition, biaxial equal stress condition and uniaxial strain condition), the sintered copperâ€™s ductility, compressibility, strength property, deformation characteristics, stressËœstrain curves and damage evolution process predicted by these models are systematically compared. The advantage of the lower bound model in describing the yield property and its limitations in evaluating the ductility, compressibility, strength variation and damage evolution process of porous materials are clarified. Systematical analysis reveals that these limitations may be attributed to the short of void interaction mechanism in the lower bound model. This discovery lays the foundation for further improvement and modification of the lower bound model in the future research.
Modeling the viscoplastic and damage behavior in deep argillaceous rocks
NASA Astrophysics Data System (ADS)
Souley, Mountaka; Armand, Gilles; Su, Kun; Ghoreychi, Mehdi
In order to demonstrate the feasibility of a radioactive waste repository in the Callovo-Oxfordian claystone formation, the French national radioactive waste management agency (ANDRA) started in 2000 to build an underground research laboratory at Bure (East of France). One of the key issues is to understand long term behavior of the drifts. More than 400 m horizontal galleries at the main level of -490 m have been instrumented since April 2005. The continuous measurements of convergence of the galleries are available, allowing a better understanding of the time-dependent response of the claystone at natural scale. Results indicate that the viscoplastic strain rates observed in the undamaged area far from the gallery walls are of the same order of magnitude as those obtained on rock samples, whereas those recorded in the damaged or fractured zone near the gallery walls are one to two orders of magnitude higher, indicating the significant influence of damage or/and macro-fractures on the viscoplastic strains. Based on these observations, a macroscopic viscoplastic model which aims to improve the viscoplastic strain prediction in the EDZ is proposed and implemented in FLAC3 DÂ©. Both the instantaneous and the time-dependent behavior are considered in the model. The short term response is assumed to be elactoplastic with strain hardening/softening whereas the time-dependent behavior is based on the concepts of viscoplasticity (LemaÄ±Ë†treâ€™s model). Finally, the damage-induced viscoplastic strains changes is examined through the plastic deformation (assumed to approach the damage rate). In order to verify both constitutive equations and their implementations, several simulations are performed: (a) triaxial tests at different confining pressures; (b) single- and multi-stage creep tests; (c) relaxation tests with different total axial strain levels, etc. Finally, an example of a blind prediction of the excavation of a drift parallel to the horizontal minor stress, Ï
Modeling of viscoelasticity and damage in composite laminates by continuum thermodynamics
NASA Astrophysics Data System (ADS)
Ahci, Elif
Time dependent analysis of fiber reinforced polymer matrix composites is essential if these materials are used in applications involving the effect of severe environmental conditions such as high temperature and humidity in addition to mechanical loading. The present research is focused on understanding and modeling the overall nonlinear viscoelastic response of polymer matrix composites incorporating the effects of distributed damage. A constitutive framework incorporating the effect of high temperature and distributed damage is developed for polymer matrix composite laminates. The use of this framework for woven fabric composites is illustrated. The viscoelastic material response and the material properties under severe environmental conditions are studied both theoretically and experimentally. The approach uses continuum thermodynamics based formulation in which stress and temperature are allowed as independent variables along with the so-called hidden variables associated with viscous flow and internal variables representing damage. The damage variables incorporate time-dependent crack separation response as well crack surface orientation. The material coefficients in the polynomial expansion of the free energy are evaluated by a computational model. A user defined material subroutine is developed to include the nonlinear viscoelastic constitutive relations into ABAQUS finite element analysis package in computational study. A combined analytical and numerical procedure to determine the unknown constants in the theoretical model is also presented. The effect of damage on the residual viscoelastic response of the material is studied by experiments to get a satisfactory and complete model. The effect of high temperature on the damage initiation and evolution is studied by microscopic observations of the undamaged and damaged specimen edges, which are exposed to high temperature. A systematic experimental procedure is followed to determine the critical temperature
Ductile damage modeling based on void coalescence and percolation theories
Tonks, D.L.; Zurek, A.K.; Thissell, W.R.
1995-09-01
A general model for ductile damage in metals is presented. It includes damage induced by shear stress as well as damage caused by volumetric tension. Spallation is included as a special case. Strain induced damage is also treated. Void nucleation and growth are included, and give rise to strain rate effects. Strain rate effects also arise in the model through elastic release wave propagation between damage centers. The underlying physics of the model is the nucleation, growth, and coalescence of voids in a plastically flowing solid. The model is intended for hydrocode based computer simulation. An experimental program is underway to validate the model.
Constitutive modeling of aluminum foam and finite element implementation for crash simulations
NASA Astrophysics Data System (ADS)
Bi, Jing
In the past decades metallic foams have been increasingly used as filler materials in crashworthiness applications due to their relatively low cost and high capacity of energy absorption. Due to the destructive nature of crashes, studies on the performance of metallic foams using physical testing have been limited to examining the crushing force histories and/or folding patterns that are insufficient for crashworthiness designs. For this reason, numerical simulations, particularly nonlinear finite element (FE) analyses, play an important role in designing crashworthy foam-filled structures. An effective and numerically stable model is needed for modeling metallic foams that are porous and encounter large nonlinear deformations in crashes. In this study a new constitutive model for metallic foams is developed to overcome the deficiency of existing models in commercial FE codes such as LS-DYNA. The new constitutive model accounts for volume changes under hydrostatic compression and combines the hydrostatic pressure and von Mises stress into one yield function. The change of the compressibility of the metallic foam is handled in the constitutive model by allowing for shape changes of the yield surface in the hydrostatic pressure-von Mises stress space. The backward Euler method is adopted to integrate the constitutive equations to achieve numerical accuracy and stability. The new foam model is verified and validated by existing experimental data before used in FE simulations of crushing of foam-filled columns that have square and hexagonal cross-sections.
Constitutive model of creep in polycrystalline halite based on workhardening and recovery
Munson, D.E.
1993-07-01
A multimechanism constitutive model of creep has been developed which incorporates the workhardening and recovery transient creep behavior. This model has been applied to the creep of polycrystalline halite. The specific application of the model is in the calculation of the closure of underground rooms in layered salt deposits. Through the use of finite element calculations, this model, with appropriate laboratory material parameters and a Tresca flow potential, has predicted the measured closure of a number of large in situ experimental rooms.
A micromechanics constitutive model of transformation plasticity with shear and dilatation effect
NASA Astrophysics Data System (ADS)
Sun, Q. P.; Hwang, K. C.; Yu, S. W.
B ASED on micromechanics, thermodynamics and microscale t â†’ m transformation mechanism considerations a micromechanics constitutive model which takes into account both the dilatation and shear effects of the transformation is proposed to describe the plastic, pseudoelastic and shape memory behaviors of structural ceramics during transformation under different temperatures. In the derivation, a constitutive element (representative material sample) was used which contains many of the transformed m-ZrO 2 grains or precipitates as the second phase inclusions embedded in an elastic matrix. Under some basic assumptions, analytic expressions for the Helmholtz and complementary free energy of the constitutive element are derived in a self-consistent manner by using the Mori-Tanaka method which takes into account the interaction between the transformed inclusions. The derived free energy is a function of externally applied macroscopic stress (or strain), temperature, volume fraction of transformed phase and the averaged stressfree transformation strain (eigenstrain) of all the transformed inclusions in the constitutive element, the latter two quantities being considered to be the internal variables describing the micro-structural rearrangement in the constitutive element. In the framework of the Hill-Rice internal variable constitutive theory, the transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for proportional and non-proportional loading histories are derived, respectively. The theoretical predictions are compared with the available experimental data of Mg-PSZ and Ce-TZP polycrystalline toughening ceramics.
Turbulence constitutive modeling of the square root of the Reynolds stress
NASA Astrophysics Data System (ADS)
Ariki, Taketo
2015-11-01
A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)], 10.1063/1.861942 in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed.
Turbulence constitutive modeling of the square root of the Reynolds stress.
Ariki, Taketo
2015-11-01
A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)] in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed. PMID:26651782
NASA Technical Reports Server (NTRS)
Koenig, Herbert A.; Chan, Kwai S.; Cassenti, Brice N.; Weber, Richard
1988-01-01
A unified numerical method for the integration of stiff time dependent constitutive equations is presented. The solution process is directly applied to a constitutive model proposed by Bodner. The theory confronts time dependent inelastic behavior coupled with both isotropic hardening and directional hardening behaviors. Predicted stress-strain responses from this model are compared to experimental data from cyclic tests on uniaxial specimens. An algorithm is developed for the efficient integration of the Bodner flow equation. A comparison is made with the Euler integration method. An analysis of computational time is presented for the three algorithms.
Constitutive model for the dynamic response of a NiTi shape memory alloy
NASA Astrophysics Data System (ADS)
Shi, Xiaohong; Zeng, Xiangguo; Chen, Huayan
2016-07-01
In this paper, based on irreversible thermodynamic theory, the Helmholtz free energy function, was selected to deduce both the master equations and evolution equations of the constitutive model of a NiTi alloy under high strain. The Helmholtz free energy function contains the parameters of the reflecting phase transition and plastic property. The constitutive model for a NiTi alloy was implemented using a semi-implicit stress integration algorithm. Four successive stages can be differentiated and simulated: parent phase elasticity, martensitic phase transition, martensitic elasticity, and dislocation yield. The simulation results are in good agreement with the experimental results.
A Dynamic Damage Mechanics Source Model for Explosions in Crystalline Rock
NASA Astrophysics Data System (ADS)
Mihaly, J. M.; Bhat, H. S.; Sammis, C. G.; Rosakis, A.
2011-12-01
The micromechanical damage mechanics formulated by Ashby and Sammis [PAGEOPH, 1990] and generalized by Deshpande and Evans [J. Mech. Phys. Solids, 2008] has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative, and thus produces strain-rate sensitivity in the constitutive response. The model is experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from to . This rate-dependent damage mechanics has been implemented in the ABAQUS dynamic finite element code and used to explore the effects of burn rate (loading rate) and lithostatic stress on the spatial extent of fracture damage and S waves generated by explosions in crystalline rock. Slower rise times and longer pressure pulses produce more damage and stronger S waves.
Constitutive Modeling of Porcine Liver in Indentation Using 3D Ultrasound Imaging
Jordan, P.; Socrate, S.; Zickler, T.E.; Howe, R.D.
2009-01-01
In this work we present an inverse finite-element modeling framework for constitutive modeling and parameter estimation of soft tissues using full-field volumetric deformation data obtained from 3D ultrasound. The finite-element model is coupled to full-field visual measurements by regularization springs attached at nodal locations. The free ends of the springs are displaced according to the locally estimated tissue motion and the normalized potential energy stored in all springs serves as a measure of model-experiment agreement for material parameter optimization. We demonstrate good accuracy of estimated parameters and consistent convergence properties on synthetically generated data. We present constitutive model selection and parameter estimation for perfused porcine liver in indentation and demonstrate that a quasilinear viscoelastic model with shear modulus relaxation offers good model-experiment agreement in terms of indenter displacement (0.19 mm RMS error) and tissue displacement field (0.97 mm RMS error). PMID:19627823
Biomechanical behavior of bovine periodontal ligament: Experimental tests and constitutive model.
Oskui, Iman Z; Hashemi, Ata; Jafarzadeh, Hamid
2016-09-01
A viscohyperelastic constitutive model with the use of the internal variables approach was formulated to evaluate the nonlinear elastic and time dependent anisotropic mechanical behavior of the periodontal ligament (PDL). Since the relaxation response was found to depend on the applied stretch, the adoption of the nonlinear viscous behavior in the present model was necessary. In this paper, Helmholtz free energy function was assigned to the material as the sum of hyperelastic and viscous terms which is based on the physical concept of internal variables. The constitutive model parameters were evaluated from the comparison of the proposed model and experimental data. For this purpose, tensile response of the bovine PDL samples under different stretch rates was obtained. The good correspondence between the proposed model and the experimental results confirmed the capability of the model to interpret the stretch rate behavior of the PDL. Moreover, the validity of structural model parameters was checked according to the results of the stress relaxation tests. PMID:27315371
Life prediction and constitutive models for engine hot section anisotropic materials program
NASA Technical Reports Server (NTRS)
Nissley, D. M.; Meyer, T. G.
1992-01-01
This report presents the results from a 35 month period of a program designed to develop generic constitutive and life prediction approaches and models for nickel-based single crystal gas turbine airfoils. The program is composed of a base program and an optional program. The base program addresses the high temperature coated single crystal regime above the airfoil root platform. The optional program investigates the low temperature uncoated single crystal regime below the airfoil root platform including the notched conditions of the airfoil attachment. Both base and option programs involve experimental and analytical efforts. Results from uniaxial constitutive and fatigue life experiments of coated and uncoated PWA 1480 single crystal material form the basis for the analytical modeling effort. Four single crystal primary orientations were used in the experiments: (001), (011), (111), and (213). Specific secondary orientations were also selected for the notched experiments in the optional program. Constitutive models for an overlay coating and PWA 1480 single crystal material were developed based on isothermal hysteresis loop data and verified using thermomechanical (TMF) hysteresis loop data. A fatigue life approach and life models were selected for TMF crack initiation of coated PWA 1480. An initial life model used to correlate smooth and notched fatigue data obtained in the option program shows promise. Computer software incorporating the overlay coating and PWA 1480 constitutive models was developed.
Life prediction and constitutive models for engine hot section anisotropic materials program
NASA Technical Reports Server (NTRS)
Nissley, D. M.; Meyer, T. G.; Walker, K. P.
1992-01-01
This report presents a summary of results from a 7 year program designed to develop generic constitutive and life prediction approaches and models for nickel-based single crystal gas turbine airfoils. The program was composed of a base program and an optional program. The base program addressed the high temperature coated single crystal regime above the airfoil root platform. The optional program investigated the low temperature uncoated single crystal regime below the airfoil root platform including the notched conditions of the airfoil attachment. Both base and option programs involved experimental and analytical efforts. Results from uniaxial constitutive and fatigue life experiments of coated and uncoated PWA 1480 single crystal material formed the basis for the analytical modeling effort. Four single crystal primary orientations were used in the experiments: group of zone axes (001), group of zone axes (011), group of zone axes (111), and group of zone axes (213). Specific secondary orientations were also selected for the notched experiments in the optional program. Constitutive models for an overlay coating and PWA 1480 single crystal materials were developed based on isothermal hysteresis loop data and verified using thermomechanical (TMF) hysteresis loop data. A fatigue life approach and life models were developed for TMF crack initiation of coated PWA 1480. A life model was developed for smooth and notched fatigue in the option program. Finally, computer software incorporating the overlay coating and PWA 1480 constitutive and life models was developed.
NASA Technical Reports Server (NTRS)
Dame, L. T.; Stouffer, D. C.
1986-01-01
A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.
Constitutive modelling of creep in a long fiber random glass mat thermoplastic composite
NASA Astrophysics Data System (ADS)
Dasappa, Prasad
The primary objective of this proposed research is to characterize and model the creep behaviour of Glass Mat Thermoplastic (GMT) composites under thermo-mechanical loads. In addition, tensile testing has been performed to study the variability in mechanical properties. The thermo-physical properties of the polypropylene matrix including crystallinity level, transitions and the variation of the stiffness with temperature have also been determined. In this work, the creep of a long fibre GMT composite has been investigated for a relatively wide range of stresses from 5 to 80 MPa and temperatures from 25 to 90Â°C. The higher limit for stress is approximately 90% of the nominal tensile strength of the material. A Design of Experiments (ANOVA) statistical method was applied to determine the effects of stress and temperature in the random mat material which is known for wild experimental scatter. Two sets of creep tests were conducted. First, preliminary short-term creep tests consisting of 30 minutes creep followed by recovery were carried out over a wide range of stresses and temperatures. These tests were carried out to determine the linear viscoelastic region of the material. From these tests, the material was found to be linear viscoelastic up-to 20 MPa at room temperature and considerable non-linearities were observed with both stress and temperature. Using Time-Temperature superposition (TTS) a long term master curve for creep compliance for up-to 185 years at room temperature has been obtained. Further, viscoplastic strains were developed in these tests indicating the need for a non-linear viscoelastic viscoplastic constitutive model. The second set of creep tests was performed to develop a general non-linear viscoelastic viscoplastic constitutive model. Long term creep-recovery tests consisting of 1 day creep followed by recovery has been conducted over the stress range between 20 and 70 MPa at four temperatures: 25Â°C, 40Â°C, 60Â°C and 80Â°C. Findley's model
Iig, Patrick
2011-01-01
Complex fluids, such as polymers, colloids, liquid-crystals etc., show intriguing viscoelastic properties, due to the complicated interplay between flow-induced structure formation and dynamical behavior. Starting from microscopic models of complex fluids, a systematic coarse-graining method is presented that allows us to derive closed-form and thermodynamically consistent constitutive equations for such fluids. Essential ingredients of the proposed approach are thermodynamically guided simulations within a consistent coarse-graining scheme. In addition to this new type of multiscale simulations, we reconstruct the building blocks that constitute the thermodynamically consistent coarse-grained model. We illustrate the method for low-molecular polymer melts, which are subject to different imposed flow fields like planar shear and different elongational flows. The constitutive equation for general flow conditions we obtain shows rheological behavior including shear thinning, normal stress differences, and elongational viscosities in good agreement with reference results. PMID:21678766
Experimental study of cancellous bone under large strains and a constitutive probabilistic model.
Kefalas, V; Eftaxiopoulos, D A
2012-02-01
Experimental study of bovine cancellous bone up to compaction under uniaxial compression and up to fracture under tension, has been pursued in this article. Compression experiments have revealed the known three stages of the constitutive response, namely the initial increasing and softening branches at moderate strains, the plateau region at large strains and the hardening part at very large strains under compaction. Tension tests have quantified the increasing and softening branches of the stress-strain curve up to fracture. Subsequently, a constitutive mechanical model, for the simulation of the experimental findings up to very large strains (75% engineering strain under compression), is proposed. The model is based on the statistical description of (a) the failure process of the trabecular structure at small and moderate strains and (b) the compaction process of the trabecular mass at very large strains under compression. Several fitting cases indicated that the presented constitutive law can capture the evolution of the experimental results. PMID:22301172
Constitutive model for shape memory alloys and its use in design and finite element analysis
NASA Astrophysics Data System (ADS)
Bose, Sudip; Santhanam, Sridhar
2002-07-01
A constitutive model for predicting the thermomechanical behavior of Shape Memory Alloys (SMAs) has been developed and validated. The model uses an approach similar to Brinson, Liang and Rogers, and Tanaka. It links key thermomechanical variables: stress, strain, temperature, and martensite fraction. A basic differential form for the SMA constitutive behavior, developed by Tanaka, forms the foundation of the model. The model is completed with a definition of the rules governing the behavior of martensite fraction. Like Brinson, the model distinguishes between de-twinned and twinned martensite. The phase transition temperatures are assumed to be a linear function of applied stress. The forward and reverse phase transformations are described by piecewise exponential functions. There are a number of parameters in the model that need to be determined using experimental data. The critical transformation temperatures are determined by resistivity measurements. All other parameters are determined by mechanical tension testing followed by nonlinear least-squares estimations. Mechanical testing consisted of displacement controlled, tension tests on Nitinol wires at several temperatures. The effectiveness of this model is demonstrated by its use in the design of an SMA actuated robotic arm. The constitutive model is used in conjunction with a lumped heat transfer model, a kinematic model, and a dynamic model to predict the behavior of the arm. Comparison between predictions and experimentally observed behavior is very good indicating a sound constitutive model. The model is also built into a finite element code that simulates pseudoelastic SMA behavior. The code considers geometric and material nonlinearities. The behavior of a simple pseudoelastic device is shown to be well predicted by the finite element code.
Damage and fatigue described by a fractional derivative model
NASA Astrophysics Data System (ADS)
Caputo, Michele; Fabrizio, Mauro
2015-07-01
As in [1], damage is associated with fatigue that a material undergoes. In this paper, because we work with viscoelastic solids represented by a fractional model, damage is described by the order of the fractional derivative, which represents the phase field satisfying Ginzburg-Landau equation, which describes the evolution of damage. Finally, in our model, damage is caused, not only by fatigue, but also directly by a source related to environmental factors and described by a positive time function.
Multi-step loading/unloading experiments that challenge constitutive models of glassy polymers
NASA Astrophysics Data System (ADS)
Caruthers, James; Medvedev, Grigori
2014-03-01
The mechanical response of glassy polymers depends on the thermal and deformational history, where the resulting relaxation phenomenon remains a significant challenge for constitutive modeling. For strain controlled experiments the stress response is measured during loading/unloading ramps and a constant strain. By judiciously combining the basic steps, a set of multi-step experiments have been designed to challenge existing constitutive models for glassy polymers. A particular example is the ``stress memory'' experiment, i.e. loading through yield, unloading to zero stress, and holding at final strain, where the subsequent evolution of the stress exhibits an overshoot. The observed dependence of the overshoot on the loading strain rate cannot be explained by the models where the relaxation time is a function of stress or strain. Another discriminating multi-step history experiment involves strain accumulation to test the common assumption that the phenomenon of strain hardening is caused by a purely elastic contribution to stress. Experimental results will be presented for a low Tg epoxy system, and the data will be used to critically analyze the predictions of both traditional viscoelastic/viscoplastic constitutive models and a recently developed Stochastic Constitutive Model.
Modeling and characterization of recompressed damaged materials
Becker, R; Cazamias, J U; Kalantar, D H; LeBlanc, M M; Springer, H K
2004-02-11
Experiments have been performed to explore conditions under which spall damage is recompressed with the ultimate goal of developing a predictive model. Spall is introduced through traditional gas gun techniques or with laser ablation. Recompression techniques producing a uniaxial stress state, such as a Hopkinson bar, do not create sufficient confinement to close the porosity. Higher stress triaxialities achieved through a gas gun or laser recompression can close the spall. Characterization of the recompressed samples by optical metallography and electron microscopy reveal a narrow, highly deformed process zone. At the higher pressures achieved in the gas gun, little evidence of spall remains other than differentially etched features in the optical micrographs. With the very high strain rates achieved with laser techniques there is jetting from voids and other signs of turbulent metal flow. Simulations of spall and recompression on micromechanical models containing a single void suggest that it might be possible to represent the recompression using models similar to those employed for void growth. Calculations using multiple, randomly distributed voids are needed to determine if such models will yield the proper behavior for more realistic microstructures.
Modeling, simulation and experimental verification of constitutive models for energetic materials
Haberman, K.S.; Bennett, J.G.; Assay, B.W.
1997-09-01
Simulation of the complete response of components and systems composed of energetic materials, such as PBX-9501 is important in the determination of the safety of various explosive systems. For example, predicting the correct state of stress, rate of deformation and temperature during penetration is essential in the prediction of ignition. Such simulation requires accurate constitutive models. These models must also be computationally efficient to enable analysis of large scale three dimensional problems using explicit lagrangian finite element codes such as DYNA3D. However, to be of maximum utility, these predictions must be validated against robust dynamic experiments. In this paper, the authors report comparisons between experimental and predicted displacement fields in PBX-9501 during dynamic deformation, and describe the modeling approach. The predictions used Visco-SCRAM and the Generalized Method of Cells which have been implemented into DYNA3D. The experimental data were obtained using laser-induced fluorescence speckle photography. Results from this study have lead to more accurate models and have also guided further experimental work.
Continuum-Based FEM Modeling of Ceramic Powder Compaction Using a Cap-Plasticity Constitutive Model
ARGUELLO JR.,JOSE G.; FOSSUM,ARLO F.; ZEUCH,DAVID H.; EWSUK,KEVIN G.
2000-05-01
Software has been developed and extended to allow finite element (FE) modeling of ceramic powder compaction using a cap-plasticity constitutive model. The underlying, general-purpose FE software can be used to model even the most complex three-dimensional (3D) geometries envisioned. Additionally, specialized software has been developed within this framework to address a general subclass of axisymmetric compacts that are common in industry. The expertise required to build the input deck, run the FE code, and post-process the results for this subclass of compacts is embedded within the specialized software. The user simply responds to a series of prompts, evaluates the quality of the FE mesh that is generated, and analyzes the graphical results that are produced. The specialized software allows users with little or no FE expertise to benefit from the tremendous power and insight that FE analysis can bring to the design cycle. The more general underlying software provides complete flexibility to model more complicated geometries and processes of interest to ceramic component manufacturers but requires significantly more user interaction and expertise.
Creep crack growth predictions in INCO 718 using a continuum damage model
NASA Technical Reports Server (NTRS)
Walker, K. P.; Wilson, D. A.
1985-01-01
Creep crack growth tests have been carried out in compact type specimens of INCO 718 at 1200 F (649 C). Theoretical creep crack growth predictions have been carried out by incorporating a unified viscoplastic constitutive model and a continuum damage model into the ARAQUS nonlinear finite element program. Material constants for both the viscoplastic model and the creep continuum damage model were determined from tests carried out on uniaxial bar specimens of INCO 718 at 1200 F (649 C). A comparison of the theoretical creep crack growth rates obtained from the finite element predictions with the experimentally observed creep crack growth rates indicates that the viscoplastic/continuum damage model can be used to successfully predict creep crack growth in compact type specimens using material constants obtained from uniaxial bar specimens of INCO 718 at 1200 F (649 C).
Coupled Hydro-Mechanical Constitutive Model for Vegetated Soils: Validation and Applications
NASA Astrophysics Data System (ADS)
Switala, Barbara Maria; Veenhof, Rick; Wu, Wei; Askarinejad, Amin
2016-04-01
It is well known, that presence of vegetation influences stability of the slope. However, the quantitative assessment of this contribution remains challenging. It is essential to develop a numerical model, which combines mechanical root reinforcement and root water uptake, and allows modelling rainfall induced landslides of vegetated slopes. Therefore a novel constitutive formulation is proposed, which is based on the modified Cam-clay model for unsaturated soils. Mechanical root reinforcement is modelled introducing a new constitutive parameter, which governs the evolution of the Cam-clay failure surface with the degree of root reinforcement. Evapotranspiration is modelled in terms of the root water uptake, defined as a sink term in the water flow continuity equation. The original concept is extended for different shapes of the root architecture in three dimensions, and combined with the mechanical model. The model is implemented in the research finite element code Comes-Geo, and in the commercial software Abaqus. The formulation is tested, performing a series of numerical examples, which allow validation of the concept. The direct shear test and the triaxial test are modelled in order to test the performance of the mechanical part of the model. In order to validate the hydrological part of the constitutive formulation, evapotranspiration from the vegetated box is simulated and compared with the experimental results. Obtained numerical results exhibit a good agreement with the experimental data. The implemented model is capable of reproducing results of basic geotechnical laboratory tests. Moreover, the constitutive formulation can be used to model rainfall induced landslides of vegetated slopes, taking into account the most important factors influencing the slope stability (root reinforcement and evapotranspiration).
Modeling continuous-fiber reinforced polymer composites for exploration of damage tolerant concepts
NASA Astrophysics Data System (ADS)
Matthews, Peter J.
This work aims to improve the predictive capability for fiber-reinforced polymer matrix composite laminates using the finite element method. A new tool for modeling composite damage was developed which considers important modes of failure. Well-known micromechanical models were implemented to predict material values for material systems of interest to aerospace applications. These generated material values served as input to intralaminar and interlaminar damage models. A three-dimensional in-plane damage material model was implemented and behavior verified. Deficiencies in current state-of-the-art interlaminar capabilities were explored using the virtual crack closure technique and the cohesive zone model. A user-defined cohesive element was implemented to discover the importance of traction-separation material constitutive behavior. A novel method for correlation of traction-separation parameters was created. This new damage modeling tool was used for evaluation of novel material systems to improve damage tolerance. Classical laminate plate theory was used in a full-factorial study of layerwise-hybrid laminates. Filament-wound laminated composite cylindrical shells were subjected to quasi-static loading to validate the finite element computational composite damage model. The new tool for modeling provides sufficient accuracy and generality for use on a wide-range of problems.
A Constitutive Model of 6111-T4 Aluminum Alloy Sheet Based on the Warm Tensile Test
NASA Astrophysics Data System (ADS)
Hua, Lin; Meng, Fanzhi; Song, Yanli; Liu, Jianing; Qin, Xunpeng; Suo, Lianbing
2014-03-01
As main light-weight material, aluminum alloy sheets have been widely applied to produce auto body panels. In order to predict the formability and springback of aluminum alloy sheets, a precise constitutive model is a necessity. In this article, a series of warm tensile tests were conducted on Gleeble-1500D thermal mechanical simulator for 6111-T4 aluminum alloy sheets. The corresponding strain rate ranged from 0.015 to 1.5 s-1, and the temperature ranged from 25 to 350 Â°C. The relationship between the temperature, the strain rate, and the flow stress were discussed. A constitutive model based on the updated Fields-Backofen equation was established to describe the flow behavior of 6111-T4 aluminum alloy during the warm tensile tests. Subsequently, the average absolute relative error (AARE) was introduced to verify the predictability of the constitutive model. The value of AARE at the uniform plastic deformation stage was calculated to be 1.677%, which demonstrates that the predicted flow stress values were in accordance with the experimental ones. The constitutive model was validated by the fact that the simulated results of the warm tensile tests coincided with the experimental ones.
Skacel, Pavel; Bursa, Jiri
2015-01-01
Several constitutive models have been proposed for the description of mechanical behaviour of soft tissues containing collagen fibres. Some of the commonly used approaches accounting for the dispersion of fibre orientations are based on the summation of (mechanical) contributions of differently oriented fibre families. This leads to the need of numerical integration on the sphere surface, and the related numerical consumption is the main disadvantage of this category of constitutive models. The paper is focused on the comparison of various numerical integration methods applied to a specific constitutive model applicable for arterial walls. Robustness and efficiency of several integration rules were tested with respect to application in finite element (FE) codes. Among all the analysed numerical integration rules, the best results were reached by Lebedev quadrature; the related parameters for the specific constitutive model are presented in the paper. The results were implemented into the commercial FE code ANSYS via user subroutines, and their applicability was demonstrated by an example of FE simulation with non-homogenous stress field. PMID:24168517
A solidification constitutive model for NIKE2D and NIKE3D
Raboin, P.J.
1994-03-17
This memo updates the current status of a solidification material model development which has been underway for more than a year. Significant modeling goals such as predicting cut-off stresses, thermo-elasto-plasticity, strain rate dependent plasticity and dynamic recovery have been completed. The model is called SOLMAT for solidification material model, and while developed for NIKE2D, it has already been implemented in NIKE3D and NIT03D by B. Maker. This memo details the future development strategy of SOLMAT including liquid and solid constitutive improvements, coupling of deviatoric and dilatational deformation and a plan to switch between constitutive theories. It explains some of the difficulties associated solidification modeling and proposes two experiments to measure properties for using SOLMAT. Due to the sensitive nature of these plans in relation to programmatic and CRADA concerns, this memo should be treated as confidential document.
An experimental assessment of internal variables constitutive models for viscoelastic materials
NASA Astrophysics Data System (ADS)
Borges, F. C. L.; Castello, D. A.; Magluta, C.; Rochinha, F. A.; Roitman, N.
2015-01-01
The present work is aimed at presenting an experimental assessment of a constitutive model used to describe viscoelastic behavior. This strategy is built on the basic principles of the Verification and Validation (V&V) philosophy. The mechanical model used to describe the viscoelastic behavior is a constitutive one based on the concept of internal variables. The parameter estimation of the model is performed using frequency domain data through the Particle Swarm Optimization algorithm. A set of different experimental set-ups were built in order to span the structural operational domain from which data can be measured. The model validation is performed based on the use of validation metrics which take into account uncertainties both in the model predictions and observed data.
A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys
NASA Astrophysics Data System (ADS)
Jin, Ke; Kou, Yong; Zheng, Xiaojing
2012-06-01
This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles-Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops.
An internal variable constitutive model for the large deformation of metals at high temperatures
NASA Technical Reports Server (NTRS)
Brown, Stuart; Anand, Lallit
1988-01-01
The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.
An automated procedure for material parameter evaluation for viscoplastic constitutive models
NASA Technical Reports Server (NTRS)
Imbrie, P. K.; James, G. H.; Hill, P. S.; Allen, D. H.; Haisler, W. E.
1988-01-01
An automated procedure is presented for evaluating the material parameters in Walker's exponential viscoplastic constitutive model for metals at elevated temperature. Both physical and numerical approximations are utilized to compute the constants for Inconel 718 at 1100 F. When intermediate results are carefully scrutinized and engineering judgement applied, parameters may be computed which yield stress output histories that are in agreement with experimental results. A qualitative assessment of the theta-plot method for predicting the limiting value of stress is also presented. The procedure may also be used as a basis to develop evaluation schemes for other viscoplastic constitutive theories of this type.
NASA Astrophysics Data System (ADS)
Dass, W.; Merkle, D. H.; Bratton, J. L.
1983-04-01
Constitutive modeling of cohesionless soil for both standard static test conditions and insitu impulsive dynamic load conditions is discussed in this annual report. Predicted laboratory response for several different types of models is evaluated using data from a coordinated testing program. The modeling of insitu soil response to explosive events (CIST and DISC Test) is considered, and the laboratory-derived models are tested for their convenience and accuracy in predicting ground motions. Several important laboratory and insitu phenomena which were not reflected by the model exercises are discussed. Based on the conclusions from this study, testing and modeling requirements for dynamic loading situations are proposed.
NASA Technical Reports Server (NTRS)
Goldberg, Robert K.; Stouffer, Donald C.
1998-01-01
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.
Micromechanics and constitutive models for soft active materials with phase evolution
NASA Astrophysics Data System (ADS)
Wang, Binglian
Soft active materials, such as shape memory polymers, liquid crystal elastomers, soft tissues, gels etc., are materials that can deform largely in response to external stimuli. Micromechanics analysis of heterogeneous materials based on finite element method is a typically numerical way to study the thermal-mechanical behaviors of soft active materials with phase evolution. While the constitutive models that can precisely describe the stress and strain fields of materials in the process of phase evolution can not be found in the databases of some commercial finite element analysis (FEA) tools such as ANSYS or Abaqus, even the specific constitutive behavior for each individual phase either the new formed one or the original one has already been well-known. So developing a computationally efficient and general three dimensional (3D) thermal-mechanical constitutive model for soft active materials with phase evolution which can be implemented into FEA is eagerly demanded. This paper first solved this problem theoretically by recording the deformation history of each individual phase in the phase evolution process, and adopted the idea of effectiveness by regarding all the new formed phase as an effective phase with an effective deformation to make this theory computationally efficient. A user material subroutine (UMAT) code based on this theoretical constitutive model has been finished in this work which can be added into the material database in Abaqus or ANSYS and can be easily used for most soft active materials with phase evolution. Model validation also has been done through comparison between micromechanical FEA and experiments on a particular composite material, shape memory elastomeric composite (SMEC) which consisted of an elastomeric matrix and the crystallizable fibre. Results show that the micromechanics and the constitutive models developed in this paper for soft active materials with phase evolution are completely relied on.
The relationship between observed fatigue damage and life estimation models
NASA Technical Reports Server (NTRS)
Kurath, Peter; Socie, Darrell F.
1988-01-01
Observations of the surface of laboratory specimens subjected to axial and torsional fatigue loadings has resulted in the identification of three damage fatigue phenomena: crack nucleation, shear crack growth, and tensile crack growth. Material, microstructure, state of stress/strain, and loading amplitude all influence which of the three types of fatigue damage occurs during a dominant fatigue life fraction. Fatigue damage maps are employed to summarize the experimental observations. Appropriate bulk stress/strain damage parameters are suggested to model fatigue damage for the dominant fatigue life fraction. Extension of the damage map concept to more complex loadings is presented.
NASA Astrophysics Data System (ADS)
Huang, Zhipeng; Gao, Lihong; Wang, Yangwei; Wang, Fuchi
2016-06-01
The Johnson-Cook (J-C) constitutive model is widely used in the finite element simulation, as this model shows the relationship between stress and strain in a simple way. In this paper, a cluster global optimization algorithm is proposed to determine the J-C constitutive model parameters of materials. A set of assumed parameters is used for the accuracy verification of the procedure. The parameters of two materials (401 steel and 823 steel) are determined. Results show that the procedure is reliable and effective. The relative error between the optimized and assumed parameters is no more than 4.02%, and the relative error between the optimized and assumed stress is 0.2% Ã— 10-5. The J-C constitutive parameters can be determined more precisely and quickly than the traditional manual procedure. Furthermore, all the parameters can be simultaneously determined using several curves under different experimental conditions. A strategy is also proposed to accurately determine the constitutive parameters.
Li, Hua; Yuan, Z; Ng, T Y; Lee, H P; Lam, K Y; Wang, Q X; Wu, Shunnian; Fu, Jie; Hanes, Justin
2003-01-01
The deployment of electroactive ionic polymer hydrogel-metal composites in artificial muscle and BioMEMS applications has recently been intensively investigated. In order to analyse their electromechanical responses to externally applied electrical fields, it is critical to develop a constitutive model linking the macro-mechanical moduli with the micro-mechanical characteristics, and to determine the geometric size and shape of the micro-structural cluster and investigate the effect of cluster morphology on the effective electro-elastic moduli of the polymer hydrogels. As a typical ionic polymer-based hydrogel, the Nafion membrane is studied in this work. Based on the Biot poroelasticity theory, a multi-scale constitutive model which includes both macro and micro characteristics is developed using an asymptotic homogenisation method. The effect of water-volume fraction on the effective elastic moduli of the hydrogel membrane is examined for different equivalent weights. Numerical investigations show that the simulated effective constitutive moduli agree well with experimental data. The presently developed constitutive model is thus validated. In order to determine the micro-structural shape of the polymer skeleton subject to fluid pressure, a representative volume element (RVE) is designed by topology optimisation of the periodic microstructures of the Nafion hydrogels, through the minimisation of the electro-elastic interaction energy between the polymer-based fluorocarbon matrix and the surrounding fluid. This optimal RVE correctly predicts the geometric shapes of the clusters. PMID:14768907