Finite plate thickness effects on the Rayleigh-Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Polavarapu, Rinosh; Banerjee, Arindam

2017-11-01

The majority of theoretical studies have tackled the Rayleigh-Taylor instability (RTI) problem in solids using an infinitely thick plate. Recent theoretical studies by Piriz et al. (PRE 95, 053108, 2017) have explored finite thickness effects. We seek to validate this recent theoretical estimate experimentally using our rotating wheel RTI experiment in an accelerated elastic-plastic material. The test section consists of a container filled with air and mayonnaise (a non-Newtonian emulsion) with an initial perturbation between two materials. The plate thickness effects are studied by varying the depth of the soft-solid. A set of experiments is run by employing different initial conditions with different container dimensions. Additionally, the effect of acceleration rate (driving pressure rise time) on the instability threshold with reference to the finite thickness will also be inspected. Furthermore, the experimental results are compared to the analytical strength models related to finite thickness effects on RTI. Authors acknowledge financial support from DOE-SSAA Grant # DE-NA0003195 and LANL subcontract #370333.

Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity

NASA Astrophysics Data System (ADS)

Hache, F.; Challamel, N.; Elishakoff, I.

2018-01-01

This paper deals with the asymptotic derivation of thin and thick nonlocal plate models at different orders from three-dimensional stress gradient elasticity, through the power series expansions of the displacements in the thickness ratio of the plate. Three nonlocal asymptotic approaches are considered: a partial nonlocality following the thickness of the plate, a partial nonlocality following the two directions of the plates and a full nonlocality (following all the directions). The three asymptotic approaches lead at the zeroth order to a nonlocal Kirchhoff-Love plate model, but differ in the expression of the length scale. The nonlocal asymptotic models coincide at this order with the stress gradient Kirchhoff-Love plate model, only when the nonlocality is following the two directions of the plate and expressed through a nabla operator. This asymptotic model also yields the nonlocal truncated Uflyand-Mindlin plate model at the second order. However, the two other asymptotic models lead to equations that differ from the current existing nonlocal engineering models (stress gradient engineering plate models). The natural frequencies for an all-edges simply supported plate are obtained for each model. It shows that the models provide similar results for low orders of frequencies or small thickness ratio or nonlocal lengths. Moreover, only the asymptotic model with a partial nonlocality following the two directions of the plates is consistent with a stress gradient plate model, whatever the geometry of the plate.

Lithospheric strength and its relationship to the elastic and seismogenic layer thickness

NASA Astrophysics Data System (ADS)

Watts, A. B.; Burov, E. B.

2003-08-01

Plate flexure is a phenomenon that describes how the lithosphere responds to long-term (>105 yr) geological loads. By comparing the flexure in the vicinity of ice, volcano, and sediment loads to predictions based on simple plate models it has been possible to estimate the effective elastic thickness of the lithosphere, Te. In the oceans, Te is the range 2-50 km and is determined mainly by plate and load age. The continents, in contrast, are characterised by Te values of up to 80 km and greater. Rheological considerations based on data from experimental rock mechanics suggest that Te reflects the integrated brittle, elastic and ductile strength of the lithosphere. Te differs, therefore, from the seismogenic layer thickness, Ts, which is indicative of the depth to which anelastic deformation occurs as unstable frictional sliding. Despite differences in their time scales, Te and Ts are similar in the oceans where loading reduces the initial mechanical thickness to values that generally coincide with the thickness of the brittle layer. They differ, however, in continents, which, unlike oceans, are characterised by a multi-layer rheology. As a result, Te≫Ts in cratons, many convergent zones, and some rifts. Most rifts, however, are characterised by a low Te that has been variously attributed to a young thermal age of the rifted lithosphere, thinning and heating at the time of rifting, and yielding due to post-rift sediment loading. Irrespective of their origin, the Wilson cycle makes it possible for low values to be inherited by foreland basins which, in turn, helps explain why similarities between Te and Ts extend beyond rifts into other tectonic regions such as orogenic belts and, occasionally, the cratons themselves.

Thickness and Elasticity of Gram-Negative Murein Sacculi Measured by Atomic Force Microscopy

PubMed Central

Yao, X.; Jericho, M.; Pink, D.; Beveridge, T.

1999-01-01

Atomic force microscopy was used to measure the thickness of air-dried, collapsed murein sacculi from Escherichia coli K-12 and Pseudomonas aeruginosa PAO1. Air-dried sacculi from E. coli had a thickness of 3.0 nm, whereas those from P. aeruginosa were 1.5 nm thick. When rehydrated, the sacculi of both bacteria swelled to double their anhydrous thickness. Computer simulation of a section of a model single-layer peptidoglycan network in an aqueous solution with a Debye shielding length of 0.3 nm gave a mass distribution full width at half height of 2.4 nm, in essential agreement with these results. When E. coli sacculi were suspended over a narrow groove that had been etched into a silicon surface and the tip of the atomic force microscope used to depress and stretch the peptidoglycan, an elastic modulus of 2.5 × 107 N/m2 was determined for hydrated sacculi; they were perfectly elastic, springing back to their original position when the tip was removed. Dried sacculi were more rigid with a modulus of 3 × 108 to 4 × 108 N/m2 and at times could be broken by the atomic force microscope tip. Sacculi aligned over the groove with their long axis at right angles to the channel axis were more deformable than those with their long axis parallel to the groove axis, as would be expected if the peptidoglycan strands in the sacculus were oriented at right angles to the long cell axis of this gram-negative rod. Polar caps were not found to be more rigid structures but collapsed to the same thickness as the cylindrical portions of the sacculi. The elasticity of intact E. coli sacculi is such that, if the peptidoglycan strands are aligned in unison, the interstrand spacing should increase by 12% with every 1 atm increase in (turgor) pressure. Assuming an unstressed hydrated interstrand spacing of 1.3 nm (R. E. Burge, A. G. Fowler, and D. A. Reaveley, J. Mol. Biol. 117:927–953, 1977) and an internal turgor pressure of 3 to 5 atm (or 304 to 507 kPa) (A. L. Koch, Adv. Microbial

Indentation-derived elastic modulus of multilayer thin films: Effect of unloading induced plasticity

DOE PAGES

Jamison, Ryan Dale; Shen, Yu -Lin

2015-08-13

Nanoindentation is useful for evaluating the mechanical properties, such as elastic modulus, of multilayer thin film materials. A fundamental assumption in the derivation of the elastic modulus from nanoindentation is that the unloading process is purely elastic. In this work, the validity of elastic assumption as it applies to multilayer thin films is studied using the finite element method. The elastic modulus and hardness from the model system are compared to experimental results to show validity of the model. Plastic strain is shown to increase in the multilayer system during the unloading process. Additionally, the indentation-derived modulus of a monolayermore » material shows no dependence on unloading plasticity while the modulus of the multilayer system is dependent on unloading-induced plasticity. Lastly, the cyclic behavior of the multilayer thin film is studied in relation to the influence of unloading-induced plasticity. Furthermore, it is found that several cycles are required to minimize unloading-induced plasticity.« less

Elastic thickness estimates at northeast passive margin of North America and its implications

NASA Astrophysics Data System (ADS)

Kumar, R. T. Ratheesh; Maji, Tanmay K.; Kandpal, Suresh Ch; Sengupta, D.; Nair, Rajesh R.

2011-06-01

Global estimates of the elastic thickness (Te) of the structure of passive continental margins show wide and varying results owing to the use of different methodologies. Earlier estimates of the elastic thickness of the North Atlantic passive continental margins that used flexural modelling yielded a Te value of ~20-100 km. Here, we compare these estimates with the Te value obtained using orthonormalized Hermite multitaper recovered isostatic coherence functions. We discuss how Te is correlated with heat flow distribution and depth of necking. The E-W segment in the southern study region comprising Nova Scotia and the Southern Grand Banks show low Te values, while the zones comprising the NE-SW zones, viz., Western Greenland, Labrador, Orphan Basin and the Northern Grand Bank show comparatively high Te values. As expected, Te broadly reflects the depth of the 200-400°C isotherm below the weak surface sediment layer at the time of loading, and at the margins most of the loading occurred during rifting. We infer that these low Te measurements indicate Te frozen into the lithosphere. This could be due to the passive nature of the margin when the loads were emplaced during the continental break-up process at high temperature gradients.

Viscous Effects in the Elastodynamics of Thick Beams

NASA Technical Reports Server (NTRS)

Johnson, A. R.; Tessler, A.

1997-01-01

A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first- order ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. A quasi-static relaxation problem is employed as a validation test for the elastodynamic algorithm. The elastodynamic code is demonstrated by analyzing the damped vibrations of the beam which is deformed and then released to freely vibrate.

Simultaneous determination of the residual stress, elastic modulus, density and thickness of ultrathin film utilizing vibrating doubly clamped micro-/nanobeams

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

Stachiv, Ivo, E-mail: stachiv@fzu.cz; Institute of Physics, Czech Academy of Sciences, Prague; Kuo, Chih-Yun

2016-04-15

Measurement of ultrathin film thickness and its basic properties can be highly challenging and time consuming due to necessity of using several very sophisticated devices. Here, we report an easy accessible resonant based method capable to simultaneously determinate the residual stress, elastic modulus, density and thickness of ultrathin film coated on doubly clamped micro-/nanobeam. We show that a general dependency of the resonant frequencies on the axial load is also valid for in-plane vibrations, and the one depends only on the considered vibrational mode. As a result, we found that the film elastic modulus, density and thickness can be evaluatedmore » from two measured in-plane and out-plane fundamental resonant frequencies of micro-/nanobeam with and without film under different prestress forces. Whereas, the residual stress can be determined from two out-plane (in-plane) measured consecutive resonant frequencies of beam with film under different prestress forces without necessity of knowing film and substrate properties and dimensions. Moreover, we also reveal that the common uncertainties in force (and thickness) determination have a negligible (and minor) impact on the determined film properties. The application potential of the present method is illustrated on the beam made of silicon and SiO{sub 2} with deposited 20 nm thick AlN and 40 nm thick Au thin films, respectively.« less

A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers.

PubMed

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

PubMed Central

Zamani Nejad, Mohammad; Jabbari, Mehdi; Ghannad, Mehdi

2014-01-01

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found. PMID:24719582

Effect of windowing on lithosphere elastic thickness estimates obtained via the coherence method: Results from northern South America

NASA Astrophysics Data System (ADS)

Ojeda, GermáN. Y.; Whitman, Dean

2002-11-01

The effective elastic thickness (Te) of the lithosphere is a parameter that describes the flexural strength of a plate. A method routinely used to quantify this parameter is to calculate the coherence between the two-dimensional gravity and topography spectra. Prior to spectra calculation, data grids must be "windowed" in order to avoid edge effects. We investigated the sensitivity of Te estimates obtained via the coherence method to mirroring, Hanning and multitaper windowing techniques on synthetic data as well as on data from northern South America. These analyses suggest that the choice of windowing technique plays an important role in Te estimates and may result in discrepancies of several kilometers depending on the selected windowing method. Te results from mirrored grids tend to be greater than those from Hanning smoothed or multitapered grids. Results obtained from mirrored grids are likely to be over-estimates. This effect may be due to artificial long wavelengths introduced into the data at the time of mirroring. Coherence estimates obtained from three subareas in northern South America indicate that the average effective elastic thickness is in the range of 29-30 km, according to Hanning and multitaper windowed data. Lateral variations across the study area could not be unequivocally determined from this study. We suggest that the resolution of the coherence method does not permit evaluation of small (i.e., ˜5 km), local Te variations. However, the efficiency and robustness of the coherence method in rendering continent-scale estimates of elastic thickness has been confirmed.

Xiphoid Process-Derived Chondrocytes: A Novel Cell Source for Elastic Cartilage Regeneration

PubMed Central

Nam, Seungwoo; Cho, Wheemoon; Cho, Hyunji; Lee, Jungsun

2014-01-01

Reconstruction of elastic cartilage requires a source of chondrocytes that display a reliable differentiation tendency. Predetermined tissue progenitor cells are ideal candidates for meeting this need; however, it is difficult to obtain donor elastic cartilage tissue because most elastic cartilage serves important functions or forms external structures, making these tissues indispensable. We found vestigial cartilage tissue in xiphoid processes and characterized it as hyaline cartilage in the proximal region and elastic cartilage in the distal region. Xiphoid process-derived chondrocytes (XCs) showed superb in vitro expansion ability based on colony-forming unit fibroblast assays, cell yield, and cumulative cell growth. On induction of differentiation into mesenchymal lineages, XCs showed a strong tendency toward chondrogenic differentiation. An examination of the tissue-specific regeneration capacity of XCs in a subcutaneous-transplantation model and autologous chondrocyte implantation model confirmed reliable regeneration of elastic cartilage regardless of the implantation environment. On the basis of these observations, we conclude that xiphoid process cartilage, the only elastic cartilage tissue source that can be obtained without destroying external shape or function, is a source of elastic chondrocytes that show superb in vitro expansion and reliable differentiation capacity. These findings indicate that XCs could be a valuable cell source for reconstruction of elastic cartilage. PMID:25205841

Effective Elastic Thickness of the Lithosphere in Continental China from Heat Flow: Implications for the Lithospheric Rheology

NASA Astrophysics Data System (ADS)

Liu, S.; Wang, L.

2006-12-01

The effective elastic thickness (Te) of lithosphere is one parameter describing the responses of the lithosphere to long term forces, and is still controversial in estimation by different methods. Here we present the effective elastic thickness of the lithosphere in continental China from heat flow data by the method proposed by Burov et al, J.G.R., 1995,100(B3):3905-3927. Our results show that Te varies much in different sub-areas in continental China due to different geological evolution and associated thermal regimes. Te is much greater than the crustal thickness in the area where the heat flow is really low and the lithosphere is really thick, indicating much more contribution from the lithospheric mantle and the dominative control of the mantle with olivine on the rheology of the lithosphere, and the major basins (Tarim, Junggar, Ordos and Sichuan basins) in central-western China share this characteristic. For instance, the Te of the Tarim basin is 66km with crustal thickness of 45km. Te is less than the crustal thickness in the region where the heat flow is relatively high, and approximates to the crustal brittle-ductile transition depth, suggesting more contribution from the crust and the dominative control of the felsic crust on the rheology of the lithosphere, and this phenomenon is obvious in the SE coastal China, eastern North China and the orogenic belts. Compared the estimated Te with the seismogenic layer thickness (Ts) available in China, it is also found that the Te is much greater than Ts in the major basins with low heat flow, and is similar to Ts in the active zones with high heat flow, which is inconsistent with that Te is usually smaller than Ts proposed by Maggi et al., Geology,2000,28(6):495-498. Generally, two end elements rheological modes for continental lithosphere of the strong crust-weak mantle and the weak crust-strong mantle are all available in continental China considering different thermal regime, composition and geological

AFM Investigation of Liquid-Filled Polymer Microcapsules Elasticity.

PubMed

Sarrazin, Baptiste; Tsapis, Nicolas; Mousnier, Ludivine; Taulier, Nicolas; Urbach, Wladimir; Guenoun, Patrick

2016-05-10

Elasticity of polymer microcapsules (MCs) filled with a liquid fluorinated core is studied by atomic force microscopy (AFM). Accurately characterized spherical tips are employed to obtain the Young's moduli of MCs having four different shell thicknesses. We show that those moduli are effective ones because the samples are composites. The strong decrease of the effective MC elasticity (from 3.0 to 0.1 GPa) as the shell thickness decreases (from 200 to 10 nm) is analyzed using a novel numerical approach. This model describes the evolution of the elasticity of a coated half-space according to the contact radius, the thickness of the film, and the elastic moduli of bulk materials. This numerical model is consistent with the experimental data and allows simulating the elastic behavior of MCs at high frequencies (5 MHz). While the quasi-static elasticity of the MCs is found to be very dependent on the shell thickness, the high frequency (5 MHz) elastic behavior of the core leads to a stable behavior of the MCs (from 2.5 to 3 GPa according to the shell thickness). Finally, the effect of thermal annealing on the MCs elasticity is investigated. The Young's modulus is found to decrease because of the reduction of the shell thickness due to the loss of the polymer.

The elasticity problem for a thick-walled cylinder containing a circumferential crack

NASA Technical Reports Server (NTRS)

Nied, H. F.; Erdogan, F.

1983-01-01

The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.

The elasticity problem for a thick-walled cylinder containing a circumferential crack

NASA Technical Reports Server (NTRS)

Nied, H. F.; Erdogan, F.

1982-01-01

The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.

Elastic Thickness Estimates for Coronae Associated with Chasmata on Venus

NASA Technical Reports Server (NTRS)

Hoogenboom, T.; Martin, P.; Housean, G. A.

2005-01-01

Coronae are large-scale circular tectonic features surrounded by annular ridges. They are generally considered unique to Venus and may offer insights into the differences in lithospheric structure or mantle convective pattern between Venus and Earth. 68% of all coronae are associated with chasmata or fracture belts. The remaining 32% are located at volcanic rises or in the plains. Chasmata are linear to arcuate troughs, with trough parallel fractures and faults which extend for 1000 s of kilometers. Estimates of the elastic thickness of the lithosphere (T(sub e)) have been calculated in a number of gravity/topography studies of Venus and for coronae specifically. None of these studies, however, have explored the dependence of T(sub e) on the tectonic history of the region, as implied from the interpretation of relative timing relationships between coronae and surrounding features. We examine the relationship between the local T(sub e) and the relative ages of coronae and chasmata with the aim of further constraining the origin and evolution of coronae and chasmata systems.

Impact of Hydration Media on Ex Vivo Corneal Elasticity Measurements

PubMed Central

Dias, Janice; Ziebarth, Noël M.

2014-01-01

Objectives To determine the effect of hydration media on ex vivo corneal elasticity. Methods Experiments were conducted on forty porcine eyes retrieved from an abattoir (10 eyes each for PBS, BSS, Optisol, 15% Dextran). The epithelium was removed and the cornea was excised with an intact scleral rim and placed in 20% Dextran overnight to restore its physiological thickness. For each hydration media, corneas were evenly divided into two groups: one with an intact scleral rim and the other without. Corneas were mounted onto a custom chamber and immersed in a hydration medium for elasticity testing. While in each medium, corneal elasticity measurements were performed for 2 hours: at 5-minute intervals for the first 30 minutes and then 15-minute intervals for the remaining 90 minutes. Elasticity testing was performed using nanoindentation with spherical indenters and Young’s modulus was calculated using the Hertz model. Thickness measurements were taken before and after elasticity testing. Results The percentage change in corneal thickness and elasticity was calculated for each hydration media group. BSS, PBS, and Optisol showed an increase in thickness and Young’s moduli for corneas with and without an intact scleral rim. 15% Dextran exhibited a dehydrating effect on corneal thickness and provided stable maintenance of corneal elasticity for both groups. Conclusions Hydration media affects the stability of corneal thickness and elasticity measurements over time. 15% Dextran was most effective in maintaining corneal hydration and elasticity, followed by Optisol. PMID:25603443

Marangoni and Gibbs elasticity of flowing soap films

NASA Astrophysics Data System (ADS)

Kim, Ildoo; Sane, Aakash; Mandre, Shreyas

2017-11-01

A flowing soap film has two elasticities. Marangoni elasticity dynamically stabilizes the film from sudden disturbance, and Gibbs elasticity is an equilibrium property that influences the film's persistence over time. In our experimental investigation, we find that Marangoni elasticity is 22 mN/m independent of the film thickness. On the other hand, Gibbs elasticity depends both on the film thickness and the soap concentration. Interestingly, the soap film made of dilute soap solution has the greater Gibbs elasticity, which is not consistent to the existing theory. Such discrepancy is originated from the flowing nature of our soap films, in which surfactants are continuously replenished.

Elastic band prediction equations for combined free-weight and elastic band bench presses and squats.

PubMed

Shoepe, Todd C; Ramirez, David A; Almstedt, Hawley C

2010-01-01

Elastic bands added to traditional free-weight techniques have become a part of suggested training routines in recent years. Because of the variable loading patterns of elastic bands (i.e., greater stretch produces greater resistance), it is necessary to quantify the exact loading patterns of bands to identify the volume and intensity of training. The purpose of this study was to determine the length vs. tension properties of multiple sizes of a set of commonly used elastic bands to quantify the resistance that would be applied to free-weight plus elastic bench presses (BP) and squats (SQ). Five elastic bands of varying thickness were affixed to an overhead support beam. Dumbbells of varying weights were progressively added to the free end while the linear deformation was recorded with each subsequent weight increment. The resistance was plotted as a factor of linear deformation, and best-fit nonlinear logarithmic regression equations were then matched to the data. For both the BP and SQ loading conditions and all band thicknesses tested, R values were greater than 0.9623. These data suggest that differences in load exist as a result of the thickness of the elastic band, attachment technique, and type of exercise being performed. Facilities should adopt their own form of loading quantification to match their unique set of circumstances when acquiring, researching, and implementing elastic band and free-weight exercises into the training programs.

Influence of soft ferromagnetic substrate on magneto-elastic behavior in a superconducting coated conductor strip

NASA Astrophysics Data System (ADS)

He, An; Xue, Cun; Yong, Huadong; Zhou, Youhe

2013-11-01

Ferromagnetic materials will affect not only the electromagnetic response but also the mechanical behaviors of coated conductors. The influence of soft ferromagnetic substrate on magneto-elastic behavior in a superconductor/ferromagnetic (SC/FM) bilayer exposed to a transverse magnetic field is investigated theoretically. The ferromagnetic substrate is regarded as ideal soft magnets with high permeability and small magnetic hysteresis. Due to the composite structure of SC/FM hybrids, magneto-elastic behavior will be subjected to combined effect of equivalent force and flexural moment. Analytical expressions for internal stress and strain components are derived by virtue of a two-dimensional elasticity analysis. It is worth pointing out that the y component of strain has much larger positive value during field ascent, which may result in the delamitation at the interface. Irreversible magnetostrictive behaviors are observed both along x direction and along y direction. For the thickness dependence of magnetostriction, the flexural moment dominates when the SC thickness is small while the equivalent force plays a critical role at higher SC thickness.

On the Opening of Thick Walled Elastic Tubes: A Fluid-Structure Model for Acid Reflux

NASA Astrophysics Data System (ADS)

Ghosh, Sudip; Kahrilas, Peter

2005-11-01

A coupled fluid-structure mathematical model was developed to quantify rapid opening of thick-walled elastic tubes, a phenomenon underlying biological flows such as gastroesophageal reflux disease (GERD). The wall was modeled using non-linear finite deformation theory to predict space-time radial distention of an axisymmetric tube with luminal fluid flow. Anisotropic azimuthal and longitudinal muscle-induced stresses were incorporated, and interstitial material properties were assumed isotropic and linearly elastic. Fluid flow was modeled using lubrication theory with inertial correction. Opening and flow were driven by a specified inflow pressure and zero pressure gradient was specified at outflow. No-slip and surface force balance were applied at the fluid-wall interface. Viscoelasticity was modeled with ad hoc damping and the evolution of the tube geometry was predicted at mid-layer. A potentially important discovery was made when applied to studies of initiation of opening with GERD: while material stiffness is of minor consequence, small changes in resting lumen distension (˜2 mm diameter) may be a sensitive distinguishing feature of the disease.

Marangoni elasticity of flowing soap films

NASA Astrophysics Data System (ADS)

Kim, Ildoo; Mandre, Shreyas

2017-08-01

We measure the Marangoni elasticity of a flowing soap film to be 22 mN/m irrespective of its width, thickness, flow speed, or the bulk soap concentration. We perform this measurement by generating an oblique shock in the soap film and measuring the shock angle, flow speed, and thickness. We postulate that the elasticity is constant because the film surface is crowded with soap molecules. Our method allows nondestructive measurement of flowing soap film elasticity and the value 22 mN/m is likely applicable to other similarly constructed flowing soap films.

Comprehensive analysis of Curie-point depths and lithospheric effective elastic thickness at Arctic Region

NASA Astrophysics Data System (ADS)

Lu, Y.; Li, C. F.

2017-12-01

Arctic Ocean remains at the forefront of geological exploration. Here we investigate its deep geological structures and geodynamics on the basis of gravity, magnetic and bathymetric data. We estimate Curie-point depth and lithospheric effective elastic thickness to understand deep geothermal structures and Arctic lithospheric evolution. A fractal exponent of 3.0 for the 3D magnetization model is used in the Curie-point depth inversion. The result shows that Curie-point depths are between 5 and 50 km. Curie depths are mostly small near the active mid-ocean ridges, corresponding well to high heat flow and active shallow volcanism. Large curie depths are distributed mainly at continental marginal seas around the Arctic Ocean. We present a map of effective elastic thickness (Te) of the lithosphere using a multitaper coherence technique, and Te are between 5 and 110 km. Te primarily depends on geothermal gradient and composition, as well as structures in the lithosphere. We find that Te and Curie-point depths are often correlated. Large Te are distributed mainly at continental region and small Te are distributed at oceanic region. The Alpha-Mendeleyev Ridge (AMR) and The Svalbard Archipelago (SA) are symmetrical with the mid-ocean ridge. AMR and SA were formed before an early stage of Eurasian basin spreading, and they are considered as conjugate large igneous provinces, which show small Te and Curie-point depths. Novaya Zemlya region has large Curie-point depths and small Te. We consider that fault and fracture near the Novaya Zemlya orogenic belt cause small Te. A series of transform faults connect Arctic mid-ocean ridge with North Atlantic mid-ocean ridge. We can see large Te near transform faults, but small Curie-point depths. We consider that although temperature near transform faults is high, but mechanically the lithosphere near transform faults are strengthened.

Strength and Elastic thickness of the lithosphere and implication on ductile crustal flow in Europe

NASA Astrophysics Data System (ADS)

Tesauro, M.; Kaban, M. K.; Cloetingh, S. A. P. L.

2012-04-01

The strength and effective elastic thickness (Te) of the lithosphere control its response to tectonic and surface processes. We present the first global strength and effective elastic thickness maps, which are determined using physical properties from recent crustal and lithospheric models. We estimated the lithospheric temperature from inversion of a tomography model and we extrapolated the results to the surface using crustal isotherms for different tectonic provinces based on characteristic values of radiogenic heat production. We assumed different rheologies of the upper and lower crust for continental areas, on the base of the geological features distribution. The results obtained allow us to compare for the first time the lithospheric characteristics of the different tectonic areas. The Te estimated from the strength is compared with the Te obtained by flexural loading and spectral studies. Lithospheric strength is primarily controlled by the crust in young (Phanerozoic) geological provinces characterized by low Te (~25 km), high topography (>1000 m) and active seismicity. In contrast, the old (Achaean and Proterozoic) cratons of the continental plates show strength primarily in the lithospheric mantle, high Te (over 100 km), low topography (<1000 m) and very low seismicity. Using high resolution crustal thickness and density data provided by the EuCRUST-07 model we compute for the European continent the associated lateral pressure gradients (LPG), which can drive horizontal ductile flow in the crust. Incorporation of these data in channel flow models allows us to use potential gravity theory to assess horizontal mass transfer and stress transmission within the European crust. We explore implications of the channel flow concept for a possible range of crustal strength, using end-member 'hard' and 'soft' crustal rheologies to estimate strain rates at the bottom of the ductile crustal layers. The models show that the effects of channel flow superimposed on the

Global model for the lithospheric strength and effective elastic thickness

NASA Astrophysics Data System (ADS)

Tesauro, Magdala; Kaban, Mikhail K.; Cloetingh, Sierd A. P. L.

2013-08-01

Global distribution of the strength and effective elastic thickness (Te) of the lithosphere are estimated using physical parameters from recent crustal and lithospheric models. For the Te estimation we apply a new approach, which provides a possibility to take into account variations of Young modulus (E) within the lithosphere. In view of the large uncertainties affecting strength estimates, we evaluate global strength and Te distributions for possible end-member 'hard' (HRM) and a 'soft' (SRM) rheology models of the continental crust. Temperature within the lithosphere has been estimated using a recent tomography model of Ritsema et al. (2011), which has much higher horizontal resolution than previous global models. Most of the strength is localized in the crust for the HRM and in the mantle for the SRM. These results contribute to the long debates on applicability of the "crème brulée" or "jelly-sandwich" model for the lithosphere structure. Changing from the SRM to HRM turns most of the continental areas from the totally decoupled mode to the fully coupled mode of the lithospheric layers. However, in the areas characterized by a high thermal regime and thick crust, the layers remain decoupled even for the HRM. At the same time, for the inner part of the cratons the lithospheric layers are coupled in both models. Therefore, rheological variations lead to large changes in the integrated strength and Te distribution in the regions characterized by intermediate thermal conditions. In these areas temperature uncertainties have a greater effect, since this parameter principally determines rheological behavior. Comparison of the Te estimates for both models with those determined from the flexural loading and spectral analysis shows that the 'hard' rheology is likely applicable for cratonic areas, whereas the 'soft' rheology is more representative for young orogens.

Temperature and porosity effects on wave propagation in nanobeams using bi-Helmholtz nonlocal strain-gradient elasticity

NASA Astrophysics Data System (ADS)

Reza Barati, Mohammad

2018-05-01

In this paper, applying a general nonlocal strain-gradient elasticity model with two nonlocal and one strain-gradient parameters, wave dispersion behavior of thermally affected and elastically bonded nanobeams is investigated. The two nanobeams are considered to have material imperfections or porosities evenly dispersed across the thickness. Each nanobeam has uniform thickness and is modeled by refined shear deformation beam theory with sinusoidal transverse shear strains. The governing equations of the system are derived by Hamilton's rule and are analytically solved to obtain wave frequencies and the velocity of wave propagation. In the presented graphs, one can see that porosities, temperature, nonlocal, strain gradient and bonding springs have great influences on the wave characteristics of the system.

Film thickness for different regimes of fluid-film lubrication

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1980-01-01

Film thickness equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic lubrication of low-elastic-modulus materials (soft EHL), or isoviscous-elastic; and elastohydrodynamic lubrication of high-elastic-modulus materials (hard EHL), or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The results are presented as a map of the lubrication regimes, with film thickness contours on a log-log grid of the viscosity and elasticity for three values of the ellipticity parameter.

The Short-Term Effect of Ketogenic Diet on Carotid Intima-Media Thickness and Elastic Properties of the Carotid Artery and the Aorta in Epileptic Children.

PubMed

Doksöz, Önder; Güzel, Orkide; Yılmaz, Ünsal; İşgüder, Rana; Çeleğen, Kübra; Meşe, Timur; Uysal, Utku

2015-10-01

The aim of this prospective study is to investigate the effect of a 6-month-long ketogenic diet on carotid intima-media thickness, carotid artery, and aortic vascular functions. Thirty-eight drug-resistant epileptic patients who were being treated with ketogenic diet were enrolled. Fasting total cholesterol, high-density lipoprotein, low-density lipoprotein, triglycerides, total cholesterol, and glucose concentrations were measured and echocardiography was performed in all patients before the beginning of ketogenic diet and at the sixth month of treatment. The body weight, height, body mass index, serum levels of triglyceride, total cholesterol, and low-density lipoprotein increased significantly at month 6 when compared to baseline values (P < .05). Carotid intima-media thickness, elastic properties of the aorta, and carotid artery did not change at the sixth month of therapy compared to baseline values. A 6-month-long ketogenic diet has no effect on carotid intima-media thickness and elastic properties of the carotid artery and the aorta. © The Author(s) 2015.

Variations in lithospheric thickness on Venus

NASA Technical Reports Server (NTRS)

Johnson, C. L.; Sandwell, David T.

1992-01-01

Recent analyses of Magellan data have indicated many regions exhibiting topograhic flexure. On Venus, flexure is associated predominantly with coronae and the chasmata with Aphrodite Terra. Modeling of these flexural signatures allows the elastic and mechanical thickness of the lithosphere to be estimated. In areas where the lithosphere is flexed beyond its elastic limit the saturation moment provides information on the strength of the lithosphere. Modeling of 12 flexural features on Venus has indicated lithospheric thicknesses comparable with terrestrial values. This has important implications for the venusian heat budget. Flexure of a thin elastic plate due simultaneously to a line load on a continuous plate and a bending moment applied to the end of a broken plate is considered. The mean radius and regional topographic gradient are also included in the model. Features with a large radius of curvature were selected so that a two-dimensional approximation could be used. Comparisons with an axisymmetric model were made for some features to check the validity of the two-dimensional assumption. The best-fit elastic thickness was found for each profile crossing a given flexural feature. In addition, the surface stress and bending moment at the first zero crossing of each profile were also calculated. Flexural amplitudes and elastic thicknesses obtained for 12 features vary significantly. Three examples of the model fitting procedures are discussed.

Stress intensity factors in a reinforced thick-walled cylinder

NASA Technical Reports Server (NTRS)

Tang, R.; Erdogan, F.

1984-01-01

An elastic thick-walled cylinder containing a radial crack is considered. It is assumed that the cylinder is reinforced by an elastic membrane on its inner surface. The model is intended to simulate pressure vessels with cladding. The formulation of the problem is reduced to a singular integral equation. Various special cases including that of a crack terminating at the cylinder-reinforcement interface are investigated and numerical examples are given. Results indicate that in the case of the crack touching the interface the crack surface displacement derivative is finite and consequently the stress state around the corresponding crack tip is bounded; and generally, for realistic values of the stiffness parameter, the effect of the reinforcement is not very significant.

The influence of time dependent flight and maneuver velocities and elastic or viscoelastic flexibilities on aerodynamic and stability derivatives

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

Cochrane, Alexander P.; Merrett, Craig G.; Hilton, Harry H.

2014-12-10

The advent of new structural concepts employing composites in primary load carrying aerospace structures in UAVs, MAVs, Boeing 787s, Airbus A380s, etc., necessitates the inclusion of flexibility as well as viscoelasticity in static structural and aero-viscoelastic analyses. Differences and similarities between aeroelasticity and aero-viscoelasticity have been investigated in [2]. An investigation is undertaken as to the dependence and sensitivity of aerodynamic and stability derivatives to elastic and viscoelastic structural flexibility and as to time dependent flight and maneuver velocities. Longitudinal, lateral and directional stabilities are investigated. It has been a well established fact that elastic lifting surfaces are subject tomore » loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings one of the critical static parameters is the velocity at which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. The influence of the twin effects of viscoelastic and elastic materials and of variable flight velocities on longitudinal, lateral, directional and spin stabilities are also investigated. It has been a well established fact that elastic lifting surfaces are subject to loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are here extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings the critical parameter is the velocity

Investigations of thickness-shear mode elastic constant and damping of shunted piezoelectric materials with a coupling resonator

NASA Astrophysics Data System (ADS)

Hu, Ji-Ying; Li, Zhao-Hui; Sun, Yang; Li, Qi-Hu

2016-12-01

Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode (TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro-mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro-mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element (FE) analyses. Finally, a prototype of the coupling electro-mechanical resonator is fabricated with two shear-mode PZT5A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5A. Project supported by the National Defense Foundation of China (Grant No. 9149A12050414JW02180).

Coal Thickness Gauging Using Elastic Waves

NASA Technical Reports Server (NTRS)

Nazarian, Soheil; Bar-Cohen, Yoseph

1999-01-01

The efforts of a mining crew can be optimized, if the thickness of the coal layers to be excavated is known before excavation. Wave propagation techniques can be used to estimate the thickness of the layer based on the contrast in the wave velocity between coal and rock beyond it. Another advantage of repeated wave measurement is that the state of the stress within the mine can be estimated. The state of the stress can be used in many safety-related decisions made during the operation of the mine. Given these two advantages, a study was carried out to determine the feasibility of the methodology. The results are presented herein.

A Review on Atherosclerotic Biology, Wall Stiffness, Physics of Elasticity, and Its Ultrasound-Based Measurement.

PubMed

Patel, Anoop K; Suri, Harman S; Singh, Jaskaran; Kumar, Dinesh; Shafique, Shoaib; Nicolaides, Andrew; Jain, Sanjay K; Saba, Luca; Gupta, Ajay; Laird, John R; Giannopoulos, Argiris; Suri, Jasjit S

2016-12-01

Functional and structural changes in the common carotid artery are biomarkers for cardiovascular risk. Current methods for measuring functional changes include pulse wave velocity, compliance, distensibility, strain, stress, stiffness, and elasticity derived from arterial waveforms. The review is focused on the ultrasound-based carotid artery elasticity and stiffness measurements covering the physics of elasticity and linking it to biological evolution of arterial stiffness. The paper also presents evolution of plaque with a focus on the pathophysiologic cascade leading to arterial hardening. Using the concept of strain, and image-based elasticity, the paper then reviews the lumen diameter and carotid intima-media thickness measurements in combined temporal and spatial domains. Finally, the review presents the factors which influence the understanding of atherosclerotic disease formation and cardiovascular risk including arterial stiffness, tissue morphological characteristics, and image-based elasticity measurement.

Brief report: reconstruction of joint hyaline cartilage by autologous progenitor cells derived from ear elastic cartilage.

PubMed

Mizuno, Mitsuru; Kobayashi, Shinji; Takebe, Takanori; Kan, Hiroomi; Yabuki, Yuichiro; Matsuzaki, Takahisa; Yoshikawa, Hiroshi Y; Nakabayashi, Seiichiro; Ik, Lee Jeong; Maegawa, Jiro; Taniguchi, Hideki

2014-03-01

In healthy joints, hyaline cartilage covering the joint surfaces of bones provides cushioning due to its unique mechanical properties. However, because of its limited regenerative capacity, age- and sports-related injuries to this tissue may lead to degenerative arthropathies, prompting researchers to investigate a variety of cell sources. We recently succeeded in isolating human cartilage progenitor cells from ear elastic cartilage. Human cartilage progenitor cells have high chondrogenic and proliferative potential to form elastic cartilage with long-term tissue maintenance. However, it is unknown whether ear-derived cartilage progenitor cells can be used to reconstruct hyaline cartilage, which has different mechanical and histological properties from elastic cartilage. In our efforts to develop foundational technologies for joint hyaline cartilage repair and reconstruction, we conducted this study to obtain an answer to this question. We created an experimental canine model of knee joint cartilage damage, transplanted ear-derived autologous cartilage progenitor cells. The reconstructed cartilage was rich in proteoglycans and showed unique histological characteristics similar to joint hyaline cartilage. In addition, mechanical properties of the reconstructed tissues were higher than those of ear cartilage and equal to those of joint hyaline cartilage. This study suggested that joint hyaline cartilage was reconstructed from ear-derived cartilage progenitor cells. It also demonstrated that ear-derived cartilage progenitor cells, which can be harvested by a minimally invasive method, would be useful for reconstructing joint hyaline cartilage in patients with degenerative arthropathies. © AlphaMed Press.

Uninduced adipose-derived stem cells repair the defect of full-thickness hyaline cartilage.

PubMed

Zhang, Hai-Ning; Li, Lei; Leng, Ping; Wang, Ying-Zhen; Lv, Cheng-Yu

2009-04-01

To testify the effect of the stem cells derived from the widely distributed fat tissue on repairing full-thickness hyaline cartilage defects. Adipose-derived stem cells (ADSCs) were derived from adipose tissue and cultured in vitro. Twenty-seven New Zealand white rabbits were divided into three groups randomly. The cultured ADSCs mixed with calcium alginate gel were used to fill the full-thickness hyaline cartilage defects created at the patellafemoral joint, and the defects repaired with gel or without treatment served as control groups. After 4, 8 and 12 weeks, the reconstructed tissue was evaluated macroscopically and microscopically. Histological analysis and qualitative scoring were also performed to detect the outcome. Full thickness hyaline cartilage defects were repaired completely with ADSCs-derived tissue. The result was better in ADSCs group than the control ones. The microstructure of reconstructed tissue with ADSCs was similar to that of hyaline cartilage and contained more cells and regular matrix fibers, being better than other groups. Plenty of collagen fibers around cells could be seen under transmission electron microscopy. Statistical analysis revealed a significant difference in comparison with other groups at each time point (t equal to 4.360, P less than 0.01). These results indicate that stem cells derived from mature adipose without induction possess the ability to repair cartilage defects.

On the anisotropic elastic properties of hydroxyapatite.

NASA Technical Reports Server (NTRS)

Katz, J. L.; Ukraincik, K.

1971-01-01

Experimental measurements of the isotropic elastic moduli on polycrystalline specimens of hydroxyapatite and fluorapatite are compared with elastic constants measured directly from single crystals of fluorapatite in order to derive a set of pseudo single crystal elastic constants for hydroxyapatite. The stiffness coefficients thus derived are given. The anisotropic and isotropic elastic properties are then computed and compared with similar properties derived from experimental observations of the anisotropic behavior of bone.

Application of nonlocal models to nano beams. Part II: Thickness length scale effect.

PubMed

Kim, Jun-Sik

2014-10-01

Applicability of nonlocal models to nano-beams is discussed in terms of the Eringen's nonlocal Euler-Bernoulli (EB) beam model. In literature, most work has taken the axial coordinate derivative in the Laplacian operator presented in nonlocal elasticity. This causes that the non-locality always makes the beam soften as compared to the local counterpart. In this paper, the thickness scale effect is solely considered to investigate if the nonlocal model can simulate stiffening effect. Taking the thickness derivative in the Laplacian operator leads to the presence of a surface stress state. The governing equation derived is compared to that of the EB model with the surface stress. The results obtained reveal that the nonlocality tends to decrease the bending moment stiffness whereas to increase the bending rigidity in the governing equation. This tendency also depends on the surface conditions.

Translation by anisotropic peeling or fracturing in elastic media

NASA Astrophysics Data System (ADS)

Zheng, Zhong; Lister, John; Neufeld, Jerome

2017-11-01

The influence of rock anisotropy on the direction of hydraulic fracturing is an important open question. Two canonical systems have been proposed to investigate the fundamental aspects of such fluid-structure interaction problems: (i) Fluid injection and fracturing into an infinite elastic matrix (e.g., solid gelatin) and (ii) Fluid invasion and peeling beneath a deforming elastic sheet (e.g., bending plate). We investigate the second system and impose a non-uniform prewetting film thickness beneath the elastic sheet. We notice that while the bulk of the elastic sheet retains the static blister shape, a non-uniform prewetting film thickness can cause a horizontal translation of the blister. In particular, for a step jump in prewetting film thickness, asymptotic analysis indicates that, under constant fluid injection, the horizontal translation follows a t 7 / 17 time dependence in cartesian coordinates, and the prefactor of power-law translation depends on the ratio of the distinct prewetting film thicknesses on either side. We also provide numerical and experimental evidence demonstrating anisotropic blister evolution. This can be thought of as a model system for fluid-driven fracturing where the non-uniform prewetting film thickness mimics heterogeneity in material toughness.

An ultrasonic method for determination of elastic moduli, density, attenuation and thickness of a polymer coating on a stiff plate.

PubMed

Lavrentyev, A I; Rokhlin, S I

2001-04-01

An ultrasonic method proposed by us for determination of the complete set of acoustical and geometrical properties of a thin isotropic layer between semispaces (J. Acoust. Soc. Am. 102 (1997) 3467) is extended to determination of the properties of a coating on a thin plate. The method allows simultaneous determination of the coating thickness, density, elastic moduli and attenuation (longitudinal and shear) from normal and oblique incidence reflection (transmission) frequency spectra. Reflection (transmission) from the coated plate is represented as a function of six nondimensional parameters of the coating which are determined from two experimentally measured spectra: one at normal and one at oblique incidence. The introduction of the set of nondimensional parameters allows one to transform the reconstruction process from one search in a six-dimensional space to two searches in three-dimensional spaces (one search for normal incidence and one for oblique). Thickness, density, and longitudinal and shear elastic moduli of the coating are calculated from the nondimensional parameters determined. The sensitivity of the method to individual properties and its stability against experimental noise are studied and the inversion algorithm is accordingly optimized. An example of the method and experimental measurement for comparison is given for a polypropylene coating on a steel foil.

Analysis of flexible layered shallow shells on elastic foundation

NASA Astrophysics Data System (ADS)

Stupishin, L.; Kolesnikov, A.; Tolmacheva, T.

2017-05-01

This paper contains numerical analysis of a layered geometric nonlinear flexible shallow shell based on an elastic foundation. Rise of arch in the center of the shell, width, length and type of support are given. The design variable is taken to be the thickness of the shallow shell, the form of the middle surface forming and the characteristic of elastic foundations. Critical force coefficient and stress of shells are calculated by Bubnov-Galerkin. Stress, characteristic of elastic foundations - thickness dependence are presented.

Consequences of elastic anisotropy in patterned substrate heteroepitaxy.

PubMed

Dixit, Gopal Krishna; Ranganathan, Madhav

2018-06-13

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi--infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film--substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro--Tiller--Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time--scale for this inversion as function of height is analyzed. © 2018 IOP Publishing Ltd.

Behaviour study of thick laminated composites: Experimentation and finite element analyses

NASA Astrophysics Data System (ADS)

Duchaine, Francois

In today's industries, it is common practice to utilize composite materials in very large and thick structures like bridge decks, high pressure vessels, wind turbine blades and aircraft parts to mention a few. Composite materials are highly favoured due to their physical characteristics: low weight, low cost, adaptable mechanical properties, high specific strength and stiffness. The use of composite materials for large structures has however raised several concerns in the prediction of the behaviour of thick laminated composite parts. A lack of knowledge and experience in the use of composite materials during the design, sizing and manufacturing of thick composite parts can lead to catastrophic events. In this thesis, it was supposed that the elastic material properties may vary with the laminate thickness. In order to measure the influence of the thickness on nine orthotropic elastic material properties (E1, E2, E3, nu12, nu 13, nu23, G12, G13 and G23), three categories of thickness have been defined using a comparison between the classical lamination theory (CLT), different beam theories and a numerical 3D solid finite element analysis (FEA) model. The defined categories are: thin laminates for thicknesses below 6 mm (0.236"), moderately thick laminates for thicknesses up to 16 mm (0.630") and thick laminates for thicknesses above 16 mm (0.630"). For three different thicknesses (thin -- 1.5 mm, moderately thick -- 10 mm and thick -- 20 mm), the influence of the thickness on the orthotropic elastic material properties of unidirectional (UD) fibreglass/epoxy laminates has been measured. A torsion test on rectangular bar is also proposed to measure the influence of the thickness on G13 and G23. The nine elastic material properties, in function of the thickness, have been used in CLT and 3D solid FEA model in order to predict the axial Young's modulus and Poisson's ratios of cross-ply and quasi-isotropic laminates. Experimental results have also been obtained for

Flexible Force Field Parameterization through Fitting on the Ab Initio-Derived Elastic Tensor

PubMed Central

2017-01-01

Constructing functional forms and their corresponding force field parameters for the metal–linker interface of metal–organic frameworks is challenging. We propose fitting these parameters on the elastic tensor, computed from ab initio density functional theory calculations. The advantage of this top-down approach is that it becomes evident if functional forms are missing when components of the elastic tensor are off. As a proof-of-concept, a new flexible force field for MIL-47(V) is derived. Negative thermal expansion is observed and framework flexibility has a negligible effect on adsorption and transport properties for small guest molecules. We believe that this force field parametrization approach can serve as a useful tool for developing accurate flexible force field models that capture the correct mechanical behavior of the full periodic structure. PMID:28661672

Film thickness for different regimes of fluid-film lubrication. [elliptical contacts

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1983-01-01

Mathematical formulas are presented which express the dimensionless minimum film thickness for the four lubrication regimes found in elliptical contacts: isoviscous-rigid regime; piezoviscous-rigid regime; isoviscous-elastic regime; and piezoviscous-elastic regime. The relative importance of pressure on elastic distortion and lubricant viscosity is the factor that distinguishes these regimes for a given conjunction geometry. In addition, these equations were used to develop maps of the lubrication regimes by plotting film thickness contours on a log-log grid of the dimensionless viscosity and elasticity parameters for three values of the ellipticity parameter. These results present a complete theoretical film thickness parameter solution for elliptical constants in the four lubrication regimes. The results are particularly useful in initial investigations of many practical lubrication problems involving elliptical conjunctions.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

Global Admittance Estimates of Elastic and Crustal Thickness of Venus: Results from Top, Hot Spot, and Bottom Loading Models

NASA Technical Reports Server (NTRS)

Smrekar, S. E.; Anderson, F. S.

2005-01-01

We have calculated admittance spectra using the spatio-spectral method [14] for Venus by moving the central location of the spectrum over a 1 grid, create 360x180 admittance spectra. We invert the observed admittance using top-loading (TL), hot spot (HS), and bottom loading (BL) models, resulting in elastic, crustal, and lithospheric thickness estimates (Te, Zc, and Zl) [0]. The result is a global map for interpreting subsurface structure. Estimated values of Te and Zc concur with previous TL local admittance results, but BL estimates indicate larger values than previously suspected.

Investigation and modeling of the elastic-plastic fracture behavior of continuous woven fabric-reinforced ceramic composites

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

Kahl, W.K.

1997-03-01

The paper describes a study which attempted to extrapolate meaningful elastic-plastic fracture toughness data from flexure tests of a chemical vapor-infiltrated SiC/Nicalon fiber-reinforced ceramic matrix composite. Fibers in the fabricated composites were pre-coated with pyrolytic carbon to varying thicknesses. In the tests, crack length was not measured and the study employed an estimate procedure, previously used successfully for ductile metals, to derive J-R curve information. Results are presented in normalized load vs. normalized displacements and comparative J{sub Ic} behavior as a function of fiber precoating thickness.

Constraining the Mean Crustal Thickness on Mercury

NASA Technical Reports Server (NTRS)

Nimmo, F.

2001-01-01

The topography of Mercury is poorly known, with only limited radar and stereo coverage available. However, radar profiles reveal topographic contrasts of several kilometers over wavelengths of approximately 1000 km. The bulk of Mercury's geologic activity took place within the first 1 Ga of the planet's history), and it is therefore likely that these topographic features derive from this period. On Earth, long wavelength topographic features are supported either convectively, or through some combination of isostasy and flexure. Photographic images show no evidence for plume-like features, nor for plate tectonics; I therefore assume that neither convective support nor Pratt isostasy are operating. The composition and structure of the crust of Mercury are almost unknown. The reflectance spectrum of the surface of Mercury is similar to that of the lunar highlands, which are predominantly plagioclase. Anderson et al. used the observed center-of-mass center-of-figure offset together with an assumption of Airy isostasy to infer a crustal thickness of 100-300 km. Based on tidal despinning arguments, the early elastic thickness (T(sub e)) of the (unfractured) lithosphere was approximately equal to or less than 100 km. Thrust faults with lengths of up to 500 km and ages of about 4 Ga B.P. are known to exist on Mercury. Assuming a semicircular slip distribution and a typical thrust fault angle of 10 degrees, the likely vertical depth to the base of these faults is about 45 km. More sophisticated modelling gives similar or slightly smaller answers. The depth to the base of faulting and the elastic layer are usually similar on Earth, and both are thought to be thermally controlled. Assuming that the characteristic temperature is about 750 K, the observed fault depth implies that the heat flux at 4 Ga B.P. is unlikely to be less than 20 mW m(exp -2) for a linear temperature gradient. For an elastic thickness of 45 km, topography at 1000 km wavelength is likely to be about 60

Mechanical Properties of Additively Manufactured Thick Honeycombs.

PubMed

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-07-23

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson's ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions.

Mechanical Properties of Additively Manufactured Thick Honeycombs

PubMed Central

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-01-01

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson’s ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions. PMID:28773735

Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study.

PubMed

Holst, Karen; Liebgott, Hervé; Wilhjelm, Jens E; Nikolov, Svetoslav; Torp-Pedersen, Søren T; Delachartre, Philippe; Jensen, Jørgen A

2013-02-01

Shock absorption is the most important function of the human heel pad. However, changes in heel pad elasticity, as seen in e.g. long-distance runners, diabetes patients, and victims of Falanga torture are affecting this function, often in a painful manner. Assessment of heel pad elasticity is usually based on one or a few strain measurements obtained by an external load-deformation system. The aim of this study was to develop a technique for quantitative measurements of heel pad elastic modulus based on several internal strain measures from within the heel pad by use of ultrasound images. Nine heel phantoms were manufactured featuring a combination of three heel pad stiffnesses and three heel pad thicknesses to model the normal human variation. Each phantom was tested in an indentation system comprising a 7MHz linear array ultrasound transducer, working as the indentor, and a connected load cell. Load-compression data and ultrasound B-mode images were simultaneously acquired in 19 compression steps of 0.1mm each. The internal tissue displacement was for each step calculated by a phase-based cross-correlation technique and internal strain maps were derived from these displacement maps. Elastic moduli were found from the resulting stress-strain curves. The elastic moduli made it possible to distinguish eight of nine phantoms from each other according to the manufactured stiffness and showed very little dependence of the thickness. Mean elastic moduli for the three soft, the three medium, and the three hard phantoms were 89kPa, 153kPa, and 168kPa, respectively. The combination of ultrasound images and force measurements provided an effective way of assessing the elastic properties of the heel pad due to the internal strain estimation. Copyright © 2012 Elsevier B.V. All rights reserved.

Pressure derivatives of elastic moduli of fused quartz to 10 kb

USGS Publications Warehouse

Peselnick, L.; Meister, R.; Wilson, W.H.

1967-01-01

Measurements of the longitudinal and shear moduli were made on fused quartz to 10 kb at 24??5??C. The anomalous behavior of the bulk modulus K at low pressure, ???K ???P 0, at higher pressures. The pressure derivative of the rigidity modulus ???G ???P remains constant and negative for the pressure range covered. A 15-kb hydrostatic pressure vessel is described for use with ultrasonic pulse instrumentation for precise measurements of elastic moduli and density changes with pressure. The placing of the transducer outside the pressure medium, and the use of C-ring pressure seals result in ease of operation and simplicity of design. ?? 1967.

An improved plate theory of order (1,2) for thick composite laminates

NASA Technical Reports Server (NTRS)

Tessler, A.

1992-01-01

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.

Sea ice thickness derived from radar altimetry: achievements and future plans

NASA Astrophysics Data System (ADS)

Ricker, R.; Hendricks, S.; Paul, S.; Kaleschke, L.; Tian-Kunze, X.

2017-12-01

The retrieval of Arctic sea ice thickness is one of the major objectives of the European CryoSat-2 radar altimeter mission and the 7-year long period of operation has produced an unprecedented record of monthly sea ice thickness information. We present CryoSat-2 results that show changes and variability of Arctic sea ice from the winter season 2010/2011 until fall 2017. CryoSat-2, however, was designed to observe thick perennial sea ice, while an accurate retrieval of thin seasonal sea ice is more challenging. We have therefore developed a method of completing and improving Arctic sea ice thickness information within the ESA SMOS+ Sea Ice project by merging CryoSat-2 and SMOS sea ice thickness retrievals. Using these satellite missions together overcomes several issues of single-mission retrievals and provides a more accurate and comprehensive view on the state of Arctic sea-ice thickness at higher temporal resolution. However, stand-alone CryoSat-2 observations can be used as reference data for the exploitation of older pulse-limited radar altimetry data sets over sea ice. In order to observe trends in sea ice thickness, it is required to minimize inter-mission biases between subsequent satellite missions. Within the ESA Climate Change Initiative (CCI) on Sea Ice, a climate data record of sea ice thickness derived from satellite radar altimetry has been developed for both hemispheres, based on the 15-year (2002-2017) monthly retrievals from Envisat and CryoSat-2 and calibrated in the 2010-2012 overlap period. The next step in promoting the utilization of sea ice thickness information from radar altimetry is to provide products by a service that meets the requirements for climate applications and operational systems. This task will be pursued within a Copernicus Climate Change Service project (C3S). This framework also aims to include additional sensors such as onboard Sentinel-3 and we will show first results of Sentinel-3 Arctic sea-ice thickness. These

Elastic properties of suspended black phosphorus nanosheets

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

Wang, Jia-Ying; Li, Yang; Zhen, Liang

2016-01-04

The mechanical properties of black phosphorus (BP) nanosheets suspended over circular holes were measured by an atomic force microscope nanoindentation method. The continuum mechanic model was introduced to calculate the elastic modulus and pretension of BP nanosheets with thicknesses ranging from 14.3 to 34 nm. Elastic modulus of BP nanosheets declines with thickness, and the maximum value is 276 ± 32.4 GPa. Besides, the effective strain of BP ranges from 8 to 17% with a breaking strength of 25 GPa. Our results show that BP nanosheets serve as a promising candidate for flexible electronic applications.

The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods

NASA Astrophysics Data System (ADS)

Ge, Z.; Kruse, H. P.; Marsden, J. E.

1996-01-01

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material and derive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to

The effective elastic thickness of the lithosphere in the collision zone between Arabia and Eurasia in Iran

NASA Astrophysics Data System (ADS)

Zamani, Ahmad; Samiee, Jafar; Kirby, Jon F.

2014-11-01

The effective elastic thickness, Te, has been calculated in the collision zone between Arabia and Eurasia in Iran from the wavelet coherence. The wavelet coherence is calculated from Bouguer anomalies and topography data using the isotropic fan wavelet method, and gives Te values between 14.2 and 62.2 km. The lower value is found in the Central Iranian Blocks and the East Iranian Belt which are bounded by several large strike-slip faults with lithospheric origin. The higher value occurs in the east of the South Caspian Sea Basin. The resulting Te map shows positive and negative correlation with shear wave velocity and surface heat flow, respectively. A comparison between the seismogenic thickness (Ts) and Te in Iran suggests that Te > Ts. Results of the load ratio in Iran indicate that in most of the study area surface loads are much more prevalent than subsurface loads, except in the Central Iranian Blocks and NW of Iran. Intermediate to low Te values in Iran were inherited from multiple rifting and orogenic activities from Late Precambrian (∼650 Ma) to present day which are not only reflected in thin and warm lithosphere but also an increasing seismicity rate.

Baseline Maritime Aerosol: Methodology to Derive the Optical Thickness and Scattering Properties

NASA Technical Reports Server (NTRS)

Kaufman, Yoram J.; Smirnov, Alexander; Holben, Brent N.; Dubovik, Oleg; Einaudi, Franco (Technical Monitor)

2001-01-01

Satellite Measurements of the global distribution of aerosol and their effect on climate should be viewed in respect to a baseline aerosol. In this concept, concentration of fine mode aerosol particles is elevated above the baseline by man-made activities (smoke or urban pollution), while coarse mode by natural processes (e.g. dust or sea-spray). Using 1-3 years of measurements in 10 stations of the Aerosol Robotic network (ACRONET we develop a methodology and derive the optical thickness and properties of this baseline aerosol for the Pacific and Atlantic Oceans. Defined as the median for periods of stable optical thickness (standard deviation < 0.02) during 2-6 days, the median baseline aerosol optical thickness over the Pacific Ocean is 0.052 at 500 am with Angstrom exponent of 0.77, and 0.071 and 1.1 respectively, over the Atlantic Ocean.

Elastic layer under axisymmetric indentation and surface energy effects

NASA Astrophysics Data System (ADS)

Intarit, Pong-in; Senjuntichai, Teerapong; Rungamornrat, Jaroon

2018-04-01

In this paper, a continuum-based approach is adopted to investigate the contact problem of an elastic layer with finite thickness and rigid base subjected to axisymmetric indentation with the consideration of surface energy effects. A complete Gurtin-Murdoch surface elasticity is employed to consider the influence of surface stresses. The indentation problem of a rigid frictionless punch with arbitrary axisymmetric profiles is formulated by employing the displacement Green's functions, derived with the aid of Hankel integral transform technique. The problem is solved by assuming the contact pressure distribution in terms of a linear combination of admissible functions and undetermined coefficients. Those coefficients are then obtained by employing a collocation technique and an efficient numerical quadrature scheme. The accuracy of proposed solution technique is verified by comparing with existing solutions for rigid indentation on an elastic half-space. Selected numerical results for the indenters with flat-ended cylindrical and paraboloidal punch profiles are presented to portray the influence of surface energy effects on elastic fields of the finite layer. It is found that the presence of surface stresses renders the layer stiffer, and the size-dependent behavior of elastic fields is observed in the present solutions. In addition, the surface energy effects become more pronounced with smaller contact area; thus, the influence of surface energy cannot be ignored in the analysis of indentation problem especially when the indenter size is very small such as in the case of nanoindentation.

Elastic properties of spherically anisotropic piezoelectric composites

NASA Astrophysics Data System (ADS)

Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming

2010-09-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.

Determination of Ice Crust Thickness from Flanking Cracks Along Ridges on Europa

NASA Technical Reports Server (NTRS)

Billings, S. E.; Kattenhorn, S. A.

2002-01-01

We use equations describing the deflection of an elastic plate below a line load to estimate ice crust thickness below ridges on Europa. Using a range of elastic parameters, ice thickness is calculated to fall in the range 0.2 2.6 km. Additional information is contained in the original extended abstract.

Multiple roles for elastic fibers in the skin.

PubMed

Starcher, Barry; Aycock, Ronnie L; Hill, Charles H

2005-04-01

Dermal elastic fibers are believed to have a primary role in providing elastic stretch and recoil to the skin. Here we compare the structural arrangement of dermal elastic fibers of chick skin and different animal species. Most elastic fibers in chick skin are derived from cells that line the feather follicle and/or smooth muscle that connects the pterial and apterial muscle bundles to feather follicles. Elastic fibers in the dermis of animals with single, primary hair follicles are derived from cells lining the hair follicle or from the ends of the pili muscle, which anchors the muscle to the matrix or to the hair follicle. Each follicle is interconnected with elastic fibers. Follicles of animals with primary and secondary (wool) hair follicles are also interconnected by elastic fibers, yet only the elastic fibers derived from the primary follicle are connected to each primary follicle. Only the primary hair follicles are connected to the pili muscle. Human skin, but not the skin of other primates, is significantly different from other animals with respect to elastic fiber organization and probably cell of origin. The data suggest that the primary role for elastic fibers in animals, with the possible exception of humans, is movement and/or placement of feathers or hair.

Elastohydrodynamics of elliptical contacts for materials of low elastic modulus

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1983-01-01

The influence of the ellipticity parameter k and the dimensionless speed U, load W, and materials G parameters on minimum film thickness for materials of low elastic modulus was investigated. The ellipticity parameter was varied from 1 (a ball-on-plane configuration) to 12 (a configuration approaching a line contact); U and W were each varied by one order of magnitude. Seventeen cases were used to generate the minimum- and central-film-thickness relations. The influence of lubricant starvation on minimum film thickness in starved elliptical, elastohydrodynamic configurations was also investigated for materials of low elastic modulus. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction in the numerical solutions. Contour plots of pressure and film thickness in and around the contact were presented for both fully flooded and starved lubrication conditions. It is evident from these figures that the inlet pressure contours become less circular and closer to the edge of the Hertzian contact zone and that the film thickness decreases substantially as the serverity of starvation increases. The results presented reveal the essential features of both fully flooded and starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus.

An elastic-plastic fracture mechanics analysis of weld-toe surface cracks in fillet welded T-butt joint

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

Fu, B.

1994-12-31

This paper describes an elastic-plastic fracture mechanics (EPFM) study of shallow weld-toe cracks. Two limiting crack configurations, plane strain edge crack and semi-circular surface crack in fillet welded T-butt plate joint, were analyzed using the finite element method. Crack depth ranging from 2 to 40% of plate thickness were considered. The elastic-plastic analysis, assuming power-law hardening relationship and Mises yield criterion, was based on incremental plasticity theory. Tension and bending loads applied were monotonically increased to a level causing relatively large scale yielding at the crack tip. Effects of weld-notch geometry and ductile material modeling on prediction of fracture mechanicsmore » characterizing parameter were assessed. It was found that the weld-notch effect reduces and the effect of material modeling increases as crack depth increases. Material modeling is less important than geometric modeling in analysis of very shallow cracks but is more important for relatively deeper cracks, e.g. crack depth more than 20% of thickness. The effect of material modeling can be assessed using a simplified structural model. Weld magnification factors derived assuming linear elastic conditions can be applied to EPFM characterization.« less

Mercury's lithospheric thickness and crustal density, as inferred from MESSENGER observations

NASA Astrophysics Data System (ADS)

James, P. B.; Mazarico, E.; Genova, A.; Smith, D. E.; Neumann, G. A.; Solomon, S. C.

2015-12-01

The gravity field and topography of Mercury measured by the MESSENGER spacecraft have provided insights into the thickness of the planet's elastic lithosphere, Te. We localized the HgM006 free-air gravity anomaly and gtmes_125v03 shape datasets to search for theoretical elastic thickness solutions that best fit a variety of localized coherence spectra between Bouguer gravity anomaly and topography. We adopted a crustal density of ρcrust =2700 kg m-3 for the Bouguer gravity correction, but density uncertainty did not markedly affect the elastic thickness estimates. A best-fit solution in the northern smooth plains (NSP) gives an elastic thickness of Te =30-60 km at the time of formation of topography for a range of ratios of top to bottom loading from 1 to 5. For a mechanical lithosphere with a thickness of ~2Te and a temperature of 1600 °C at the base, this solution is consistent with a geothermal gradient of 9-18 K km-1. A similar coherence analysis exterior to the NSP produces an elastic thickness estimate of Te =20-50 km, albeit with a poorer fit. Coherence in the northern hemisphere as a whole does not approach zero at any wavelength, because of the presence of variations in crustal thickness that are unassociated with elastic loading. The ratios and correlations of gravity and topography at intermediate wavelengths (harmonic degree l between 30 and 50) also constrain regional crustal densities. We localized gravity and topography with a moving Slepian taper and calculated regionally averaged crustal densities with the approximation ρcrust=Zl/(2πG), where Zl is the localized admittance and G is the gravitational constant. The only regional density estimates greater than 2000 kg m-3 for l=30 correspond to the NSP. Density estimates outside of the NSP were unreasonably low, even for highly porous crust. We attribute these low densities to the confounding effects of crustal thickness variations and Kaula filtering of the gravity dataset at the highest harmonic

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

A comparison between different finite elements for elastic and aero-elastic analyses.

PubMed

Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani

2017-11-01

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

Full-Thickness Skin Wound Healing Using Human Placenta-Derived Extracellular Matrix Containing Bioactive Molecules

PubMed Central

Choi, Ji Suk; Kim, Jae Dong; Yoon, Hyun Soo

2013-01-01

The human placenta, a complex organ, which facilitates exchange between the fetus and the mother, contains abundant extracellular matrix (ECM) components and well-preserved endogenous growth factors. In this study, we designed a new dermal substitute from human placentas for full-thickness wound healing. Highly porous, decellularized ECM sheets were fabricated from human placentas via homogenization, centrifugation, chemical and enzymatic treatments, molding, and freeze-drying. The physical structure and biological composition of human placenta-derived ECM sheets dramatically supported the regeneration of full-thickness wound in vivo. At the early stage, the ECM sheet efficiently absorbed wound exudates and tightly attached to the wound surface. Four weeks after implantation, the wound was completely closed, epidermic cells were well arranged and the bilayer structure of the epidermis and dermis was restored. Moreover, hair follicles and microvessels were newly formed in the ECM sheet-implanted wounds. Overall, the ECM sheet produced a dermal substitute with similar cellular organization to that of normal skin. These results suggest that human placenta-derived ECM sheets provide a microenvironment favorable to the growth and differentiation of cells, and positive modulate the healing of full-thickness wounds. PMID:22891853

Modeling and characterization of through-the-thickness properties of 3D woven composites

NASA Technical Reports Server (NTRS)

Hartranft, Dru; Pravizi-Majidi, Azar; Chou, Tsu-Wei

1995-01-01

The through-the-thickness properties of three-dimensionally (3D) woven carbon/epoxy composites have been studied. The investigation aimed at the evaluation and development of test methodologies for the property characterization in the thickness direction, and the establishment of fiber architectures were studied: layer-to-layer Angle Interlock, through-the-thickness Orthogonal woven preform with surface pile was also designed and manufactured for the fabrication of tensile test coupons with integrated grips. All the preforms were infiltrated by the resin transfer molding technique. The microstructures of the composites were characterized along the warp and fill (weft) directions to determine the degree of yarn undulations, yarn cross-sectional shapes, and microstructural dimensions. These parameters were correlated to the fiber architecture. Specimens were designed and tested for the direct measurement of the through-the-thickness tensile, compressive and shear properties of the composites. Design optimization was conducted through the analysis of the stress fields within the specimen coupled with experimental verification. The experimentally-derived elastic properties in the thickness direction compared well with analytical predictions obtained from a volume averaging model.

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

NASA Technical Reports Server (NTRS)

Tessler, A.; Annett, M. S.; Gendron, G.

2001-01-01

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Irrigation water demand: A meta-analysis of price elasticities

NASA Astrophysics Data System (ADS)

Scheierling, Susanne M.; Loomis, John B.; Young, Robert A.

2006-01-01

Metaregression models are estimated to investigate sources of variation in empirical estimates of the price elasticity of irrigation water demand. Elasticity estimates are drawn from 24 studies reported in the United States since 1963, including mathematical programming, field experiments, and econometric studies. The mean price elasticity is 0.48. Long-run elasticities, those that are most useful for policy purposes, are likely larger than the mean estimate. Empirical results suggest that estimates may be more elastic if they are derived from mathematical programming or econometric studies and calculated at a higher irrigation water price. Less elastic estimates are found to be derived from models based on field experiments and in the presence of high-valued crops.

Assessing Impact of High-Dose Pitavastatin on Carotid Artery Elasticity with Speckle-Tracking Strain Imaging.

PubMed

Kim, Chee Hae; Wang, Shuang; Park, Jun-Bean; Jung, Keun-Hwa; Yoon, Yeonyee E; Lee, Seung-Pyo; Kim, Hyung-Kwan; Kim, Yong-Jin; Cho, Goo-Yeong; Sohn, Dae-Won

2018-03-07

Speckle-tracking imaging has been introduced for the precise assessment of vessel mechanics. However, there are no data on the role of this imaging tool in assessing the changes in vasculature with statin therapy, which is known to enhance vascular elasticity. This study was a prospective study including 48 statin-naïve patients (age, 58.2±8.4 years; 29.2% male) with hypercholesterolemia. Circumferential carotid artery strain (CAS) and stiffness index (β 2 ) were measured using speckle-tracking imaging before and after 3 months of high-dose pitavastatin treatment (4 mg daily). For the comparison, we measured conventional carotid elasticity parameters and intima-media thickness using B-mode ultrasound at the same time points. Compared with baseline, there was significant improvement in circumferential CAS (2.98%±1.18% to 3.40%±1.43%, p=0.008) and β 2 (0.19±0.07 to 0.17±0.08, p=0.047) after statin therapy. Contrariwise, there were no significant changes in all conventional carotid elasticity metrics and intima-media thickness. When stratifying patients into two subgroups by 10 year atherosclerotic cardiovascular disease (ASCVD) risk, speckle-tracking-derived circumferential CAS and β 2 improved significantly only in patients with ASCVD risk ≥ 7.5%. Short-term treatment with high-dose pitavastatin improved carotid artery elasticity measured by speckle-tracking method, but not conventional parameters by B-mode ultrasound. Speckle-tracking-based measurements may allow the early noninvasive assessment of statin effects on vascular function in hypercholesterolemic patients.

Acoustic Radiation Force Elasticity Imaging in Diagnostic Ultrasound

PubMed Central

Doherty, Joshua R.; Trahey, Gregg E.; Nightingale, Kathryn R.; Palmeri, Mark L.

2013-01-01

The development of ultrasound-based elasticity imaging methods has been the focus of intense research activity since the mid-1990s. In characterizing the mechanical properties of soft tissues, these techniques image an entirely new subset of tissue properties that cannot be derived with conventional ultrasound techniques. Clinically, tissue elasticity is known to be associated with pathological condition and with the ability to image these features in vivo, elasticity imaging methods may prove to be invaluable tools for the diagnosis and/or monitoring of disease. This review focuses on ultrasound-based elasticity imaging methods that generate an acoustic radiation force to induce tissue displacements. These methods can be performed non-invasively during routine exams to provide either qualitative or quantitative metrics of tissue elasticity. A brief overview of soft tissue mechanics relevant to elasticity imaging is provided, including a derivation of acoustic radiation force, and an overview of the various acoustic radiation force elasticity imaging methods. PMID:23549529

Acoustic radiation force elasticity imaging in diagnostic ultrasound.

PubMed

Doherty, Joshua R; Trahey, Gregg E; Nightingale, Kathryn R; Palmeri, Mark L

2013-04-01

The development of ultrasound-based elasticity imaging methods has been the focus of intense research activity since the mid-1990s. In characterizing the mechanical properties of soft tissues, these techniques image an entirely new subset of tissue properties that cannot be derived with conventional ultrasound techniques. Clinically, tissue elasticity is known to be associated with pathological condition and with the ability to image these features in vivo; elasticity imaging methods may prove to be invaluable tools for the diagnosis and/or monitoring of disease. This review focuses on ultrasound-based elasticity imaging methods that generate an acoustic radiation force to induce tissue displacements. These methods can be performed noninvasively during routine exams to provide either qualitative or quantitative metrics of tissue elasticity. A brief overview of soft tissue mechanics relevant to elasticity imaging is provided, including a derivation of acoustic radiation force, and an overview of the various acoustic radiation force elasticity imaging methods.

On geoid heights derived from GEOS 3 altimeter data along the Hawaiian-Emperor seamount chain

NASA Technical Reports Server (NTRS)

Watts, A. B.

1979-01-01

The geoid heights derived from preliminary GEOS 3 satellite radar altimeter data over the Hawaiian-Emperor seamount chain are examined. Two objectives are pursued: (1) to evaluate the contribution of the topography of the seamount chain and its compensation to the marine geoid; and (2) to determine whether geoid heights derived from GEOS 3 altimeter data can be used to provide information on isostasy at geological features such as the Hawaiian-Emperor seamount chain which formed as relatively young loads on the oceanic lithosphere. Short-wavelength geoid highs of 5-12 m over the crest of the seamount chain and geoid lows over flanking regions are observed. The geological undulations can be explained by a simple model in which the seamount-chain load is supported by a strong rigid lithospheric plate. The elastic thickness estimates agree with values based on surface ship gravity and bathymetry observations, and provide further support to the hypothesis that the elastic thickness acquired at a surface load depends on the temperature gradient of the lithosphere at the time of loading.

Regeneration of Full-Thickness Rotator Cuff Tendon Tear After Ultrasound-Guided Injection With Umbilical Cord Blood-Derived Mesenchymal Stem Cells in a Rabbit Model.

PubMed

Park, Gi-Young; Kwon, Dong Rak; Lee, Sang Chul

2015-11-01

Rotator cuff tendon tear is one of the most common causes of chronic shoulder pain and disability. In this study, we investigated the therapeutic effects of ultrasound-guided human umbilical cord blood (UCB)-derived mesenchymal stem cell (MSC) injection to regenerate a full-thickness subscapularis tendon tear in a rabbit model by evaluating the gross morphology and histology of the injected tendon and motion analysis of the rabbit's activity. At 4 weeks after ultrasound-guided UCB-derived MSC injection, 7 of the 10 full-thickness subscapularis tendon tears were only partial-thickness tears, and 3 remained full-thickness tendon tears. The tendon tear size and walking capacity at 4 weeks after UCB-derived MSC injection under ultrasound guidance were significantly improved compared with the same parameters immediately after tendon tear. UCB-derived MSC injection under ultrasound guidance without surgical repair or bioscaffold resulted in the partial healing of full-thickness rotator cuff tendon tears in a rabbit model. Histology revealed that UCB-derived MSCs induced regeneration of rotator cuff tendon tear and that the regenerated tissue was predominantly composed of type I collagens. In this study, ultrasound-guided injection of human UCB-derived MSCs contributed to regeneration of the full-thickness rotator cuff tendon tear without surgical repair. The results demonstrate the effectiveness of local injection of MSCs into the rotator cuff tendon. The results of this study suggest that ultrasound-guided umbilical cord blood-derived mesenchymal stem cell injection may be a useful conservative treatment for full-thickness rotator cuff tendon tear repair. ©AlphaMed Press.

Regeneration of Full-Thickness Rotator Cuff Tendon Tear After Ultrasound-Guided Injection With Umbilical Cord Blood-Derived Mesenchymal Stem Cells in a Rabbit Model

PubMed Central

Park, Gi-Young; Lee, Sang Chul

2015-01-01

Rotator cuff tendon tear is one of the most common causes of chronic shoulder pain and disability. In this study, we investigated the therapeutic effects of ultrasound-guided human umbilical cord blood (UCB)-derived mesenchymal stem cell (MSC) injection to regenerate a full-thickness subscapularis tendon tear in a rabbit model by evaluating the gross morphology and histology of the injected tendon and motion analysis of the rabbit’s activity. At 4 weeks after ultrasound-guided UCB-derived MSC injection, 7 of the 10 full-thickness subscapularis tendon tears were only partial-thickness tears, and 3 remained full-thickness tendon tears. The tendon tear size and walking capacity at 4 weeks after UCB-derived MSC injection under ultrasound guidance were significantly improved compared with the same parameters immediately after tendon tear. UCB-derived MSC injection under ultrasound guidance without surgical repair or bioscaffold resulted in the partial healing of full-thickness rotator cuff tendon tears in a rabbit model. Histology revealed that UCB-derived MSCs induced regeneration of rotator cuff tendon tear and that the regenerated tissue was predominantly composed of type I collagens. In this study, ultrasound-guided injection of human UCB-derived MSCs contributed to regeneration of the full-thickness rotator cuff tendon tear without surgical repair. The results demonstrate the effectiveness of local injection of MSCs into the rotator cuff tendon. Significance The results of this study suggest that ultrasound-guided umbilical cord blood-derived mesenchymal stem cell injection may be a useful conservative treatment for full-thickness rotator cuff tendon tear repair. PMID:26371340

Reconstruction of full-thickness defects with bovine-derived collagen/elastin matrix: a series of challenging cases and the first reported post-burn facial reconstruction.

PubMed

Haik, Josef; Weissman, Oren; Hundeshagen, Gabriel; Farber, Nimrod; Harats, Moti; Rozenblatt, Shira M; Kamolz, Lars Peter; Winkler, Eyal; Zilinsky, Isaac

2012-07-01

Reconstruction of full-thickness defects may benefit from integration of dermal substitutes, which serve as a foundation for split-thickness skin grafts, thus enhancing short and long-term results. We present a series of 7 patients who were treated between 2010 and 2012 for complicated full-thickness defects by the second-generation collagen/elastin matrix Matriderm® covered by a split-thickness skin graft. The defects resulted from malignancy resection, trauma, and post-burn scar reconstruction. Overall graft take was excellent and no complications were noted regarding the dermal substitute. Graft quality was close to normal skin in terms of elasticity, pliability, texture, and color. Good contour and cushioning of defects in weight bearing areas was also achieved. Matriderm was found to be a useful adjunct to full-thickness defect reconstruction, especially in difficult areas where the desired result is a scar of the highest quality possible.

Effect of ceramic thickness and composite bases on stress distribution of inlays--a finite element analysis.

PubMed

Durand, Letícia Brandão; Guimarães, Jackeline Coutinho; Monteiro Junior, Sylvio; Baratieri, Luiz Narciso

2015-01-01

The purpose of this study was to determine the effect of cavity depth, ceramic thickness, and resin bases with different elastic modulus on von Mises stress patterns of ceramic inlays. Tridimensional geometric models were developed with SolidWorks image software. The differences between the models were: depth of pulpal wall, ceramic thickness, and presence of composite bases with different thickness and elastic modulus. The geometric models were constrained at the proximal surfaces and base of maxillary bone. A load of 100 N was applied. The stress distribution pattern was analyzed with von Mises stress diagrams. The maximum von Mises stress values ranged from 176 MPa to 263 MPa and varied among the 3D-models. The highest von Mises stress value was found on models with 1-mm-thick composite resin base and 1-mm-thick ceramic inlay. Intermediate values (249-250 MPa) occurred on models with 2-mm-thick composite resin base and 1-mm-thick ceramic inlay and 1-mm-thick composite resin base and 2-mm-thick ceramic inlay. The lowest values were observed on models restored exclusively with ceramic inlay (176 MPa to 182 MPa). It was found that thicker inlays distribute stress more favorably and bases with low elastic modulus increase stress concentrations on the internal surface of the ceramic inlay. The increase of ceramic thickness tends to present more favorable stress distribution, especially when bonded directly onto the cavity without the use of supporting materials. When the use of a composite base is required, composite resin with high elastic modulus and reduced thickness should be preferred.

Relationship between the Uncompensated Price Elasticity and the Income Elasticity of Demand under Conditions of Additive Preferences.

PubMed

Sabatelli, Lorenzo

2016-01-01

Income and price elasticity of demand quantify the responsiveness of markets to changes in income and in prices, respectively. Under the assumptions of utility maximization and preference independence (additive preferences), mathematical relationships between income elasticity values and the uncompensated own and cross price elasticity of demand are here derived using the differential approach to demand analysis. Key parameters are: the elasticity of the marginal utility of income, and the average budget share. The proposed method can be used to forecast the direct and indirect impact of price changes and of financial instruments of policy using available estimates of the income elasticity of demand.

Estimates of elastic plate thicknesses beneath large volcanos on Venus

NASA Technical Reports Server (NTRS)

Mcgovern, Patrick J.; Solomon, Sean C.

1992-01-01

Megellan radar imaging and topography data are now available for a number of volcanos on Venus greater than 100 km in radius. These data can be examined to reveal evidence of the flexural response of the lithosphere to the volcanic load. On Earth, flexure beneath large hotspot volcanos results in an annual topographic moat that is partially to completely filled in by sedimentation and mass wasting from the volcano's flanks. On Venus, erosion and sediment deposition are considered to be negligible at the resolution of Magellan images. Thus, it may be possible to observe evidence of flexure by the ponding of recent volcanic flows in the moat. We also might expect to find topographic signals from unfilled moats surrounding large volcanos on Venus, although these signals may be partially obscured by regional topography. Also, in the absence of sedimentation, tectonic evidence of deformation around large volcanos should be evident except where buried by very young flows. We use analytic solutions in axisymmetric geometry for deflections and stresses resulting from loading of a plate overlying an inviscid fluid. Solutions for a set of disk loads are superimposed to obtain a solution for a conical volcano. The deflection of the lithosphere produces an annular depression or moat, the extent of which can be estimated by measuring the distance from the volcano's edge to the first zero crossing or to the peak of the flexural arch. Magellan altimetry data records (ARCDRs) from data cycle 1 are processed using the GMT mapping and graphics software to produce topographic contour maps of the volcanos. We then take topographic profiles that cut across the annular and ponded flows seen on the radar images. By comparing the locations of these flows to the predicted moat locations from a range of models, we estimate the elastic plate thickness that best fits the observations, together with the uncertainty in that estimate.

Derive Arctic Sea-ice Freeboard and Thickness from NASA's LVIS Observations

NASA Astrophysics Data System (ADS)

Yi, D.; Hofton, M. A.; Harbeck, J.; Cornejo, H.; Kurtz, N. T.

2015-12-01

The sea-ice freeboard and thickness are derived from the six sea-ice flights of NASA's IceBridge Land, Vegetation, and Ice Sensor (LVIS) over the Arctic from 2009 to 2013. The LVIS is an airborne scanning laser altimeter. It can operate at an altitude up to 10 km above the ground and produce a data swath up to 2 km wide with 20-m wide footprints. The laser output wavelength is 1064 nm and pulse repetition rate is 1000 Hz. The LVIS L2 geolocated surface elevation product and Level-1b waveform product (http://nsidc.org/data/ilvis2.html and http://nsidc.org/data/ilvis1b.html) at National Snow and Ice Data Center, USA (NSIDC) are used in this study. The elevations are referenced to a geoid with tides and dynamic atmospheric corrections applied. The LVIS waveforms were fitted with Gaussian curves to calculate pulse width, peak location, pulse amplitude, and signal baseline. For each waveform, the centroid, skewness, kurtosis, and pulse area were also calculated. The waveform parameters were calibrated based on laser off pointing angle and laser channels. Calibrated LVIS waveform parameters show a coherent response to variations in surface features along their ground tracks. These parameters, combined with elevation, can be used to identify leads, enabling the derivation of sea-ice freeboard and thickness without relying upon visual images. Preliminary results show that the elevations in some of the LVIS campaigns may vary with laser incident angle; this can introduce an elevation bias if not corrected. Further analysis of the LVIS data shown that the laser incident angle related elevation bias can be removed empirically. The sea-ice freeboard and thickness results from LVIS are compared with NASA's Airborne Topographic Mapper (ATM) for an April 20, 2010 flight, when both LVIS and ATM sensors were on the same aircraft and made coincidental measurements along repeat ground tracks.

Nonlocal elasticity tensors in dislocation and disclination cores

DOE PAGES

Taupin, V.; Gbemou, K.; Fressengeas, C.; ...

2017-01-07

We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum andmore » moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.« less

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

NASA Astrophysics Data System (ADS)

Yin, H. M.; Sun, L. Z.; Chen, J. S.

2006-05-01

Magneto-elastic behavior is investigated for two-phase composites containing chain-structured magnetostrictive particles under both magnetic and mechanical loading. To derive the local magnetic and elastic fields, three modified Green's functions are derived and explicitly integrated for the infinite domain containing a spherical inclusion with a prescribed magnetization, body force, and eigenstrain. A representative volume element containing a chain of infinite particles is introduced to solve averaged magnetic and elastic fields in the particles and the matrix. Effective magnetostriction of composites is derived by considering the particle's magnetostriction and the magnetic interaction force. It is shown that there exists an optimal choice of the Young's modulus of the matrix and the volume fraction of the particles to achieve the maximum effective magnetostriction. A transversely isotropic effective elasticity is derived at the infinitesimal deformation. Disregarding the interaction term, this model provides the same effective elasticity as Mori-Tanaka's model. Comparisons of model results with the experimental data and other models show the efficacy of the model and suggest that the particle interactions have a considerable effect on the effective magneto-elastic properties of composites even for a low particle volume fraction.

Reflection of acoustic wave from the elastic seabed with an overlying gassy poroelastic layer

NASA Astrophysics Data System (ADS)

Chen, Weiyun; Wang, Zhihua; Zhao, Kai; Chen, Guoxing; Li, Xiaojun

2015-10-01

Based on the multiphase poroelasticity theory, the reflection characteristics of an obliquely incident acoustic wave upon a plane interface between overlying water and a gassy marine sediment layer with underlying elastic solid seabed are investigated. The sandwiched gassy layer is modelled as a porous material with finite thickness, which is saturated by two compressible and viscous fluids (liquid and gas). The closed-form expression for the amplitude ratio of the reflected wave, called reflection coefficient, is derived theoretically according to the boundary conditions at the upper and lower interfaces in our proposed model. Using numerical calculation, the influences of layer thickness, incident angle, wave frequency and liquid saturation of sandwiched porous layer on the reflection coefficient are analysed, respectively. It is revealed that the reflection coefficient is closely associated with incident angle and sandwiched layer thickness. Moreover, in different frequency ranges, the dependence of the wave reflection characteristics on moisture (or gas) variations in the intermediate marine sediment layer is distinguishing.

Effect of dermal thickness, tissue composition, and body site on skin biomechanical properties.

PubMed

Smalls, Lola K; Randall Wickett, R; Visscher, Marty O

2006-02-01

Quantitative measurement of skin biomechanical properties has been used effectively in the investigation of physiological changes in tissue structure and function and to determine treatment efficacy. As the methods are applied to new questions, tissue characteristics that may influence the resultant biomechanical properties are important considerations in the research design. For certain applications, variables such as dermal thickness and subdermal tissue composition, as well as age and/or solar exposure, may influence the skin biomechanics. We determined the influence of dermal thickness, tissue composition, and age on the skin biomechanical properties at the shoulder, thigh, and calf among 30 healthy females. We compared two devices, the Biomechanical Tissue Characterization System and the Cutometer SEM 575 Skin Elasticity Meter , to determine the effect of tissue sampling size. Dermal thickness was measured with 20 MHz ultrasound (Dermascan C) and tissue composition was inferred from anthropomorphic data. Skin thickness was significantly correlated with stiffness, energy absorption, and U(r)/U(f) for the shoulder. Body mass index (BMI) was significantly correlated with stiffness (negative correlation), energy absorption (positive), and skin thickness (negative) for the shoulder. Significant differences across body sites were observed. The calf was significantly different from the thigh and shoulders for all parameters (P<0.05, one-way anova). The calf had significantly lower laxity, laxity%, elastic deformation, energy absorption, elasticity, elasticity %, U(r), U(f), and U(r)/U(f) and significantly higher stiffness compared with the thighs and shoulders. sites. The thigh and shoulder sites were significantly different for all parameters except U(r)/U(f), elasticity %, laxity%, and stiffness. The dominant and non-dominant sides were significantly different. The dominant side (right for 90% of the subjects) had increased stiffness and decreased energy absorption

Relationship between the Uncompensated Price Elasticity and the Income Elasticity of Demand under Conditions of Additive Preferences

PubMed Central

Sabatelli, Lorenzo

2016-01-01

Income and price elasticity of demand quantify the responsiveness of markets to changes in income and in prices, respectively. Under the assumptions of utility maximization and preference independence (additive preferences), mathematical relationships between income elasticity values and the uncompensated own and cross price elasticity of demand are here derived using the differential approach to demand analysis. Key parameters are: the elasticity of the marginal utility of income, and the average budget share. The proposed method can be used to forecast the direct and indirect impact of price changes and of financial instruments of policy using available estimates of the income elasticity of demand. PMID:26999511

Two-zone elastic-plastic single shock waves in solids.

PubMed

Zhakhovsky, Vasily V; Budzevich, Mikalai M; Inogamov, Nail A; Oleynik, Ivan I; White, Carter T

2011-09-23

By decoupling time and length scales in moving window molecular dynamics shock-wave simulations, a new regime of shock-wave propagation is uncovered characterized by a two-zone elastic-plastic shock-wave structure consisting of a leading elastic front followed by a plastic front, both moving with the same average speed and having a fixed net thickness that can extend to microns. The material in the elastic zone is in a metastable state that supports a pressure that can substantially exceed the critical pressure characteristic of the onset of the well-known split-elastic-plastic, two-wave propagation. The two-zone elastic-plastic wave is a general phenomenon observed in simulations of a broad class of crystalline materials and is within the reach of current experimental techniques.

Accuracy Evaluation in the Measurement of a Small Change in the Thickness of Arterial Walls and the Measurement of Elasticity of the Human Carotid Artery

NASA Astrophysics Data System (ADS)

Hasegawa, Hideyuki; Kanai, Hiroshi; Hoshimiya, Nozomu; Chubachi, Noriyoshi; Koiwa, Yoshiro

1998-05-01

For the diagnosis of the early stages of atherosclerosis, it isimportant to evaluate the local acoustic characteristics of thearterial wall. For this purpose, it is necessary to increase thespatial resolution in the axial direction to several millimeters,which corresponds to the size of the macular lesion on the surface ofthe wall. We have proposed a method for measuring small velocitysignals on the intima and adventitia of the arterial wall from theskin surface using pulsive ultrasonic waves. The small change inthickness of the arterial wall is obtained by integrating thedifference between the two velocity signals on the intima andadventitia. The elastic property of the arterial wall is noninvasivelyevaluated from the change in thickness and the arterial innerpressure. In this paper, we evaluate the accuracy of the proposedmethod for measuring the small displacement. Moreover, we applied thismethod to evaluate the elastic property of the arterial wall of 50patients and 8 healthy subjects.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Collective Cell Behavior in Mechanosensing of Substrate Thickness.

PubMed

Tusan, Camelia G; Man, Yu-Hin; Zarkoob, Hoda; Johnston, David A; Andriotis, Orestis G; Thurner, Philipp J; Yang, Shoufeng; Sander, Edward A; Gentleman, Eileen; Sengers, Bram G; Evans, Nicholas D

2018-06-05

Extracellular matrix stiffness has a profound effect on the behavior of many cell types. Adherent cells apply contractile forces to the material on which they adhere and sense the resistance of the material to deformation-its stiffness. This is dependent on both the elastic modulus and the thickness of the material, with the corollary that single cells are able to sense underlying stiff materials through soft hydrogel materials at low (<10 μm) thicknesses. Here, we hypothesized that cohesive colonies of cells exert more force and create more hydrogel deformation than single cells, therefore enabling them to mechanosense more deeply into underlying materials than single cells. To test this, we modulated the thickness of soft (1 kPa) elastic extracellular-matrix-functionalized polyacrylamide hydrogels adhered to glass substrates and allowed colonies of MG63 cells to form on their surfaces. Cell morphology and deformations of fluorescent fiducial-marker-labeled hydrogels were quantified by time-lapse fluorescence microscopy imaging. Single-cell spreading increased with respect to decreasing hydrogel thickness, with data fitting to an exponential model with half-maximal response at a thickness of 3.2 μm. By quantifying cell area within colonies of defined area, we similarly found that colony-cell spreading increased with decreasing hydrogel thickness but with a greater half-maximal response at 54 μm. Depth-sensing was dependent on Rho-associated protein kinase-mediated cellular contractility. Surface hydrogel deformations were significantly greater on thick hydrogels compared to thin hydrogels. In addition, deformations extended greater distances from the periphery of colonies on thick hydrogels compared to thin hydrogels. Our data suggest that by acting collectively, cells mechanosense rigid materials beneath elastic hydrogels at greater depths than individual cells. This raises the possibility that the collective action of cells in colonies or sheets may allow

Form finding in elastic gridshells.

PubMed

Baek, Changyeob; Sageman-Furnas, Andrew O; Jawed, Mohammad K; Reis, Pedro M

2018-01-02

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Form finding in elastic gridshells

NASA Astrophysics Data System (ADS)

Baek, Changyeob; Sageman-Furnas, Andrew O.; Jawed, Mohammad K.; Reis, Pedro M.

2018-01-01

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Improving the estimate of the effective elastic modulus derived from three-point bending tests of long bones.

PubMed

Kourtis, Lampros C; Carter, Dennis R; Beaupre, Gary S

2014-08-01

Three-point bending tests are often used to determine the apparent or effective elastic modulus of long bones. The use of beam theory equations to interpret such tests can result in a substantial underestimation of the true effective modulus. In this study three-dimensional, nonlinear finite element analysis is used to quantify the errors inherent in beam theory and to create plots that can be used to correct the elastic modulus calculated from beam theory. Correction plots are generated for long bones representative of a variety of species commonly used in research studies. For a long bone with dimensions comparable to the mouse femur, the majority of the error in the effective elastic modulus results from deformations to the bone cross section that are not accounted for in the equations from beam theory. In some cases, the effective modulus calculated from beam theory can be less than one-third of the true effective modulus. Errors are larger: (1) for bones having short spans relative to bone length; (2) for bones with thin vs. thick cortices relative to periosteal diameter; and (3) when using a small radius or "knife-edge" geometry for the center loading ram and the outer supports in the three-point testing system. The use of these correction plots will enable researchers to compare results for long bones from different animal strains and to compare results obtained using testing systems that differ with regard to length between the outer supports and the radius used for the loading ram and outer supports.

The Propagation of a Liquid Bolus Through an Elastic Tube and Airway Reopening

NASA Technical Reports Server (NTRS)

Howell, Peter D.; Grotberg, James B.

1996-01-01

We use lubrication theory and matched asymptotic expansions to model the quasi-steady propagation of a liquid bridge through an elastic tube. In the limit of small capillary number, asymptotic expressions are found for the pressure drop across the bridge and the thickness of the liquid film left behind, as functions of the capillary number, the thickness of the liquid lining ahead of the bridge and the elastic characteristics of the tube wall. For a given precursor thickness, we find a critical propagation speed, and hence a critical imposed pressure drop, above which the bridge will eventually burst, and hence the tube will reopen.

Elastic Gauge Fields in Weyl Semimetals

NASA Astrophysics Data System (ADS)

Cortijo, Alberto; Ferreiros, Yago; Landsteiner, Karl; Hernandez Vozmediano, Maria Angeles

We show that, as it happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudo gauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated to these elastic gauge fields, we derive a non-zero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings. European Union structural funds and the Comunidad de Madrid MAD2D-CM Program (S2013/MIT-3007).

Elastic response of binary hard-sphere fluids

NASA Astrophysics Data System (ADS)

Rickman, J. M.; Ou-Yang, H. Daniel

2011-07-01

We derive expressions for the high-frequency, wave-number-dependent elastic constants of a binary hard-sphere fluid and employ Monte Carlo computer simulation to evaluate these constants in order to highlight the impact of composition and relative sphere diameter on the elastic response of this system. It is found that the elastic constant c11(k) exhibits oscillatory behavior as a function of k whereas the high-frequency shear modulus, for example, does not. This behavior is shown to be dictated by the angular dependence (in k⃗ space) of derivatives of the interatomic force at contact. The results are related to recent measurements of the compressibility of colloidal fluids in laser trapping experiments.

Impedance method for measuring shear elasticity of liquids

NASA Astrophysics Data System (ADS)

Badmaev, B. B.; Dembelova, T. S.; Damdinov, B. B.; Gulgenov, Ch. Zh.

2017-11-01

Experimental results of studying low-frequency (74 kHz) shear elasticity of polymer liquids by the impedance method (analogous to the Mason method) are presented. A free-volume thick liquid layer is placed on the horizontal surface of a piezoelectric quartz crystal with dimensions 34.7 × 12 × 5.5 cm. The latter performs tangential vibrations at resonance frequency. The liquid layer experiences shear strain, and shear waves should propagate in it. From the theory of the method, it follows that, with an increase in the layer thickness, both real and imaginary resonance frequency shifts should exhibit damped oscillations and tend to limiting values. For the liquids under study, the imaginary frequency shift far exceeds the real one, which testifies to the presence of bulk shear elasticity.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Elasticity of a soap film junction

NASA Astrophysics Data System (ADS)

Elias, F.; Janiaud, E.; Bacri, J.-C.; Andreotti, B.

2014-03-01

We investigate the elasticity of an isolated, threefold junction of soap films (Plateau border), which displays static undulations when liquid rapidly flows into it. By analyzing the shape of the Plateau border (thickness R and transverse displacement) as a function of the liquid flow rate Q, we show experimentally and theoretically that the elasticity of the Plateau border is dominated by the bending of the soap films pulling on the Plateau border. In this asymptotic regime, the undulation wavelength obeys the scaling law ˜Q2 R-2 and the decay length ˜Q2 R-4.

Determination of the elastic and stiffness characteristics of cross-laminated timber plates from flexural wave velocity measurements

NASA Astrophysics Data System (ADS)

Santoni, Andrea; Schoenwald, Stefan; Van Damme, Bart; Fausti, Patrizio

2017-07-01

Cross-laminated timber (CLT) is an engineered wood with good structural properties and it is also economically competitive with the traditional building construction materials. However, due to its low volume density combined with its high stiffness, it does not provide sufficient sound insulation, thus it is necessary to develop specific acoustic treatments in order to increase the noise reduction performance. The material's mechanical properties are required as input data to perform the vibro-acoustic analyses necessary during the design process. In this paper the elastic constants of a CLT plate are derived by fitting the real component of the experimental flexural wave velocity with Mindlin's dispersion relation for thick plates, neglecting the influence of the plate's size and boundary conditions. Furthermore, its apparent elastic and stiffness properties are derived from the same set of experimental data, for the plate considered to be thin. Under this latter assumption the orthotropic behaviour of an equivalent thin CLT plate is described by using an elliptic model and verified with experimental results.

Elastomer modulus and dielectric strength scaling with sample thickness

NASA Astrophysics Data System (ADS)

Larson, Kent

2015-04-01

Material characteristics such as adhesion and dielectric strength have well recognized dependencies on material thickness. There is disagreement, however, on the scale: the long held dictum that dielectric strength is inversely proportional to the square root of sample thickness has been shown to not always hold true for all materials, nor for all possible thickness regions. In D-EAP applications some studies have postulated a "critical thickness" below which properties show significantly less thickness dependency. While a great deal of data is available for dielectric strength, other properties are not nearly as well documented as samples get thinner. In particular, elastic modulus has been found to increase and elongation to decrease as sample thickness is lowered. This trend can be observed experimentally, but has been rarely reported and certainly does not appear in typical suppliers' product data sheets. Both published and newly generated data were used to study properties such as elastic modulus and dielectric strength vs sample thickness in silicone elastomers. Several theories are examined to explain such behavior, such as the impact of defect size and of common (but not well reported) concentration gradients that occur during elastomer curing that create micron-sized layers at the upper and lower interfaces with divergent properties to the bulk material. As Dielectric Electro-Active Polymer applications strive to lower and lower material thickness, changing mechanical properties must be recognized and taken into consideration for accurate electro-mechanical predictions of performance.

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

Abnormal elastic modulus behavior in a crystalline-amorphous core-shell nanowire system.

PubMed

Lee, Jeong Hwan; Choi, Su Ji; Kwon, Ji Hwan; Van Lam, Do; Lee, Seung Mo; Kim, An Soon; Baik, Hion Suck; Ahn, Sang Jung; Hong, Seong Gu; Yun, Yong Ju; Kim, Young Heon

2018-06-13

We investigated the elastic modulus behavior of crystalline InAs/amorphous Al2O3 core-shell heterostructured nanowires with shell thicknesses varying between 10 and 90 nm by conducting in situ tensile tests inside a transmission electron microscope (TEM). Counterintuitively, the elastic modulus behaviors of InAs/Al2O3 core-shell nanowires differ greatly from those of bulk-scale composite materials, free from size effects. According to our results, the elastic modulus of InAs/Al2O3 core-shell nanowires increases, peaking at a shell thickness of 40 nm, and then decreases in the range of 50-90 nm. This abnormal behavior is attributed to the continuous decrease in the elastic modulus of the Al2O3 shell as the thickness increases, which is caused by changes in the atomic/electronic structure during the atomic layer deposition process and the relaxation of residual stress/strain in the shell transferred from the interfacial mismatch between the core and shell materials. A novel method for estimating the elastic modulus of the shell in a heterostructured core-shell system was suggested by considering these two effects, and the predictions from the suggested method coincided well with the experimental results. We also found that the former and latter effects account for 89% and 11% of the change in the elastic modulus of the shell. This study provides new insight by showing that the size dependency, which is caused by the inhomogeneity of the atomic/electronic structure and the residual stress/strain, must be considered to evaluate the mechanical properties of heterostructured nanowires.

Effective elastic thickness of Africa and its relationship to other proxies for lithospheric structure and surface tectonics

NASA Astrophysics Data System (ADS)

Pérez-Gussinyé, M.; Metois, M.; Fernández, M.; Vergés, J.; Fullea, J.; Lowry, A. R.

2009-09-01

Detailed information on lateral variations in lithospheric properties can aid in understanding how surface deformation relates to deep Earth processes. The effective elastic thickness, Te, of the lithosphere is a proxy for lithospheric strength. Here, we present a new Te map of the African lithosphere estimated from coherence analysis of topography and Bouguer anomaly data. The latter data set derives from the EGM 2008 model, the highest resolution gravity database over Africa, enabling a significant improvement in lateral resolution of Te. The methodology used for Te estimation improves upon earlier approaches by optimally combining estimates from several different window sizes and correcting for an estimation bias term. Our analysis finds that Te is high, ~ 100 km, in the West African, Congo, Kalahari and Tanzania cratons. Of these, the Kalahari exhibits the lowest Te. Based in part on published seismic and mineral physics constraints, we suggest this may reflect modification of Kalahari lithosphere by anomalously hot asthenospheric mantle. Similarly, the Tanzania craton exhibits relatively lower Te east of Lake Victoria, where a centre of seismic radial anisotropy beneath the craton has been located and identified with a plume head, thus suggesting that here too, low Te reflects modification of cratonic lithosphere by an underlying hot mantle. The lowest Te in Africa occurs in the Afar and Main Ethiopian rifts, where lithospheric extension is maximum. In the western Ethiopian plateau a local Te minimum coincides with published images of a low P and S seismic velocity anomaly extending to ~ 400 km depth. Finally, the Darfur, Tibesti, Hoggar and Cameroon line volcanic provinces are characterised by low Te and no deep-seated seismic anomalies in the mantle. Corridors of relatively low Te connect these volcanic provinces to the local Te minima within the western Ethiopian plateau. We interpret the low Te to indicate thinner lithosphere within the corridors than in

Effective elastic thickness of Africa and its relationship to other proxies for lithospheric structure and surface tectonics

NASA Astrophysics Data System (ADS)

Perez-Gussinye, M.; Metois, M.; Fernandez, M.; Verges, J.; Fullea, J.; Lowry, A. R.

2009-12-01

Detailed information on lateral variations in lithospheric properties can aid in understanding how surface deformation relates to deep Earth processes. The effective elastic thickness, Te, of the lithosphere is a proxy for lithospheric strength. Here, we present a new Te map of the African lithosphere estimated from coherence analysis of topography and Bouguer anomaly data. The latter data set derives from the EGM 2008 model, the highest resolution gravity database over Africa, enabling a significant improvement in lateral resolution of Te. The methodology used for Te estimation improves upon earlier approaches by optimally combining estimates from several different window sizes and correcting for an estimation bias term. Our analysis finds that Te is high, ~ 100 km, in the West African, Congo, Kalahari and Tanzania cratons. Of these, the Kalahari exhibits the lowest Te. Based in part on published seismic and mineral physics constraints, we suggest this may reflect modification of Kalahari lithosphere by anomalously hot asthenospheric mantle. Similarly, the Tanzania craton exhibits relatively lower Te east of Lake Victoria, where a centre of seismic radial anisotropy beneath the craton has been located and identified with a plume head, thus suggesting that here too, low Te reflects modification of cratonic lithosphere by an underlying hot mantle. The lowest Te in Africa occurs in the Afar and Main Ethiopian rifts, where lithospheric extension is maximum. In the western Ethiopian plateau a local Te minimum coincides with published images of a low P and S seismic velocity anomaly extending to ~400 km depth. Finally, the Darfur, Tibesti, Hoggar and Cameroon line vo provinces lcanic are characterised by low Te and no deep-seated seismic anomalies in the mantle. Corridors of relatively low Te connect these volcanic provinces to the local Te minima within the western Ethiopian plateau. We interpret the low Te to indicate thinner lithosphere within the corridors than in

The role of elastic stored energy in controlling the long term rheological behaviour of the lithosphere

NASA Astrophysics Data System (ADS)

Regenauer-Lieb, Klaus; Weinberg, Roberto F.; Rosenbaum, Gideon

2012-04-01

The traditional definition of lithospheric strength is derived from the differential stresses required to form brittle and ductile structures at a constant strain rate. This definition is based on dissipative brittle and ductile deformation and does not take into account the ability of the lithosphere to store elastic strain. Here we show the important role of elasticity in controlling the long-term behaviour of the lithosphere. This is particularly evident when describing deformation in a thermodynamic framework, which differentiates between stored (Helmholtz free energy) and dissipative (entropy) energy potentials. In our model calculations we stretch a continental lithosphere with a wide range of crustal thickness (30-60 km) and heat flow (50-80 mW/m2) at a constant velocity. We show that the Helmholtz free energy, which in our simple calculation describes the energy stored elastically, converges for all models within a 25% range, while the dissipated energy varies over an order of magnitude. This variation stems from complex patterns in the local strain distributions of the different models, which together operate to minimize the Helmholtz free energy. This energy minimization is a fundamental material behaviour of the lithosphere, which in our simple case is defined by its elastic properties. We conclude from this result that elasticity (more generally Helmholtz free energy) is an important regulator of the long-term geological strength of the lithosphere.

Thermal sensitivity of elastic coefficients of langasite and langatate.

PubMed

Bourquin, Roger; Dulmet, Bernard

2009-10-01

Thermal coefficients of elastic constants of langasite and langatate crystals have been determined from frequency-temperature curves of contoured resonators operating in thickness modes. The effect of the trapping of the vibration has been taken into account to improve the accuracy. In a first step, the thermal sensitivities of stiffness coefficients in Lagrangian description are obtained. Thermal sensitivities of the usual elastic constants are further deduced. Predictions of thermally compensated cuts are given.

[Experimental study on porcine acellular dermal matrix and split-thickness skin grafts to repair full-thickness skin defects].

PubMed

Ma, Shaoying; Li, Baoming; Wang, Xusheng; Li, Youchen; Kang, Yue; Dong, Li; Chen, Xueying; Zhao, Yaping; Li, Baoxing

2010-02-01

To compare the effect of the composite skin graft consisting of split-thickness skin grafts (STSGs) and porcine acellular dermal matrix (PADM) with STSGs only, and to histologically observe the turnover of the PADM in rats. Twenty female Sprague-Dawley rats, weighing 200-225 g, were included. The size of 4.0 cm x 2.5 cm PADM was implanted into hypoderm of the left side of Sprague-Dawley rats' back. After 10-14 days, the size of 4.0 cm x 2.5 cm full-thickness skin defects were made on the left to expose the PADM under the skin and the same size of full-thickness skin defects were made on the right of the rats' back. The excised full-thickness skin was made to STSGs about 0.2 mm by drum dermatome. The defects were grafted with composite skin (STSGs on the PADM, experimental group) and STSGs only (control group). The survival rate, the construction degree of grafts, and the histological change in grafts area were observed at 2, 4, 8, and 20 weeks after operation. At 2 weeks after STSGs (0.2 mm) placed on vascularized PADM, STSGs and PADM adhered together and the composite skin had a good survival. The control group also had a good survival. Histological observations showed that STSGs and PADM grew together, neutrophilic granulocytes and lymphocytes infiltrated in the PADM and some macrophages around the PADM. Fibrous connective tissues were filled under the STSGs in control group. At 4-8 weeks after transplantation, the composite skin had a good survival and the composite skin was thick, soft, and elastic. STSGs survived almost totally in control group, but the grafts were thin. Histological observations showed that inflammatory reactions of PADM faded gradually in experimental group; scar tissues formed under the STSGs in control group. At 20 weeks after transplantation, composite skin was flat, thick, and elastic in experimental group, but the STSGs were thinner and less elastic in control group. Histological observations showed that histological structures of the

Effect of ceramic thickness and shade on mechanical properties of a resin luting agent.

PubMed

Passos, Sheila Pestana; Kimpara, Estevão Tomomitsu; Bottino, Marco Antonio; Rizkalla, Amin S; Santos, Gildo Coelho

2014-08-01

This study aimed to investigate the influence of ceramic thickness and shade on the Knoop hardness and dynamic elastic modulus of a dual-cured resin cement. Six ceramic shades (Bleaching, A1, A2, A3, A3.5, B3) and two ceramic thicknesses (1 mm, 3 mm) were evaluated. Disk specimens (diameter: 7 mm; thickness: 2 mm) of the resin cement were light cured under a ceramic block. Light-cured specimens without the ceramic block at distances of 1 and 3 mm were also produced. The Knoop hardness number (KHN), density, and dynamic Young's moduli were determined. Statistical analysis was conducted using ANOVA and a Tukey B rank order test (p = 0.05). The bleaching 1-mm-thick group exhibited significantly higher dynamic Young's modulus. Lower dynamic Young's moduli were observed for the 3-mm-thick ceramic groups compared to bleaching 3-mm-thick group, and no difference was found among the other 3-mm groups. For the KHN, when A3.5 3-mm-thick was used, the KHN was significantly lower than bleaching and A1 1-mm-thick ceramic; however, no difference was exhibited between the thicknesses of the same shade. The dual-cured resin cement studied irradiated through the 1-mm-thick ceramic with the lightest shade (bleaching ceramic) exhibited a better elastic modulus, and there was no effect in KHN of the resin cement when light cured under different ceramic shades and thicknesses (1 and 3 mm), except when the A3.5 3-mm-thick ceramic was used. Variolink II irradiated through ceramic with the lowest chroma exhibited the highest elastic modulus; therefore, the light activation method might not be the same for all clinical situations. © 2014 by the American College of Prosthodontists.

Elastic plate spallation

NASA Technical Reports Server (NTRS)

Oline, L.; Medaglia, J.

1972-01-01

The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.

Uniform-load and actuator influence functions of a thin or thick annular mirror: application to active mirror support optimization

NASA Astrophysics Data System (ADS)

Arnold, Luc

1996-03-01

Explicit analytical expressions are derived for the elastic deformation of a thin or thick mirror of uniform thickness and with a central hole. Thin-plate theory is used to derive the general influence function, caused by uniform and/or discrete loads, for a mirror supported by discrete points. No symmetry considerations of the locations of the points constrain the model. An estimate of the effect of the shear forces is added to the previous pure bending model to take into account the effect of the mirror thickness. Two particular cases of general influence are the uniform-load (equivalent to gravity in the case of a thin mirror) influence function for a ring support of k discrete points with k-fold symmetry. The influence of the size of the support pads is studied. A method for optimizing an active mirror cell is presented that couples the minimization of the gravity influence function with the optimization of the combined actuator influence functions to fit low-order aberrations. These low-spatial-frequency aberrations can be of elastic or optical origin. In the latter case they are due, for example, to great residual polishing errors corresponding to the soft polishing specifications relaxed for cost reductions. Results show that the correction range of the active cell can thus be noticeably enlarged, compared with an active cell designed as a passive cell, i.e., by minimizing only the deflection under gravitational loading. In the example treated here of the European Southern Observatory's New Technology Telescope I show that the active correction range can be enlarged by approximately 50% in the case of third-order astigmatic correction.

Third-order elastic constants of diamond determined from experimental data

DOE PAGES

Winey, J. M.; Hmiel, A.; Gupta, Y. M.

2016-06-01

The pressure derivatives of the second-order elastic constants (SOECs) of diamond were determined by analyzing previous sound velocity measurements under hydrostatic stress [McSkimin and Andreatch, J. Appl. Phys. 43, 294 (1972)]. Furthermore, our analysis corrects an error in the previously reported results.We present a complete and corrected set of third-order elastic constants (TOECs) using the corrected pressure derivatives, together with published data for the nonlinear elastic response of shock compressed diamond [Lang and Gupta, Phys. Rev. Lett. 106, 125502 (2011)] and it differs significantly from TOECs published previously.

Sea Ice Mass Reconciliation Exercise (SIMRE) for altimetry derived sea ice thickness data sets

NASA Astrophysics Data System (ADS)

Hendricks, S.; Haas, C.; Tsamados, M.; Kwok, R.; Kurtz, N. T.; Rinne, E. J.; Uotila, P.; Stroeve, J.

2017-12-01

Satellite altimetry is the primary remote sensing data source for retrieval of Arctic sea-ice thickness. Observational data sets are available from current and previous missions, namely ESA's Envisat and CryoSat as well as NASA ICESat. In addition, freeboard results have been published from the earlier ESA ERS missions and candidates for new data products are the Sentinel-3 constellation, the CNES AltiKa mission and NASA laser altimeter successor ICESat-2. With all the different aspects of sensor type and orbit configuration, all missions have unique properties. In addition, thickness retrieval algorithms have evolved over time and data centers have developed different strategies. These strategies may vary in choice of auxiliary data sets, algorithm parts and product resolution and masking. The Sea Ice Mass Reconciliation Exercise (SIMRE) is a project by the sea-ice radar altimetry community to bridge the challenges of comparing data sets across missions and algorithms. The ESA Arctic+ research program facilitates this project with the objective to collect existing data sets and to derive a reconciled estimate of Arctic sea ice mass balance. Starting with CryoSat-2 products, we compare results from different data centers (UCL, AWI, NASA JPL & NASA GSFC) at full resolution along selected orbits with independent ice thickness estimates. Three regions representative of first-year ice, multiyear ice and mixed ice conditions are used to compare the difference in thickness and thickness change between products over the seasonal cycle. We present first results and provide an outline for the further development of SIMRE activities. The methodology for comparing data sets is designed to be extendible and the project is open to contributions by interested groups. Model results of sea ice thickness will be added in a later phase of the project to extend the scope of SIMRE beyond EO products.

Energy in elastic fiber embedded in elastic matrix containing incident SH wave

NASA Technical Reports Server (NTRS)

Williams, James H., Jr.; Nagem, Raymond J.

1989-01-01

A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials.

Determination of corneal elasticity coefficient using the ORA database.

PubMed

Avetisov, Sergei E; Novikov, Ivan A; Bubnova, Irina A; Antonov, Alexei A; Siplivyi, Vladimir I

2010-07-01

To propose a new approach for the study of corneal biomechanics using the Reichert Ocular Response Analyzer (ORA) database, which is based on changes in velocity retardation in the central cornea at the peak of flattening. The ORA applanation curve was analyzed using a mathematical technique, which allowed calculation of the elasticity coefficient (Ke), which is primarily characteristic of the elastic properties of the cornea. Elasticity coefficient values were obtained in patients with presumably different biomechanical properties of the cornea: "normal" cornea (71 eyes, normal group), keratoconus (34 eyes, keratoconus group), LASIK (36 eyes, LASIK group), and glaucoma with elevated and compensated intraocular pressure (lOP) (38 eyes, glaucoma group). The mean Ke value in the normal group was 11.05 +/- 1.6, and the corneal thickness correlation coefficient r2 was 0.48. In the keratoconus group, the mean Ke value was 4.91 +/- 1.87 and the corneal thickness correlation coefficient r2 was 0.47. In the LASIK group, Ke and r2 were 5.99 +/- 1.18 and 0.39, respectively. In the glaucoma group, the same eyes that experienced a two-fold reduction in lOP developed a statistically significant reduction in the Ke (1.06 times lower), whereas their corneal hysteresis value increased 1.25 times. The elasticity coefficient calculated using the ORA applanation curve can be used in the evaluation of corneal biomechanical properties.

Elastic properties of external cortical bone in the craniofacial skeleton of the rhesus monkey.

PubMed

Wang, Qian; Dechow, Paul C

2006-11-01

Knowledge of elastic properties and of their variation in the cortical bone of the craniofacial skeleton is indispensable for creating accurate finite-element models to explore the biomechanics and adaptation of the skull in primates. In this study, we measured elastic properties of the external cortex of the rhesus monkey craniofacial skeleton, using an ultrasonic technique. Twenty-eight cylindrical cortical specimens were removed from each of six craniofacial skeletons of adult Macaca mulatta. Thickness, density, and a set of longitudinal and transverse ultrasonic velocities were measured on each specimen to allow calculation of the elastic properties in three dimensions, according to equations derived from Newton's second law and Hooke's law. The axes of maximum stiffness were determined by fitting longitudinal velocities measured along the perimeter of each cortical specimen to a sinusoidal function. Results showed significant differences in elastic properties between different functional areas of the rhesus cranium, and that many sites have a consistent orientation of maximum stiffness among specimens. Overall, the cortical bones of the rhesus monkey skull can be modeled as orthotropic in many regions, and as transversely isotropic in some regions, e.g., the supraorbital region. There are differences from human crania, suggesting that structural differences in skeletal form relate to differences in cortical material properties across species. These differences also suggest that we require more comparative data on elastic properties in primate craniofacial skeletons to explore effectively the functional significance of these differences, especially when these differences are elucidated through modeling approaches, such as finite-element modeling. (c) 2006 Wiley-Liss, Inc.

Airborne and ground based measurements in McMurdo Sound, Antarctica, for the validation of satellite derived ice thickness

NASA Astrophysics Data System (ADS)

Rack, Wolfgang; Haas, Christian; Langhorne, Pat; Leonard, Greg; Price, Dan; Barnsdale, Kelvin; Soltanzadeh, Iman

2014-05-01

Melting and freezing processes in the ice shelf cavities of the Ross and McMurdo Ice Shelves significantly influence the sea ice formation in McMurdo Sound. Between 2009 and 2013 we used a helicopter-borne laser and electromagnetic induction sounder (EM bird) to measure thickness and freeboard profiles across the ice shelf and the landfast sea ice, which was accompanied by extensive field validation, and coordinated with satellite altimeter overpasses. Using freeboard and thickness, the bulk density of all ice types was calculated assuming hydrostatic equilibrium. Significant density steps were detected between first-year and multi-year sea ice, with higher values for the younger sea ice. Values are overestimated in areas with abundance of sub-ice platelets because of overestimation in both ice thickness and freeboard. On the ice shelf, bulk ice densities were sometimes higher than that of pure ice, which can be explained by both the accretion of marine ice and glacial sediments. For thin ice, the freeboard to thickness conversion critically depends on the knowledge of snow properties. Our measurements allow tuning and validation of snow cover simulations using the Weather Research Forecasting (WRF) model. The simulated snowcover is used to calculate ice thickness from satellite derived freeboard. The results of our measurements, which are supported by the New Zealand Antarctic programme, draw a picture of how oceanographic processes influence the ice shelf morphology and sea ice formation in McMurdo Sound, and how satellite derived freeboard of ICESat and CryoSat together with information on snow cover can potentially capture the signature of these processes.

Derivation of a variational principle for plane strain elastic-plastic silk biopolymers

NASA Astrophysics Data System (ADS)

He, J. H.; Liu, F. J.; Cao, J. H.; Zhang, L.

2014-01-01

Silk biopolymers, such as spider silk and Bombyx mori silk, behave always elastic-plastically. An elastic-plastic model is adopted and a variational principle for the small strain, rate plasticity problem is established by semi-inverse method. A trial Lagrangian is constructed where an unknown function is included which can be identified step by step.

Global variations in gravity-derived oceanic crustal thickness: Implications on oceanic crustal accretion and hotspot-lithosphere interactions

NASA Astrophysics Data System (ADS)

Lin, J.; Zhu, J.

2012-12-01

We present a new global model of oceanic crustal thickness based on inversion of global oceanic gravity anomaly with constrains from seismic crustal thickness profiles. We first removed from the observed marine free-air gravity anomaly all gravitational effects that can be estimated and removed using independent constraints, including the effects of seafloor topography, marine sediment thickness, and the age-dependent thermal structure of the oceanic lithosphere. We then calculated models of gravity-derived crustal thickness through inversion of the residual mantle Bouguer anomaly using best-fitting gravity-modeling parameters obtained from comparison with seismically determined crustal thickness profiles. Modeling results show that about 5% of the global crustal volume (or 9% of the global oceanic surface area) is associated with model crustal thickness <5.2 km (designated as "thin" crust), while 56% of the crustal volume (or 65% of the surface area) is associated with crustal thickness of 5.2-8.6 km thick (designated as "normal" crust). The remaining 39% of the crustal volume (or 26% of the surface area) is associated with crustal thickness >8.6 km and is interpreted to have been affected by excess magmatism. The percentage of oceanic crustal volume that is associated with thick crustal thickness (>8.6 km) varies greatly among tectonic plates: Pacific (33%), Africa (50%), Antarctic (33%), Australia (30%), South America (34%), Nazca (23%), North America (47%), India (74%), Eurasia (68%), Cocos (20%), Philippine (26%), Scotia (41%), Caribbean (89%), Arabian (82%), and Juan de Fuca (21%). We also found that distribution of thickened oceanic crust (>8.6 km) seems to depend on spreading rate and lithospheric age: (1) On ocean basins younger than 5 Ma, regions of thickened crust are predominantly associated with slow and ultraslow spreading ridges. The relatively strong lithospheric plate at slow and ultraslow ridges might facilitate the loading of large magmatic

Relativistic elasticity of stationary fluid branes

NASA Astrophysics Data System (ADS)

Armas, Jay; Obers, Niels A.

2013-02-01

Fluid mechanics can be formulated on dynamical surfaces of arbitrary codimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of the number of space-time dimensions and of the fluid arising from a gravitational dual, reveal the (electro)elastic character of (charged) black branes when considering extrinsic perturbations.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.

1993-01-01

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

Investigation of free vibration characteristics for skew multiphase magneto-electro-elastic plate

NASA Astrophysics Data System (ADS)

Kiran, M. C.; Kattimani, S.

2018-04-01

This article presents the investigation of skew multiphase magneto-electro-elastic (MMEE) plate to assess its free vibration characteristics. A finite element (FE) model is formulated considering the different couplings involved via coupled constitutive equations. The transformation matrices are derived to transform local degrees of freedom into the global degrees of freedom for the nodes lying on the skew edges. Effect of different volume fraction (Vf) on the free vibration behavior is explicitly studied. In addition, influence of width to thickness ratio, the aspect ratio, and the stacking arrangement on natural frequencies of skew multiphase MEE plate investigated. Particular attention has been paid to investigate the effect of skew angle on the non-dimensional Eigen frequencies of multiphase MEE plate with simply supported edges.

Nonlinear adaptive control of an elastic robotic arm

NASA Technical Reports Server (NTRS)

Singh, S. N.

1986-01-01

An approach to control of a class of nonlinear flexible robotic systems is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. An adaptive torquer control law is derived for controlling the joint angles. This controller includes a dynamic system in the feedback path, requires only joint angle and rate for feedback, and asymptotically decomposes the elastic dynamics into two subsystems representing the transverse vibrations of the elastic link in two orthogonal planes. To damp out the elastic vibration, a force control law using modal feedback is synthesized. The combination of the torque and force control laws accomplishes joint angle control and elastic mode stabilization.

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

Destabilization of the Mg-H system through elastic constraints.

PubMed

Baldi, A; Gonzalez-Silveira, M; Palmisano, V; Dam, B; Griessen, R

2009-06-05

We tune the thermodynamics of hydrogen absorption in Mg by means of elastic clamping. The loading isotherms measured by hydrogenography show that Mg films covered with Mg-alloy-forming elements, such as Pd and Ni, have hydrogen plateau pressures more than 2 orders of magnitude higher than bulk Mg at the same temperature. An elastic model allows us to interpret the Mg thickness dependence of the hydrogen plateau pressure. Our results suggest an alternative route for the development of new hydrogen storage materials with optimized thermodynamic properties.

Destabilization of the Mg-H System through Elastic Constraints

NASA Astrophysics Data System (ADS)

Baldi, A.; Gonzalez-Silveira, M.; Palmisano, V.; Dam, B.; Griessen, R.

2009-06-01

We tune the thermodynamics of hydrogen absorption in Mg by means of elastic clamping. The loading isotherms measured by hydrogenography show that Mg films covered with Mg-alloy-forming elements, such as Pd and Ni, have hydrogen plateau pressures more than 2 orders of magnitude higher than bulk Mg at the same temperature. An elastic model allows us to interpret the Mg thickness dependence of the hydrogen plateau pressure. Our results suggest an alternative route for the development of new hydrogen storage materials with optimized thermodynamic properties.

Effect of length to thickness ratio on free vibration analysis of thick fiber reinforced plastic skew cross-ply laminate with circular cutout

NASA Astrophysics Data System (ADS)

Srividya, K.; Reddy, Ch. Kishore; Sumanth, Ch. Mohan; Krishnaiah, P. Gopala; Kishan, V. Mallikharjuna

2018-04-01

The present investigation deals with the free vibration analysis of a thick four-layered symmetric cross-ply skew laminated composite plate with a circular cutout. Three dimensional finite element models (FEM) which use the elasticity theory for the determination of stiffness matrices are modeled in ANSYS software to evaluate first five natural frequencies of the laminate. The variations of the first five natural frequencies with respect to length to thickness ratio (S) for different diameter to length ratios (d/l) are presented. It is observed that, the natural frequencies decreases with increase of thickness ratio(S).

Introduction to physical properties and elasticity models: Chapter 20

USGS Publications Warehouse

Dvorkin, Jack; Helgerud, Michael B.; Waite, William F.; Kirby, Stephen H.; Nur, Amos

2003-01-01

Estimating the in situ methane hydrate volume from seismic surveys requires knowledge of the rock physics relations between wave speeds and elastic moduli in hydrate/sediment mixtures. The elastic moduli of hydrate/sediment mixtures depend on the elastic properties of the individual sedimentary particles and the manner in which they are arranged. In this chapter, we present some rock physics data currently available from literature. The unreferenced values in Table I were not measured directly, but were derived from other values in Tables I and II using standard relationships between elastic properties for homogeneous, isotropic material. These derivations allow us to extend the list of physical property estimates, but at the expense of introducing uncertainties due to combining property values measured under different physical conditions. This is most apparent in the case of structure II (sII) hydrate for which very few physical properties have been measured under identical conditions.

Effective elastic thicknesses of the lithosphere and mechanisms of isostatic compensation in Australia

NASA Technical Reports Server (NTRS)

Zuber, Maria T.; Bechtel, Timothy D.; Forsyth, Donald W.

1989-01-01

The isostatic compensation of Australia is investigated using an isostatic model for the Australian lithosphere that assumes regional compensation of an elastic plate which undergoes flexure in response to surface and subsurface loading. Using the coherence between Bouguer gravity and topography and two separate gravity/topography data sets, it was found that, for the continent as a whole, loads with wavelengths above 1500 km are locally compensated. Loads with wavelengths in the range 600-1500 km are partially supported by regional stresses, and loads with wavelengths less than 600 km are almost entirely supported by the strength of the lithosphere. It was found that the predicted coherence for a flexural model of a continuous elastic plate does not provide a good fit to the observed coherence of central Australia. The disagreement between model and observations is explained.

Achilles and patellar tendinopathy display opposite changes in elastic properties: A shear wave elastography study.

PubMed

Coombes, B K; Tucker, K; Vicenzino, B; Vuvan, V; Mellor, R; Heales, L; Nordez, A; Hug, F

2018-03-01

To compare tendon elastic and structural properties of healthy individuals with those with Achilles or patellar tendinopathy. Sixty-seven participants (22 Achilles tendinopathy, 17 patellar tendinopathy, and 28 healthy controls) were recruited between March 2015 and March 2016. Shear wave velocity (SWV), an index of tissue elastic modulus, and tendon thickness were measured bilaterally at mid-tendon and insertional regions of Achilles and patellar tendons by an examiner blinded to group. Analysis of covariance, adjusted for age, body mass index, and sex was used to compare differences in tendon thickness and SWV between the two tendinopathy groups (relative to controls) and regions. Tendon thickness was included as a covariate for analysis of SWV. Compared to controls, participants with Achilles tendinopathy had lower SWV at the distal insertion (Mean difference MD; 95% CI: -1.56; -2.49 to -0.62 m/s; P < .001) and greater thickness at the mid-tendon (MD 0.19; 0.05-0.33 cm; P = .007). Compared to controls, participants with patellar tendinopathy had higher SWV at both regions (MD 1.25; 0.40-2.10 m/s; P = .005) and greater thickness proximally (MD 0.17; 0.06-0.29 cm; P = .003). Compared to controls, participants with Achilles and patellar tendinopathy displayed lower Achilles tendon elastic modulus and higher patellar tendon elastic modulus, respectively. More research is needed to explore whether maturation, aging, or chronic load underlie these findings and whether current management programs for Achilles and patellar tendinopathy need to be tailored to the tendon. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Linear elastic properties derivation from microstructures representative of transport parameters.

PubMed

Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

2014-06-01

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Synthetic Analysis of the Effective Elastic Thickness of the Lithosphere in China

NASA Astrophysics Data System (ADS)

Lu, Z.; Li, C.

2017-12-01

Effective elastic thickness (Te) represents the response of the lithosphere to a long-term (larger than 105 years) geological loading and reflects the deformation mechanism of plate and its thermodynamic state. Temperature and composition of the lithosphere, coupling between crust and lithospheric mantle, and lithospheric structures affect Te. Regional geology in China is quite complex, influenced by the subduction of the Pacific and Philippine Sea plates in the east and the collision of the Eurasia plate with the India-Australia plate in the southwest. Te can help understand the evolution and strength of the lithospheres in different areas and tectonic units. Here we apply the multitaper coherence method to estimate Te in China using the topography (ETOPO1) and Bouguer gravity anomalies (WGM2012) , at different window sizes (600km*600km, 800km*800km, 1000km*1000km) and moving steps. The lateral variation of Te in China coincides well with the geology. The old stable cratons or basins always correspond to larger Te, whereas the oceanic lithosphere or active orogen blocks tend to get smaller Te. We further correlate Te to curie-point depths (Zb) and heat flow to understand how temperature influences the strength of the lithosphere. Despite of a complex correlation between Te and Zb, good positive correlations are found in the North China Block, Tarim Basin, and Lower Yangtze, showing strong influence of temperature on lithospheric strength. Conversely, the Tibetan Plateau, Upper and Middle Yangtze, and East China Sea Basin even show negative correlation, suggesting that lithospheric structures and compositions play more important roles than temperature in these blocks. We also find that earthquakes tend to occur preferably in a certain range of Te. Deeper earthquakes are more likely to occur where the lithosphere is stronger with larger Te. Crust with a larger Te may also have a deeper ductile-brittle boundary, along which deep large earthquakes tend to cluster.

Towards a global accurate model for horizontal and vertical elastic response of the Earth to seasonal hydrology derived from GRACE

NASA Astrophysics Data System (ADS)

Chanard, K.; Fleitout, L.; Calais, E.; Barbot, S.; Avouac, J. P.

2016-12-01

Elastic deformation of the Earth induced by seasonal variations in hydrology is now well established. We compute the vertical and horizontal deformation induced by large variations of continental water storage at a set of 195 globally distributed continuous Global Positioning System (cGPS) stations. Seasonal loading is derived from the Gravity and Recovery Climate experiment (GRACE) equivalent water height data, where we first account for non observable degree-1 components using previous results (Swenson et al., 2010). While the vertical displacements are well predicted by the model, the horizontal components are systematically underpredicted and out-of- phase with the observations. This global result confirms previous difficulties to predict horizontal seasonal site positions at a regional scale. We discuss possible contributions to this misfit (thermal expansion, draconitic effects, etc.) and show a dramatic improvement when we derive degree-one deformation plus reference frame differences between model and observations. The fit in phase and amplitude of the seasonal deformation model to the horizontal GPS measurements is improved and the fit to the vertical component is not affected. However, the amplitude of global seasonal horizontal displacement remains slightly underpredicted. We explore several hypothesis including the validity of a purely elastic model derived from seismic estimates at an annual time scale. We show that mantle volume variations due to mineral phase transitions may play a role in the seasonal deformation and, as a by-product, use this seasonal deformation to provide a lower bound of the transient astenospheric viscosity. Our study aims at providing an accurate model for horizontal and vertical seasonal deformation of the Earth induced by variations in surface hydrology derived from GRACE.

Thickness Measurement of Surface Attachment on Plate with Lamb Wave

NASA Astrophysics Data System (ADS)

Ma, Xianglong; Zhang, Yinghong; Wen, Lichao; He, Yehu

2017-12-01

Aiming at the thickness detection of the plate surface attachment, a nondestructive testing method based on the Lamb wave is presented. This method utilizes Lamb wave propagation characteristics of signals in a bi-layer medium to measure the surface attachment plate thickness. Propagation of Lamb wave in bi-layer elastic is modeled and analyzed. The two-dimensional simulation model of electromagnetic ultrasonic plate - scale is established. The simulation is conducted by software COMSOL for simulation analysis under different boiler scale thickness wave form curve. Through this study, the thickness of the attached material can be judged by analyzing the characteristics of the received signal when the thickness of the surface of the plate is measured.

Brain-derived neurotrophic factor promoter methylation and cortical thickness in recurrent major depressive disorder.

PubMed

Na, Kyoung-Sae; Won, Eunsoo; Kang, June; Chang, Hun Soo; Yoon, Ho-Kyoung; Tae, Woo Suk; Kim, Yong-Ku; Lee, Min-Soo; Joe, Sook-Haeng; Kim, Hyun; Ham, Byung-Joo

2016-02-15

Recent studies have reported that methylation of the brain-derived neurotrophic factor (BDNF) gene promoter is associated with major depressive disorder (MDD). This study aimed to investigate the association between cortical thickness and methylation of BDNF promoters as well as serum BDNF levels in MDD. The participants consisted of 65 patients with recurrent MDD and 65 age- and gender-matched healthy controls. Methylation of BDNF promoters and cortical thickness were compared between the groups. The right medial orbitofrontal, right lingual, right lateral occipital, left lateral orbitofrontal, left pars triangularis, and left lingual cortices were thinner in patients with MDD than in healthy controls. Among the MDD group, right pericalcarine, right medical orbitofrontal, right rostral middle frontal, right postcentral, right inferior temporal, right cuneus, right precuneus, left frontal pole, left superior frontal, left superior temporal, left rostral middle frontal and left lingual cortices had inverse correlations with methylation of BDNF promoters. Higher levels of BDNF promoter methylation may be closely associated with the reduced cortical thickness among patients with MDD. Serum BDNF levels were significantly lower in MDD, and showed an inverse relationship with BDNF methylation only in healthy controls. Particularly the prefrontal and occipital cortices seem to indicate key regions in which BDNF methylation has a significant effect on structure.

Elastic fiber-mediated enthesis in the human middle ear

PubMed Central

Kawase, Tetsuaki; Shibata, Shunichi; Katori, Yukio; Ohtsuka, Aiji; Murakami, Gen; Fujimiya, Mineko

2012-01-01

Adaptation to constant vibration (acoustic oscillation) is likely to confer a specific morphology at the bone–tendon and bone–ligament interfaces at the ear ossicles, which therefore represent an exciting target of enthesis research. We histologically examined (i) the bone attachments of the tensor tympani and stapedius muscles and (ii) the annular ligament of the incudostapedial joint obtained from seven elderly donated cadavers. Notably, both aldehyde-fuchsin and elastic-Masson staining demonstrated that the major fibrous component of the entheses was not collagen fibers but mature elastic fibers. The positive controls for elastic fiber staining were the arterial wall elastic laminae included in the temporal bone materials. The elastic fibers were inserted deeply into the type II collagen-poor fibrocartilage covering the ear ossicles. The muscle tendons were composed of an outer thin layer of collagen fibers and an inner thick core of elastic fibers near the malleus or stapes. In the unique elastic fiber-mediated entheses, hyaluronan, versican and fibronectin were expressed strongly along the elastic fibers. The hyaluronan seemed to act as a friction-reducing lubricant for the elastic fibers. Aggrecan was labeled strongly in a disk- or plica-like fibrous mass on the inner side of the elastic fiber-rich ligament, possibly due to compression stress from the ligament. Tenascin-c was not evident in the entheses. The elastic fiber-mediated entheses appeared resistant to tissue destruction in an environment exposed to constant vibration. The morphology was unlikely to be the result of age-related degeneration. PMID:22803514

Elastic fiber-mediated enthesis in the human middle ear.

PubMed

Kawase, Tetsuaki; Shibata, Shunichi; Katori, Yukio; Ohtsuka, Aiji; Murakami, Gen; Fujimiya, Mineko

2012-10-01

Adaptation to constant vibration (acoustic oscillation) is likely to confer a specific morphology at the bone-tendon and bone-ligament interfaces at the ear ossicles, which therefore represent an exciting target of enthesis research. We histologically examined (i) the bone attachments of the tensor tympani and stapedius muscles and (ii) the annular ligament of the incudostapedial joint obtained from seven elderly donated cadavers. Notably, both aldehyde-fuchsin and elastic-Masson staining demonstrated that the major fibrous component of the entheses was not collagen fibers but mature elastic fibers. The positive controls for elastic fiber staining were the arterial wall elastic laminae included in the temporal bone materials. The elastic fibers were inserted deeply into the type II collagen-poor fibrocartilage covering the ear ossicles. The muscle tendons were composed of an outer thin layer of collagen fibers and an inner thick core of elastic fibers near the malleus or stapes. In the unique elastic fiber-mediated entheses, hyaluronan, versican and fibronectin were expressed strongly along the elastic fibers. The hyaluronan seemed to act as a friction-reducing lubricant for the elastic fibers. Aggrecan was labeled strongly in a disk- or plica-like fibrous mass on the inner side of the elastic fiber-rich ligament, possibly due to compression stress from the ligament. Tenascin-c was not evident in the entheses. The elastic fiber-mediated entheses appeared resistant to tissue destruction in an environment exposed to constant vibration. The morphology was unlikely to be the result of age-related degeneration. © 2012 The Authors Journal of Anatomy © 2012 Anatomical Society.

Revisiting Marshall's Third Law: Why Does Labor's Share Interact with the Elasticity of Substitution to Decrease the Elasticity of Labor Demand?

ERIC Educational Resources Information Center

Hoffman, Saul D.

2009-01-01

The third Marshall-Hicks-Allen rule of elasticity of derived demand purports to show that labor demand is less elastic when labor is a smaller share of total costs. As Hicks, Allen, and then Bronfenbrenner showed, this rule is not quite correct, and actually is complicated by an unexpected negative relationship involving labor's share of total…

The use of type 1 collagen scaffold containing stromal cell-derived factor-1 to create a matrix environment conducive to partial-thickness cartilage defects repair.

PubMed

Zhang, Wei; Chen, Jialin; Tao, Jiadong; Jiang, Yangzi; Hu, Changchang; Huang, Lu; Ji, Junfeng; Ouyang, Hong Wei

2013-01-01

Despite the presence of cartilage-derived mesenchymal stem cells (C-MSCs) and synovial membrane-derived mesenchymal stem cells (SM-MSCs) populations, partial-thickness cartilage defects, in contrast to the full-thickness defects, are devoid of spontaneous repair capacity. This study aims to create an in situ matrix environment conducive to C-MSCs and SM-MSCs to promote cartilage self-repair. Spontaneous repair with MSCs migration into the defect area was observed in full-thickness defects, but not in partial-thickness defects in rabbit model. Ex vivo and in vitro studies showed that subchondral bone or type 1 collagen (col1) scaffold was more permissive for MSCs adhesion than cartilage or type 2 collagen (col2) scaffold and induced robust stromal cell-derived factors-1 (SDF-1) dependent migration of MSCs. Furthermore, creating a matrix environment with col1 scaffold containing SDF-1 enhanced in situ self-repair of partial-thickness defects in rabbit 6 weeks post-injury. Hence, the inferior self-repair capacity in partial-thickness defects is partially owing to the non-permissive matrix environment. Creating an in situ matrix environment conducive to C-MSCs and SM-MSCs migration and adhesion with col1 scaffold containing SDF-1 can be exploited to improve self-repair capacity of cartilage. Copyright © 2012 Elsevier Ltd. All rights reserved.

Applications of film thickness equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1983-01-01

A number of applications of elastohydrodynamic film thickness expressions were considered. The motion of a steel ball over steel surfaces presenting varying degrees of conformity was examined. The equation for minimum film thickness in elliptical conjunctions under elastohydrodynamic conditions was applied to roller and ball bearings. An involute gear was also introduced, it was again found that the elliptical conjunction expression yielded a conservative estimate of the minimum film thickness. Continuously variable-speed drives like the Perbury gear, which present truly elliptical elastohydrodynamic conjunctions, are favored increasingly in mobile and static machinery. A representative elastohydrodynamic condition for this class of machinery is considered for power transmission equipment. The possibility of elastohydrodynamic films of water or oil forming between locomotive wheels and rails is examined. The important subject of traction on the railways is attracting considerable attention in various countries at the present time. The final example of a synovial joint introduced the equation developed for isoviscous-elastic regimes of lubrication.

The effect of multi-directional nanocomposite materials on the vibrational response of thick shell panels with finite length and rested on two-parameter elastic foundations

NASA Astrophysics Data System (ADS)

Tahouneh, Vahid; Naei, Mohammad Hasan

2016-03-01

The main purpose of this paper is to investigate the effect of bidirectional continuously graded nanocomposite materials on free vibration of thick shell panels rested on elastic foundations. The elastic foundation is considered as a Pasternak model after adding a shear layer to the Winkler model. The panels reinforced by randomly oriented straight single-walled carbon nanotubes are considered. The volume fractions of SWCNTs are assumed to be graded not only in the radial direction, but also in axial direction of the curved panel. This study presents a 2-D six-parameter power-law distribution for CNTs volume fraction of 2-D continuously graded nanocomposite that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. The material properties are determined in terms of local volume fractions and material properties by Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient numerical tool is used to discretize governing equations and to implement boundary conditions. The fast rate of convergence of the method is shown and results are compared against existing results in literature. Some new results for natural frequencies of the shell are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded nanocomposite volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded nanocomposite materials.

Underwater sound transmission through arrays of disk cavities in a soft elastic medium.

PubMed

Calvo, David C; Thangawng, Abel L; Layman, Christopher N; Casalini, Riccardo; Othman, Shadi F

2015-10-01

Scattering from a cavity in a soft elastic medium, such as silicone rubber, resembles scattering from an underwater bubble in that low-frequency monopole resonance is obtainable in both cases. Arrays of cavities can therefore be used to reduce underwater sound transmission using thin layers and low void fractions. This article examines the role of cavity shape by microfabricating arrays of disk-shaped air cavities into single and multiple layers of polydimethylsiloxane. Comparison is made with the case of equivalent volume cylinders which approximate spheres. Measurements of ultrasonic underwater sound transmission are compared with finite element modeling predictions. The disks provide a deeper transmission minimum at a lower frequency owing to the drum-type breathing resonance. The resonance of a single disk cavity in an unbounded medium is also calculated and compared with a derived estimate of the natural frequency of the drum mode. Variation of transmission is determined as a function of disk tilt angle, lattice constant, and layer thickness. A modeled transmission loss of 18 dB can be obtained at a wavelength about 20 times the three-layer thickness, and thinner results (wavelength/thickness ∼ 240) are possible for the same loss with a single layer depending on allowable hydrostatic pressure.

Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

NASA Technical Reports Server (NTRS)

Moore, W.; Schubert, Gerald; Sandwell, David T.

1992-01-01

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

Thickness effects on the texture development of fluorine-doped SnO2 thin films: The role of surface and strain energy

NASA Astrophysics Data System (ADS)

Consonni, V.; Rey, G.; Roussel, H.; Bellet, D.

2012-02-01

Polycrystalline fluorine-doped SnO2 thin films have been grown by ultrasonic spray pyrolysis with a thickness varying in the range of 40 to 600 nm. A texture transition from ⟨110⟩ to ⟨100⟩ and ⟨301⟩ crystallographic orientations has experimentally been shown by x-ray diffraction measurements as film thickness is increased, showing that a process of abnormal grain growth has occurred. The texture effects are considered within a thermodynamic approach, in which the minimization of total free energy constitutes the driving force for grain growth. For very small film thickness, it is found that the ⟨110⟩ preferred orientation is due to surface energy minimization, as the (110) planes have the lowest surface energy in the rutile structure. In contrast, as film thickness is increased, the ⟨100⟩ and ⟨301⟩ crystallographic orientations are progressively predominant, owing to elastic strain energy minimization in which the anisotropic character is considered in the elastic biaxial modulus. A texture map is eventually determined, revealing the expected texture as a function of elastic strain and film thickness.

Lithospheric flexural strength and effective elastic thicknesses of the Eastern Anatolia (Turkey) and surrounding region

NASA Astrophysics Data System (ADS)

Oruç, Bülent; Gomez-Ortiz, David; Petit, Carole

2017-12-01

The Lithospheric structure of Eastern Anatolia and the surrounding region, including the northern part of the Arabian platform is investigated via the analysis and modeling of Bouguer anomalies from the Earth Gravitational Model EGM08. The effective elastic thickness of the lithosphere (EET) that corresponds to the mechanical cores of the crust and lithospheric mantle is determined from the spectral coherence between Bouguer anomalies and surface elevation data. Its average value is 18.7 km. From the logarithmic amplitude spectra of Bouguer anomalies, average depths of the lithosphere-asthenosphere boundary (LAB), Moho, Conrad and basement in the study area are constrained at 84 km, 39 km, 16 km and 7 km, respectively. The geometries of the LAB and Moho are then estimated using the Parker-Oldenburg inversion algorithm. We also present a lithospheric strength map obtained from the spatial variations of EET determined by Yield Stress Envelopes (YSE). The EET varies in the range of 12-23 km, which is in good agreement with the average value obtained from spectral analysis. Low EET values are interpreted as resulting from thermal and flexural lithospheric weakening. According to the lithospheric strength of the Eastern Anatolian region, the rheology model consists of a strong but brittle upper crust, a weak and ductile lower crust, and a weak lower part of the lithosphere. On the other hand, lithosphere strength corresponds to weak and ductile lower crust, a strong upper crust and a strong uppermost lithospheric mantle for the northern part of the Arabian platform.

Application of gradient elasticity to benchmark problems of beam vibrations

NASA Astrophysics Data System (ADS)

Kateb, K. M.; Almitani, K. H.; Alnefaie, K. A.; Abu-Hamdeh, N. H.; Papadopoulos, P.; Askes, H.; Aifantis, E. C.

2016-04-01

The gradient approach, specifically gradient elasticity theory, is adopted to revisit certain typical configurations on mechanical vibrations. New results on size effects and scale-dependent behavior not captured by classical elasticity are derived, aiming at illustrating the usefulness of this approach to applications in advanced technologies. In particular, elastic prismatic straight beams in bending are discussed using two different governing equations: the gradient elasticity bending moment equation (fourth order) and the gradient elasticity deflection equation (sixth order). Different boundary/support conditions are examined. One problem considers the free vibrations of a cantilever beam loaded by an end force. A second problem is concerned with a simply supported beam disturbed by a concentrated force in the middle of the beam. Both problems are solved analytically. Exact free vibration frequencies and mode shapes are derived and presented. The difference between the gradient elasticity solution and its classical counterpart is revealed. The size ratio c/L (c denotes internal length and L is the length of the beam) induces significant effects on vibration frequencies. For both beam configurations, it turns out that as the ratio c/L increases, the vibration frequencies decrease, a fact which implies lower beam stiffness. Numerical examples show this behavior explicitly and recover the classical vibration behavior for vanishing size ratio c/L.

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

Spatial variations in effective elastic thickness in the Western Pacific Ocean and their implications for Mesozoic volcanism

NASA Astrophysics Data System (ADS)

Kalnins, L. M.; Watts, A. B.

2009-08-01

We have used free-air gravity anomaly and bathymetric data, together with a moving window admittance technique, to determine the spatial variation in oceanic elastic thickness, Te, in the Western Pacific ocean. Synthetic tests using representative seamounts show that Te can be recovered to an accuracy of ± 5 km for plates up to 30 km thick, with increased accuracy of ± 3 km for Te ≤ 20 km. The Western Pacific has a T e range of 0-50 km, with a mean of 9.4 km and a standard deviation of 6.8 km. The T e structure of the region is dominated by relatively high Te over the Hawaiian-Emperor Seamount Chain, intermediate values over the Marshall Islands, Gilbert Ridge, and Marcus-Wake Guyots, and low values over the Line Islands, Mid-Pacific Mountains, Caroline Islands, Shatsky Rise, Hess Rise, and Musician Seamounts. Plots of Te at sites with radiometric ages suggest that Te is to first order controlled by the age of the lithosphere at the time of loading. In areas that backtrack into the South Pacific Isotopic and Thermal Anomaly (SOPITA), Te may be as low as the depth to the 180 ± 120 °C isotherm at least locally. In the northern part of the study area including the Hawaiian-Emperor Seamount Chain, Te correlates with the depth to 310 ± 120 °C. These best-fitting isotherms imply peak rates of volcanism during 100-120 Ma (Early Cretaceous) and 140-150 Ma (Late Jurassic). The corresponding addition of 8 × 10 6 km 3 and 4 × 10 6 km 3 of volcanic material to the surface of the oceanic crust would result in long-term sea-level rises of 20 m and 10 m respectively. The Late Jurassic volcanic event, like the later Early Cretaceous event, appears to have influenced the tectonic evolution of the Pacific plate convergent boundaries, resulting in increased volcanism and orogenesis.

Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1978-01-01

The film-parameter equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic of low-elastic-modulus materials, or isoviscous-elastic; and elastohydrodynamic, or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The film-parameter equations for the respective regimes come from earlier theoretical studies by the authors on elastohydrodynamic and hydrodynamic lubrication of elliptical conjunctions. These equations are restated and the results are presented as a map of the lubrication regimes, with film-thickness contours on a log-log grid of the viscosity and elasticity parameters for five values of the ellipticity parameter. The results present a complete theoretical film-parameter solution for elliptical contacts in the four lubrication regimes.

Treatment of ice cover and other thin elastic layers with the parabolic equation method.

PubMed

Collins, Michael D

2015-03-01

The parabolic equation method is extended to handle problems involving ice cover and other thin elastic layers. Parabolic equation solutions are based on rational approximations that are designed using accuracy constraints to ensure that the propagating modes are handled properly and stability constrains to ensure that the non-propagating modes are annihilated. The non-propagating modes are especially problematic for problems involving thin elastic layers. It is demonstrated that stable results may be obtained for such problems by using rotated rational approximations [Milinazzo, Zala, and Brooke, J. Acoust. Soc. Am. 101, 760-766 (1997)] and generalizations of these approximations. The approach is applied to problems involving ice cover with variable thickness and sediment layers that taper to zero thickness.

Effects of ablation depth and repair time on the corneal elastic modulus after laser in situ keratomileusis.

PubMed

Wang, Xiaojun; Li, Xiaona; Chen, Weiyi; He, Rui; Gao, Zhipeng; Feng, Pengfei

2017-01-17

The biomechanical properties of the cornea should be taken into account in the refractive procedure in order to perform refractive surgery more accurately. The effects of the ablation depth and repair time on the elastic modulus of the rabbit cornea after laser in situ keratomileusis (LASIK) are still unclear. In this study, LASIK was performed on New Zealand rabbits with different ablation depth (only typical LASIK flaps were created; residual stroma bed was 50 or 30% of the whole cornea thickness respectively). The animals without any treatment were served as normal controls. The corneal thickness was measured by ultrasonic pachymetry before animals were humanly killed after 7 or 28 days post-operatively. The corneal elastic modulus was measured by uniaxial tensile testing. A mathematical procedure considering the actual geometrics of the cornea was created to analyze the corneal elastic modulus. There were no obvious differences among all groups in the elastic modulus on after 7 days post-operatively. However, after 28th days post-operatively, there was a significant increase in the elastic modulus with 50 and 30% residual stroma bed; only the elastic modulus of the cornea with 30% residual stroma bed was significantly higher than that of 7 days. Changes in elastic modulus after LASIK suggest that this biomechanical effect may correlate with the ablation depth and repair time.

On the Identication of Wrinkles of Membrane by Traveling Elastic Wave

NASA Astrophysics Data System (ADS)

Akaike, Yusuke; Yokozeki, Tomhiro

2012-07-01

Wrinkling is one of the critical factors that degrade the performance of space membrane structures. This paper proposes the way to detect the size and the position of wrinkles by observing reflection of the elastic waves at the boundary between the wrinkled section and the flat section. A wrinkle is modeled as a part of an annulus, and the effects of thickness, material properties and curvature of the membrane on the reflection rates of elastic waves are investigated. Finally, the proposed identification method is experimentally demonstrated.

Tactile mapping system: a novel imaging technology for surface topography and elasticity of tissues or organs.

PubMed

Oie, Tomonori; Suzuki, Hisato; Fukuda, Toru; Murayama, Yoshinobu; Omata, Sadao; Kanda, Keiichi; Nakayama, Yasuhide

2009-11-01

: We demonstrated that the tactile mapping system (TMS) has a high degree of spatial precision in the distribution mapping of surface elasticity of tissues or organs. : Samples used were a circumferential section of a small-caliber porcine artery (diameter: ∼3 mm) and an elasticity test pattern with a line and space configuration for the distribution mapping of elasticity, prepared by regional micropatterning of a 14-μm thick gelatin hydrogel coating on a polyurethane sheet. Surface topography and elasticity in normal saline were simultaneously investigated by TMS using a probe with a diameter of 5 or 12 μm, a spatial interval of 1 to 5 μm, and an indentation depth of 4 μm. : In the test pattern, a spatial resolution in TMS of <5 μm was acquired under water with a minimal probe diameter and spatial interval of the probe movement. TMS was used for the distribution mapping of surface elasticity in a flat, circumferential section (thickness: ∼0.5 mm) of a porcine artery, and the concentric layers of the vascular wall, including the collagen-rich and elastin-rich layers, could be clearly differentiated in terms of surface elasticity at the spatial resolution of <2 μm. : TMS is a simple and inexpensive technique for the distribution mapping of the surface elasticity in vascular tissues at the spatial resolution <2 μm. TMS has the ability to analyze a complex structure of the tissue samples under normal saline.

Shear elastic modulus estimation from indentation and SDUV on gelatin phantoms

PubMed Central

Amador, Carolina; Urban, Matthew W.; Chen, Shigao; Chen, Qingshan; An, Kai-Nan; Greenleaf, James F.

2011-01-01

Tissue mechanical properties such as elasticity are linked to tissue pathology state. Several groups have proposed shear wave propagation speed to quantify tissue mechanical properties. It is well known that biological tissues are viscoelastic materials; therefore velocity dispersion resulting from material viscoelasticity is expected. A method called Shearwave Dispersion Ultrasound Vibrometry (SDUV) can be used to quantify tissue viscoelasticity by measuring dispersion of shear wave propagation speed. However, there is not a gold standard method for validation. In this study we present an independent validation method of shear elastic modulus estimation by SDUV in 3 gelatin phantoms of differing stiffness. In addition, the indentation measurements are compared to estimates of elasticity derived from shear wave group velocities. The shear elastic moduli from indentation were 1.16, 3.40 and 5.6 kPa for a 7, 10 and 15% gelatin phantom respectively. SDUV measurements were 1.61, 3.57 and 5.37 kPa for the gelatin phantoms respectively. Shear elastic moduli derived from shear wave group velocities were 1.78, 5.2 and 7.18 kPa for the gelatin phantoms respectively. The shear elastic modulus estimated from the SDUV, matched the elastic modulus measured by indentation. On the other hand, shear elastic modulus estimated by group velocity did not agree with indentation test estimations. These results suggest that shear elastic modulus estimation by group velocity will be bias when the medium being investigated is dispersive. Therefore a rheological model should be used in order to estimate mechanical properties of viscoelastic materials. PMID:21317078

Determination of elastic stresses in gas-turbine disks

NASA Technical Reports Server (NTRS)

Manson, S S

1947-01-01

A method is presented for the calculation of elastic stresses in symmetrical disks typical of those of a high-temperature gas turbine. The method is essentially a finite-difference solution of the equilibrium and compatibility equations for elastic stresses in a symmetrical disk. Account can be taken of point-to-point variations in disk thickness, in temperature, in elastic modulus, in coefficient of thermal expansion, in material density, and in Poisson's ratio. No numerical integration or trial-and-error procedures are involved and the computations can be performed in rapid and routine fashion by nontechnical computers with little engineering supervision. Checks on problems for which exact mathematical solutions are known indicate that the method yields results of high accuracy. Illustrative examples are presented to show the manner of treating solid disks, disks with central holes, and disks constructed either of a single material or two or more welded materials. The effect of shrink fitting is taken into account by a very simple device.

Elastic modulus of tree frog adhesive toe pads.

PubMed

Barnes, W Jon P; Goodwyn, Pablo J Perez; Nokhbatolfoghahai, Mohsen; Gorb, Stanislav N

2011-10-01

Previous work using an atomic force microscope in nanoindenter mode indicated that the outer, 10- to 15-μm thick, keratinised layer of tree frog toe pads has a modulus of elasticity equivalent to silicone rubber (5-15 MPa) (Scholz et al. 2009), but gave no information on the physical properties of deeper structures. In this study, micro-indentation is used to measure the stiffness of whole toe pads of the tree frog, Litoria caerulea. We show here that tree frog toe pads are amongst the softest of biological structures (effective elastic modulus 4-25 kPa), and that they exhibit a gradient of stiffness, being stiffest on the outside. This stiffness gradient results from the presence of a dense network of capillaries lying beneath the pad epidermis, which probably has a shock absorbing function. Additionally, we compare the physical properties (elastic modulus, work of adhesion, pull-off force) of the toe pads of immature and adult frogs.

Elastic properties of porous low-k dielectric nano-films

NASA Astrophysics Data System (ADS)

Zhou, W.; Bailey, S.; Sooryakumar, R.; King, S.; Xu, G.; Mays, E.; Ege, C.; Bielefeld, J.

2011-08-01

Low-k dielectrics have predominantly replaced silicon dioxide as the interlayer dielectric for interconnects in state of the art integrated circuits. In order to further reduce interconnect RC delays, additional reductions in k for these low-k materials are being pursued via the introduction of controlled levels of porosity. The main challenge for such dielectrics is the substantial reduction in elastic properties that accompanies the increased pore volume. We report on Brillouin light scattering measurements used to determine the elastic properties of these films at thicknesses well below 200 nm, which are pertinent to their introduction into present ultralarge scale integrated technology. The observation of longitudinal and transverse standing wave acoustic resonances and their transformation into traveling waves with finite in-plane wave vectors provides for a direct non-destructive measure of the principal elastic constants that characterize the elastic properties of these porous nano-scale films. The mode dispersion further confirms that for porosity levels of up to 25%, the reduction in the dielectric constant does not result in severe degradation in the Young's modulus and Poisson's ratio of the films.

Stressor-layer-induced elastic strain sharing in SrTiO 3 complex oxide sheets

DOE PAGES

Tilka, J. A.; Park, J.; Ahn, Y.; ...

2018-02-26

A precisely selected elastic strain can be introduced in submicron-thick single-crystal SrTiO 3 sheets using a silicon nitride stressor layer. A conformal stressor layer deposited using plasma-enhanced chemical vapor deposition produces an elastic strain in the sheet consistent with the magnitude of the nitride residual stress. Synchrotron x-ray nanodiffraction reveals that the strain introduced in the SrTiO 3 sheets is on the order of 10 -4, matching the predictions of an elastic model. Using this approach to elastic strain sharing in complex oxides allows the strain to be selected within a wide and continuous range of values, an effect notmore » achievable in heteroepitaxy on rigid substrates.« less

Stressor-layer-induced elastic strain sharing in SrTiO 3 complex oxide sheets

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

Tilka, J. A.; Park, J.; Ahn, Y.

A precisely selected elastic strain can be introduced in submicron-thick single-crystal SrTiO 3 sheets using a silicon nitride stressor layer. A conformal stressor layer deposited using plasma-enhanced chemical vapor deposition produces an elastic strain in the sheet consistent with the magnitude of the nitride residual stress. Synchrotron x-ray nanodiffraction reveals that the strain introduced in the SrTiO 3 sheets is on the order of 10 -4, matching the predictions of an elastic model. Using this approach to elastic strain sharing in complex oxides allows the strain to be selected within a wide and continuous range of values, an effect notmore » achievable in heteroepitaxy on rigid substrates.« less

Fabrication of slender elastic shells by the coating of curved surfaces

NASA Astrophysics Data System (ADS)

Lee, A.; Brun, P.-T.; Marthelot, J.; Balestra, G.; Gallaire, F.; Reis, P. M.

2016-04-01

Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.

Elastic Moduli of Permanently Densified Silica Glasses

PubMed Central

Deschamps, T.; Margueritat, J.; Martinet, C.; Mermet, A.; Champagnon, B.

2014-01-01

Modelling the mechanical response of silica glass is still challenging, due to the lack of knowledge concerning the elastic properties of intermediate states of densification. An extensive Brillouin Light Scattering study on permanently densified silica glasses after cold compression in diamond anvil cell has been carried out, in order to deduce the elastic properties of such glasses and to provide new insights concerning the densification process. From sound velocity measurements, we derive phenomenological laws linking the elastic moduli of silica glass as a function of its densification ratio. The found elastic moduli are in excellent agreement with the sparse data extracted from literature, and we show that they do not depend on the thermodynamic path taken during densification (room temperature or heating). We also demonstrate that the longitudinal sound velocity exhibits an anomalous behavior, displaying a minimum for a densification ratio of 5%, and highlight the fact that this anomaly has to be distinguished from the compressibility anomaly of a-SiO2 in the elastic domain. PMID:25431218

Elastic Properties of Chimpanzee Craniofacial Cortical Bone

PubMed Central

Gharpure, Poorva; Kontogiorgos, Elias D.; Opperman, Lynne A.; Ross, Callum F.; Strait, David S.; Smith, Amanda; Pryor, Leslie C.; Wang, Qian; Dechow, Paul C.

2017-01-01

Relatively few assessments of cranial biomechanics formally take into account variation in the material properties of cranial cortical bone. Our aim was to characterize the elastic properties of chimpanzee craniofacial cortical bone and compare these to the elastic properties of dentate human craniofacial cortical bone. From seven cranial regions, 27 cylindrical samples were harvested from each of five chimpanzee crania. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived using modified equations of Hooke’s law in a Mathcad program. Consistent orientations among individuals were observed in the zygomatic arch and alveolus. The density of cortical bone showed significant regional variation (P<0.001). The elastic moduli demonstrated significant differences between sites, and a distinct pattern where E3 >E2 > E1. Shear moduli were significantly different among regions (P<0.001). The pattern by which chimpanzee cranial cortical bone varies in elastic properties resembled that seen in humans, perhaps suggesting that the elastic properties of craniofacial bone in fossil hominins can be estimated with at least some degree of confidence. PMID:27870344

An irregular lattice method for elastic wave propagation

NASA Astrophysics Data System (ADS)

O'Brien, Gareth S.; Bean, Christopher J.

2011-12-01

Lattice methods are a class of numerical scheme which represent a medium as a connection of interacting nodes or particles. In the case of modelling seismic wave propagation, the interaction term is determined from Hooke's Law including a bond-bending term. This approach has been shown to model isotropic seismic wave propagation in an elastic or viscoelastic medium by selecting the appropriate underlying lattice structure. To predetermine the material constants, this methodology has been restricted to regular grids, hexagonal or square in 2-D or cubic in 3-D. Here, we present a method for isotropic elastic wave propagation where we can remove this lattice restriction. The methodology is outlined and a relationship between the elastic material properties and an irregular lattice geometry are derived. The numerical method is compared with an analytical solution for wave propagation in an infinite homogeneous body along with comparing the method with a numerical solution for a layered elastic medium. The dispersion properties of this method are derived from a plane wave analysis showing the scheme is more dispersive than a regular lattice method. Therefore, the computational costs of using an irregular lattice are higher. However, by removing the regular lattice structure the anisotropic nature of fracture propagation in such methods can be removed.

Pattern zoology in biaxially pre-stretched elastic bilayers: from wrinkles and creases to fracture-like ridges

NASA Astrophysics Data System (ADS)

Al-Rashed, Rashed; Lopez JiméNez, Francisco; Reis, Pedro

The wrinkling of elastic bilayers under compression has been explored as a method to produce reversible surface topography, with applications ranging from microfluidics to tunable optics. We introduce a new experimental system to study the effects of pre-stretching on the instability patterns that result from the biaxial compression of thin shells bound to an elastic substrate. A pre-stretched substrate is first prepared by pressurizing an initially flat elastomeric disk and bulging it into a nearly hemispherical thick shell. The substrate is then coated with a thin layer of a polymer suspension, which, upon curing, results in a thin shell of nearly constant thickness. Releasing the pre-stretch in the substrate by deflating the system places the outer film in a state of biaxial compression, resulting in a variety of buckling patterns. We explore the parameter space by systematically varying the pre-stretch, the substrate/film stiffness mismatch, and the thickness of the film. This results in a continuous transition between different buckling patterns, from the dimples and wrinkles that are traditionally associated with the buckling of elastic bilayers, to creases and high aspect ratio `fracture-like' ridges, where the pre-stretch plays an essential role.

Capillary origami: spontaneous wrapping of a droplet with an elastic sheet.

PubMed

Py, Charlotte; Reverdy, Paul; Doppler, Lionel; Bico, José; Roman, Benoît; Baroud, Charles N

2007-04-13

The interaction between elasticity and capillarity is used to produce three-dimensional structures through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tailoring the initial geometry of the flat membrane. Balancing interfacial energy with elastic bending energy provides a critical length scale below which encapsulation cannot occur, which is verified experimentally. This length is found to depend on the thickness as h3/2, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nanoscale objects.

The elastic properties of cancerous skin: Poisson's ratio and Young's modulus.

PubMed

Tilleman, Tamara Raveh; Tilleman, Michael M; Neumann, Martino H A

2004-12-01

The physical properties of cancerous skin tissue have rarely been measured in either fresh or frozen skin specimens. Of interest are the elastic properties associated with the skin's ability to deform, i.e., to stretch and compress. Two constants--Young's modulus and Poisson's ratio--represent the basic elastic behavior pattern of any elastic material, including skin. The former relates the applied stress on a specimen to its deformation via Hooke's law, while the latter is the ratio between the axial and lateral strains. To investigate the elastic properties of cancerous skin tissue. For this purpose 23 consecutive cancerous tissue specimens prepared during Mohs micrographic surgery were analyzed. From these specimens we calculated the change in radial length (defined as the radial strain) and the change in tissue thickness (defined as axial strain). Based on the above two strains we determined a Poisson ratio of 0.43 +/- 0.12 and an average Young modulus of 52 KPa. Defining the elastic properties of cancerous skin may become the first step in turning elasticity into a clinical tool. Correlating these constants with the histopathologic features of a cancerous tissue can contribute an additional non-invasive, in vivo and in vitro diagnostic tool.

Stress Formulation in Three-Dimensional Elasticity

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.

2001-01-01

The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary, the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation: differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function. This Completed Beltrami-Michell Formulation (CBMF) can be specialized to derive the traditional methods, but the reverse is not possible. Elasticity solutions must be verified for the compliance of the new equation because the boundary compatibility conditions expressed in terms of displacement are not trivially satisfied. This paper presents the variational derivation of the stress formulation, illustrates the method, examines attributes and benefits, and outlines the future course of research.

Mercury's Low-Degree Geoid and Topography from Insolation-Driven Elastic Deformation

NASA Astrophysics Data System (ADS)

Tosi, N.; Cadek, O.; Padovan, S.; Wieczorek, M. A.

2014-12-01

Because of Mercury's high eccentricity, nearly zero obliquity, and 3:2 spin-orbit resonance, the planet's surface is characterized by an average insolation pattern resulting in longitudinal and latitudinal temperature variations that can be expressed in terms of the (2,0), (2,2) and (4,0) harmonics [Vasavada et al., 1999]. We show that the temperature anomalies that propagate from the surface into the deep mantle can be used to interpret the above harmonics of the geoid and topography spectra in terms of the elastic response of the lithosphere and mantle. Using 3D numerical simulations of thermal evolution constrained by MESSENGER observations [Tosi et al., 2013], we first demonstrate that mantle convection either ceased in the past or, at most, is very weak at present, implying that the mantle is in a conductive or nearly-conductive state. As a consequence, the power spectra of the geoid and topography due to present-day mantle convection only are orders of magnitude smaller than the observed ones. We assume therefore that present-day heat transport in the mantle occurs primarily via thermal conduction and numerically solve the diffusion equation in a 3D spherical shell with variable surface temperature and internal heat sources partitioned between the mantle and a crust of variable thickness according to different enrichment factors. We obtain a set of temperature distributions that are employed to calculate the deformation of a compressible elastic layer overlying a quasi-hydrostatic mantle in which shear stresses are assumed to be relaxed and deformation solely induced by thermal and mechanical compressibility. The surface displacements calculated with this model are then compared against the observed topography, while the internal density anomalies and the displacements of the surface and core-mantle boundary are used to calculate Mercury's geoid. We thoroughly explore the parameter space by varying the thickness of the boundary between the elastic and quasi

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

Entropic Elasticity in the Giant Muscle Protein Titin

NASA Astrophysics Data System (ADS)

Morgan, Ian; Saleh, Omar

Intrinsically disordered proteins (IDPs) are a large and functionally important class of proteins that lack a fixed three-dimensional structure. Instead, they adopt a conformational ensemble of states which facilitates their biological function as molecular linkers, springs, and switches. Due to their conformational flexibility, it can be difficult to study IDPs using typical experimental methods. To overcome this challenge, we use a high-resolution single-molecule magnetic stretching technique to quantify IDP flexibility. We apply this technique to the giant muscle protein titin, measuring its elastic response at low forces. We present results demonstrating that titin's native elastic response derives from the combined entropic elasticity of its ordered and disordered domains.

Elasticity and Fluctuations of Frustrated Nanoribbons

NASA Astrophysics Data System (ADS)

Grossman, Doron; Sharon, Eran; Diamant, Haim

2016-06-01

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes nonmonotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of nonfrustrated fluctuating filaments.

Construction of Reference Data for Tissue Characterization of Arterial Wall Based on Elasticity Images

NASA Astrophysics Data System (ADS)

Inagaki, Jun; Hasegawa, Hideyuki; Kanai, Hiroshi; Ichiki, Masataka; Tezuka, Fumiaki

2005-06-01

Previously, we developed the phased tracking method [H. Kanai et al.: IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43 (1996) 791] for measuring the minute change in thickness during one heartbeat and the elasticity of the arterial wall. By comparing pathological images with elasticity images measured with ultrasound, elasticity distributions for respective tissues in the arterial wall were determined. We have already measured the elasticity distributions for lipids and fibrous tissues (mixtures of smooth-muscle and collagen fiber) [H. Kanai et al.: Circulation 107 (2003) 3018]. In this study, elasticity distributions were measured for blood clots and calcified tissues. We discuss whether these elasticity distributions, which were measuerd in vitro, can be used as reference data for classifying cross-sectional elasticity images measured in vivo into respective tissues. In addition to the measurement of elasticity distributions, correlations between collagen content and elasticity were investigated with respect to fibrous tissue to estimate the collagen and smooth-muscle content based on elasticity. Collagen and smooth-muscle content may be important factors in determining the stability of the fibrous cap of atherosclerotic plaque. Therefore, correlations between elasticity and elements of the tissue in the arterial wall may provide useful information for the noninvasive diagnosis of plaque vulnerability.

Matched Interface and Boundary Method for Elasticity Interface Problems

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface problems. Linear elasticity theory for both isotropic homogeneous and inhomogeneous media is employed. In our approach, Lamé’s parameters can have jumps across the interface and are allowed to be position dependent in modeling isotropic inhomogeneous material. Both strong discontinuity, i.e., discontinuous solution, and weak discontinuity, namely, discontinuous derivatives of the solution, are considered in the present study. In the proposed method, fictitious values are utilized so that the standard central finite different schemes can be employed regardless of the interface. Interface jump conditions are enforced on the interface, which in turn, accurately determines fictitious values. We design new MIB schemes to account for complex interface geometries. In particular, the cross derivatives in the elasticity equations are difficult to handle for complex interface geometries. We propose secondary fictitious values and construct geometry based interpolation schemes to overcome this difficulty. Numerous analytical examples are used to validate the accuracy, convergence and robustness of the present MIB method for elasticity interface problems with both small and large curvatures, strong and weak discontinuities, and constant and variable coefficients. Numerical tests indicate second order accuracy in both L∞ and L2 norms. PMID:25914439

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

The effect of dynamic topography and gravity on lithospheric effective elastic thickness estimation: a case study

NASA Astrophysics Data System (ADS)

Bai, Yongliang; Dong, Dongdong; Kirby, Jon F.; Williams, Simon E.; Wang, Zhenjie

2018-04-01

Lithospheric effective elastic thickness (Te), a proxy for plate strength, is helpful for the understanding of subduction characteristics. Affected by curvature, faulting and magma activity, lithospheric strength near trenches should be weakened but some regional inversion studies have shown much higher Te values along some trenches than in their surroundings. In order to improve Te estimation accuracy, here we discuss the long-wavelength effect of dynamic topography and gravity on Te estimation by taking the Izu-Bonin-Mariana (IBM) Trench as a case study area. We estimate the long-wavelength influence of the density and negative buoyancy of the subducting slab on observed gravity anomalies and seafloor topography. The residual topography and gravity are used to map Te using the fan-wavelet coherence method. Maps of Te, both with and without the effects of dynamic topography and slab gravity anomaly, contain a band of high-Te values along the IBM Trench, though these values and their errors are lower when slab effects are accounted for. Nevertheless, tests show that the Te map is relatively insensitive to the choice of slab-density modelling method, even though the dynamic topography and slab-induced gravity anomaly vary considerably when the slab density is modelled by different methods. The continued presence of a high-Te band along the trench after application of dynamic corrections shows that, before using 2D inversion methods to estimate Te variations in subduction zones, there are other factors that should be considered besides the slab dynamic effects on the overriding plate.

The effect of dynamic topography and gravity on lithospheric effective elastic thickness estimation: a case study

NASA Astrophysics Data System (ADS)

Bai, Yongliang; Dong, Dongdong; Kirby, Jon F.; Williams, Simon E.; Wang, Zhenjie

2018-07-01

Lithospheric effective elastic thickness (Te), a proxy for plIate strength, is helpful for the understanding of subduction characteristics. Affected by curvature, faulting and magma activity, lithospheric strength near trenches should be weakened but some regional inversion studies have shown much higher Te values along some trenches than in their surroundings. In order to improve Te-estimation accuracy, here we discuss the long-wavelength effect of dynamic topography and gravity on Te estimation by taking the Izu-Bonin-Mariana (IBM) Trench as a case study area. We estimate the long-wavelength influence of the density and negative buoyancy of the subducting slab on observed gravity anomalies and seafloor topography. The residual topography and gravity are used to map Te using the fan-wavelet coherence method. Maps of Te, both with and without the effects of dynamic topography and slab gravity anomaly, contain a band of high-Te values along the IBM Trench, though these values and their errors are lower when slab effects are accounted for. Nevertheless, tests show that the Te map is relatively insensitive to the choice of slab-density modelling method, even though the dynamic topography and slab-induced gravity anomaly vary considerably when the slab density is modelled by different methods. The continued presence of a high-Te band along the trench after application of dynamic corrections shows that, before using 2-D inversion methods to estimate Te variations in subduction zones, there are other factors that should be considered besides the slab dynamic effects on the overriding plate.

Influence of elastic parameters on the evolution of elasticity modulus of thin films

NASA Astrophysics Data System (ADS)

Gacem, A.; Doghmane, A.; Hadjoub, Z.; Beldi, I.; Doghmane, M.

2012-09-01

In recent years, it appears many structures in the form of thin films or multilayers, used as coatings for surface protection, or to provide materials with new properties different from those of substrates. These properties are the subject of a growing number of studies in order to produce Nano or micro structures with different degrees of quality, and cost as well as the manufacture of thin film properties more functional and more controllable. As the thicknesses are close to micrometric or nanometric scales, the modulus of elasticity are difficult to measure and experimental results are rarely published in the literature. In this context, we propose an analytical qualitative methodology to describe the influence of acoustic parameters of thin films on the evolution of elastic moduli the most used. This method is based on the determination of the acoustic signature V(z) of several thin layers deposited on different substrates, as well the information on the propagation velocity of ultrasonic waves are obtained. Thus, the dispersion curves representing the variation of the modulus of elasticity (Young and the shear), were determined. We have noticed that, according to the type of substrate (light, medium or heavy), we observed the appearance of some anomalies in curves that are generally associated with changes in the acoustic properties of each of the examined layers. We have shown that these anomalies are mainly due to the effect loading, and represent one of the fundamental parameters determining the appearance or disappearance of a phenomenon and represent one of the basic parameters determining the appearance or disappearance of phenomena. Finally, we determine the Poisson ratio of thin films in order to calculate other elastic parameters such as the compressor modulus.

Revisit of the relationship between the elastic properties and sound velocities at high pressures

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

Wang, Chenju; Yan, Xiaozhen; Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065

2014-09-14

The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find thatmore » the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.« less

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

The Use of Deconstructed Tires as Elastic Elements in Railway Tracks.

PubMed

Sol-Sánchez, Miguel; Moreno-Navarro, Fernando; Rubio-Gámez, Mª Carmen

2014-08-18

Elastic elements such as rail pads, under sleeper pads and under ballast mats are railway components that allow for a reduction in track deterioration and vibrations. And they are furthermore commonly used to obtain an optimal vertical stiffness of the infrastructure. However, the use of elastomeric materials can increase construction costs and the consumption of raw materials. Thus, the utilization of used tire layers offers an alternative to reuse an abundant waste reducing the cost of elastic elements. In addition, an innovator technique allows deconstructing tire layers without grinding up the material, reducing production costs at the same time that tire properties are remained. This research is focused on the study of the viability of developing elastic components from used tire layers by evaluating the influence of thickness, the resistance capacity of the elements and their behavior in a ballast box. Results indicate the ability of tire pads to manufacture elastic elements (rail pads, under sleeper pads and under ballast mats) to be used in railway tracks.

Elastic wave generated by granular impact on rough and erodible surfaces

NASA Astrophysics Data System (ADS)

Bachelet, Vincent; Mangeney, Anne; de Rosny, Julien; Toussaint, Renaud; Farin, Maxime

2018-01-01

The elastic waves generated by impactors hitting rough and erodible surfaces are studied. For this purpose, beads of variable materials, diameters, and velocities are dropped on (i) a smooth PMMA plate, (ii) stuck glass beads on the PMMA plate to create roughness, and (iii) the rough plate covered with layers of free particles to investigate erodible beds. The Hertz model validity to describe impacts on a smooth surface is confirmed. For rough and erodible surfaces, an empirical scaling law that relates the elastic energy to the radius Rb and normal velocity Vz of the impactor is deduced from experimental data. In addition, the radiated elastic energy is found to decrease exponentially with respect to the bed thickness. Lastly, we show that the variability of the elastic energy among shocks increases from some percents to 70% between smooth and erodible surfaces. This work is a first step to better quantify seismic emissions of rock impacts in natural environment, in particular on unconsolidated soils.

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

PubMed Central

2017-01-01

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales. PMID:29225507

Moon Crustal Thickness

NASA Image and Video Library

2013-11-08

Global map of crustal thickness of the moon derived from gravity data obtained by NASA GRAIL spacecraft. The lunar near side is represented on the left hemisphere. The far side is represented in the right hemisphere.

Characterization of elasticity and hydration of composite hydrogel based on collagen-iota carrageenan as a corneal tissue engineering

NASA Astrophysics Data System (ADS)

Rinawati, M.; Triastuti, J.; Pursetyo, K. T.

2018-04-01

The cornea is a refractive element of the eye that serves to continue the stimulation of light into the eye it has a clear, transparent, elastic and relatively thick tissue. Factors caused corneal blindness, are dystrophy, keratoconus, corneal scaring. Hydrogels can be made from polysaccharide derivatives that have gelation properties such as iota carrageenan. Therefore, it is a need to develop composite hydrogel based collagen-iota carragenan as an engineeried corneal tissue with high elasticity and hydration properties. Collagen hydrogel has a maximum water content an has equlibrium up to 40 %, less than the human cornea, 81 % and under normal hydration conditions, the human cornea can transmit 87 % of visible light. In addition, the refractive index on the surface of the cornea with air is 1.375-1.380. Based on this study, it is necessary to conduct research on the development and composition of hydrogel composite collagen-iota carrageen hydrogen based on. The best result was K5 (5:5) treatment, which has the equilibrium water content of 87.07 % and viscosity of 10.7346 Pa.s.

Second order Method for Solving 3D Elasticity Equations with Complex Interfaces

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422

Three-dimensional elasticity solution of an infinite plate with a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

Elastic Properties of Chimpanzee Craniofacial Cortical Bone.

PubMed

Gharpure, Poorva; Kontogiorgos, Elias D; Opperman, Lynne A; Ross, Callum F; Strait, David S; Smith, Amanda; Pryor, Leslie C; Wang, Qian; Dechow, Paul C

2016-12-01

Relatively few assessments of cranial biomechanics formally take into account variation in the material properties of cranial cortical bone. Our aim was to characterize the elastic properties of chimpanzee craniofacial cortical bone and compare these to the elastic properties of dentate human craniofacial cortical bone. From seven cranial regions, 27 cylindrical samples were harvested from each of five chimpanzee crania. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived using modified equations of Hooke's law in a Mathcad program. Consistent orientations among individuals were observed in the zygomatic arch and alveolus. The density of cortical bone showed significant regional variation (P < 0.001). The elastic moduli demonstrated significant differences between sites, and a distinct pattern where E 3  > E 2  > E 1 . Shear moduli were significantly different among regions (P < 0.001). The pattern by which chimpanzee cranial cortical bone varies in elastic properties resembled that seen in humans, perhaps suggesting that the elastic properties of craniofacial bone in fossil hominins can be estimated with at least some degree of confidence. Anat Rec, 299:1718-1733, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Nematic elastomers: from a microscopic model to macroscopic elasticity theory.

PubMed

Xing, Xiangjun; Pfahl, Stephan; Mukhopadhyay, Swagatam; Goldbart, Paul M; Zippelius, Annette

2008-05-01

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

Super-elastic and fatigue resistant carbon material with lamellar multi-arch microstructure

NASA Astrophysics Data System (ADS)

Gao, Huai-Ling; Zhu, Yin-Bo; Mao, Li-Bo; Wang, Feng-Chao; Luo, Xi-Sheng; Liu, Yang-Yi; Lu, Yang; Pan, Zhao; Ge, Jin; Shen, Wei; Zheng, Ya-Rong; Xu, Liang; Wang, Lin-Jun; Xu, Wei-Hong; Wu, Heng-An; Yu, Shu-Hong

2016-09-01

Low-density compressible materials enable various applications but are often hindered by structure-derived fatigue failure, weak elasticity with slow recovery speed and large energy dissipation. Here we demonstrate a carbon material with microstructure-derived super-elasticity and high fatigue resistance achieved by designing a hierarchical lamellar architecture composed of thousands of microscale arches that serve as elastic units. The obtained monolithic carbon material can rebound a steel ball in spring-like fashion with fast recovery speed (~580 mm s-1), and demonstrates complete recovery and small energy dissipation (~0.2) in each compress-release cycle, even under 90% strain. Particularly, the material can maintain structural integrity after more than 106 cycles at 20% strain and 2.5 × 105 cycles at 50% strain. This structural material, although constructed using an intrinsically brittle carbon constituent, is simultaneously super-elastic, highly compressible and fatigue resistant to a degree even greater than that of previously reported compressible foams mainly made from more robust constituents.

Acoustic scattering reduction using layers of elastic materials

NASA Astrophysics Data System (ADS)

Dutrion, Cécile; Simon, Frank

2017-02-01

Making an object invisible to acoustic waves could prove useful for military applications or measurements in confined space. Different passive methods have been proposed in recent years to avoid acoustic scattering from rigid obstacles. These techniques are exclusively based on acoustic phenomena, and use for instance multiple resonators or scatterers. This paper examines the possibility of designing an acoustic cloak using a bi-layer elastic cylindrical shell to eliminate the acoustic field scattered from a rigid cylinder hit by plane waves. This field depends on the dimensional and mechanical characteristics of the elastic layers. It is computed by a semi-analytical code modelling the vibrations of the coating under plane wave excitation. Optimization by genetic algorithm is performed to determine the characteristics of a bi-layer material minimizing the scattering. Considering an external fluid consisting of air, realistic configurations of elastic coatings emerge, composed of a thick internal orthotopic layer and a thin external isotropic layer. These coatings are shown to enable scattering reduction at a precise frequency or over a larger frequency band.

Thermodynamic potential of free energy for thermo-elastic-plastic body

NASA Astrophysics Data System (ADS)

Śloderbach, Z.; Pająk, J.

2018-01-01

The procedure of derivation of thermodynamic potential of free energy (Helmholtz free energy) for a thermo-elastic-plastic body is presented. This procedure concerns a special thermodynamic model of a thermo-elastic-plastic body with isotropic hardening characteristics. The classical thermodynamics of irreversible processes for material characterized by macroscopic internal parameters is used in the derivation. Thermodynamic potential of free energy may be used for practical determination of the level of stored energy accumulated in material during plastic processing applied, e.g., for industry components and other machinery parts received by plastic deformation processing. In this paper the stored energy for the simple stretching of austenitic steel will be presented.

Measurement of the residual stress distribution in a thick pre-stretched aluminum plate

NASA Astrophysics Data System (ADS)

Yuan, S. X.; Li, X. Q.; M, S.; Zhang, Y. C.; Gong, Y. D.

2008-12-01

Thick pre-stretched aluminum alloy plates are widely used in aircraft, while machining distortion caused by initial residual stress release in thick plates is a common and serious problem. To reduce the distortion, the residual stress distribution in thick plate must be measured. According to the characteristics of the thick pre-stretched aluminum alloy plate, based the elastic mechanical theory, this article deduces the modified layer-removal strain method adapting two different strain situations, which are caused by tensile and compressive stress. To validate this method, the residual stresses distribution along the thick direction of plate 2D70T351 is measured by this method, it is shown that the new method deduced in this paper is simple and accurate, and is very useful in engineering.

Dynamic energy release rate in couple-stress elasticity

NASA Astrophysics Data System (ADS)

Morini, L.; Piccolroaz, A.; Mishuris, G.

2013-07-01

This paper is concerned with energy release rate for dynamic steady state crack problems in elastic materials with microstructures. A Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behaviour of the material is described by the theory of couple-stress elasticity developed by Koiter. A general expression for the dynamic J-integral including both traslational and micro-rotational inertial contributions is derived, and the conservation of this integral on a path surrounding the crack tip is demonstrated.

Energy-loss- and thickness-dependent contrast in atomic-scale electron energy-loss spectroscopy

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

Tan, Haiyan; Zhu, Ye; Dwyer, Christian

2014-12-31

Atomic-scale elemental maps of materials acquired by core-loss inelastic electron scattering often exhibit an undesirable sensitivity to the unavoidable elastic scattering, making the maps counter-intuitive to interpret. Here, we present a systematic study that scrutinizes the energy-loss and sample-thickness dependence of atomic-scale elemental maps acquired using 100 keV incident electrons in a scanning transmission electron microscope. For single-crystal silicon, the balance between elastic and inelastic scattering means that maps generated from the near-threshold Si-L signal (energy loss of 99 eV) show no discernible contrast for a thickness of 0.5λ (λ is the electron mean-free path, here approximately 110 nm). Atmore » greater thicknesses we observe a counter-intuitive “negative” contrast. Only at much higher energy losses is an intuitive “positive” contrast gradually restored. Our quantitative analysis shows that the energy-loss at which a positive contrast is restored depends linearly on the sample thickness. This behavior is in very good agreement with our double-channeling inelastic scattering calculations. We test a recently-proposed experimental method to correct the core-loss inelastic scattering and restore an intuitive “positive” chemical contrast. The method is demonstrated to be reliable over a large range of energy losses and sample thicknesses. The corrected contrast for near-threshold maps is demonstrated to be (desirably) inversely proportional to sample thickness. As a result, implications for the interpretation of atomic-scale elemental maps are discussed.« less

Influence of ceramic dental crown coating substrate thickness ratio on strain energy release rate

NASA Astrophysics Data System (ADS)

Khasnulhadi, K.; Daud, R.; Mat, F.; Noor, S. N. F. M.; Basaruddin, K. S.; Sulaiman, M. H.

2017-10-01

This paper presents the analysis of coating substrate thickness ratio effect on the crown coating fracture behaviour. The bi-layer material is examined under four point bending with pre-crack at the bottom of the core material by using finite element. Three different coating thickness of core/substrate was tested which is 1:1, 1:2 and 2:1. The fracture parameters are analysed based on bilayer and homogenous elastic interaction. The result shows that the ratio thickness of core/veneer provided a significant effect on energy release rate.

Layer-by-layer-based silica encapsulation of individual yeast with thickness control.

PubMed

Lee, Hojae; Hong, Daewha; Choi, Ji Yu; Kim, Ji Yup; Lee, Sang Hee; Kim, Ho Min; Yang, Sung Ho; Choi, Insung S

2015-01-01

In the area of cell-surface engineering with nanomaterials, the metabolic and functional activities of the encapsulated cells are manipulated and controlled by various parameters of the artificial shells that encase the cells, such as stiffness and elasticity, thickness, and porosity. The mechanical durability and physicochemical stability of inorganic shells prove superior to layer-by-layer-based organic shells with regard to cytoprotection, but it has been difficult to vary the parameters of inorganic shells including their thickness. In this work, we combine the layer-by-layer technique with a process of bioinspired silicification to control the thickness of the silica shells that encapsulate yeast Saccharomyces cerevisiae cells individually, and investigate the thickness-dependent microbial growth. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Stress-stress fluctuation formula for elastic constants in the NPT ensemble

NASA Astrophysics Data System (ADS)

Lips, Dominik; Maass, Philipp

2018-05-01

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the NPT ensemble based on known expressions in the NVT ensemble. We validate the formula in the NPT ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the NVT ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the formula, we apply it to determine the elastic constants of a simulated lipid bilayer.

Measurements of the Stiffness and Thickness of the Pavement Asphalt Layer Using the Enhanced Resonance Search Method

PubMed Central

Zakaria, Nur Mustakiza; Yusoff, Nur Izzi Md.; Hardwiyono, Sentot; Mohd Nayan, Khairul Anuar

2014-01-01

Enhanced resonance search (ERS) is a nondestructive testing method that has been created to evaluate the quality of a pavement by means of a special instrument called the pavement integrity scanner (PiScanner). This technique can be used to assess the thickness of the road pavement structure and the profile of shear wave velocity by using the principle of surface wave and body wave propagation. In this study, the ERS technique was used to determine the actual thickness of the asphaltic pavement surface layer, while the shear wave velocities obtained were used to determine its dynamic elastic modulus. A total of fifteen locations were identified and the results were then compared with the specifications of the Malaysian PWD, MDD UKM, and IKRAM. It was found that the value of the elastic modulus of materials is between 3929 MPa and 17726 MPa. A comparison of the average thickness of the samples with the design thickness of MDD UKM showed a difference of 20 to 60%. Thickness of the asphalt surface layer followed the specifications of Malaysian PWD and MDD UKM, while some of the values of stiffness obtained are higher than the standard. PMID:25276854

Measurements of the stiffness and thickness of the pavement asphalt layer using the enhanced resonance search method.

PubMed

Zakaria, Nur Mustakiza; Yusoff, Nur Izzi Md; Hardwiyono, Sentot; Nayan, Khairul Anuar Mohd; El-Shafie, Ahmed

2014-01-01

Enhanced resonance search (ERS) is a nondestructive testing method that has been created to evaluate the quality of a pavement by means of a special instrument called the pavement integrity scanner (PiScanner). This technique can be used to assess the thickness of the road pavement structure and the profile of shear wave velocity by using the principle of surface wave and body wave propagation. In this study, the ERS technique was used to determine the actual thickness of the asphaltic pavement surface layer, while the shear wave velocities obtained were used to determine its dynamic elastic modulus. A total of fifteen locations were identified and the results were then compared with the specifications of the Malaysian PWD, MDD UKM, and IKRAM. It was found that the value of the elastic modulus of materials is between 3929 MPa and 17726 MPa. A comparison of the average thickness of the samples with the design thickness of MDD UKM showed a difference of 20 to 60%. Thickness of the asphalt surface layer followed the specifications of Malaysian PWD and MDD UKM, while some of the values of stiffness obtained are higher than the standard.

Elasticity of methane hydrate phases at high pressure.

PubMed

Beam, Jennifer; Yang, Jing; Liu, Jin; Liu, Chujie; Lin, Jung-Fu

2016-04-21

Determination of the full elastic constants (cij) of methane hydrates (MHs) at extreme pressure-temperature environments is essential to our understanding of the elastic, thermodynamic, and mechanical properties of methane in MH reservoirs on Earth and icy satellites in the solar system. Here, we have investigated the elastic properties of singe-crystal cubic MH-sI, hexagonal MH-II, and orthorhombic MH-III phases at high pressures in a diamond anvil cell. Brillouin light scattering measurements, together with complimentary equation of state (pressure-density) results from X-ray diffraction and methane site occupancies in MH from Raman spectroscopy, were used to derive elastic constants of MH-sI, MH-II, and MH-III phases at high pressures. Analysis of the elastic constants for MH-sI and MH-II showed intriguing similarities and differences between the phases' compressional wave velocity anisotropy and shear wave velocity anisotropy. Our results show that these high-pressure MH phases can exhibit distinct elastic, thermodynamic, and mechanical properties at relevant environments of their respective natural reservoirs. These results provide new insight into the determination of how much methane exists in MH reservoirs on Earth and on icy satellites elsewhere in the solar system and put constraints on the pressure and temperature conditions of their environment.

Decreased Thickness and Integrity of the Macular Elastic Layer of Bruch’s Membrane Correspond to the Distribution of Lesions Associated with Age-Related Macular Degeneration

PubMed Central

Chong, N.H. Victor; Keonin, Jason; Luthert, Phil J.; Frennesson, Christina I.; Weingeist, David M.; Wolf, Rachel L.; Mullins, Robert F.; Hageman, Gregory S.

2005-01-01

Age-related macular degeneration (AMD) is a leading cause of blindness in the elderly. In its severest form, choroidal neovessels breach the macular Bruch’s membrane, an extracellular matrix compartment comprised of elastin and collagen laminae, and grow into the retina. We sought to determine whether structural properties of the elastic lamina (EL) correspond to the region of the macula that is predilected toward degeneration in AMD. Morphometric assessment of the macular and extramacular regions of 121 human donor eyes, with and without AMD, revealed a statistically significant difference in both the integrity (P < 0.0001) and thickness (P < 0.0001) of the EL between the macular and extramacular regions in donors of all ages. The EL was three to six times thinner and two to five times less abundant in the macula than in the periphery. The integrity of the macular EL was significantly lower in donors with early-stage AMD (P = 0.028), active choroidal neovascularization (P = 0.020), and disciform scars (P = 0.003), as compared to unaffected, age-matched controls. EL thickness was significantly lower only in individuals with disciform scars (P = 0.008). The largest gaps in macular EL integrity were significantly larger in all categories of AMD (each P < 0.0001), as compared to controls. EL integrity, thickness, and gap length in donors with geographic atrophy did not differ from those of controls. These structural properties of the macular EL correspond spatially to the distribution of macular lesions associated with AMD and may help to explain why the macula is more susceptible to degenerative events that occur in this disease. PMID:15632016

Simulating wave-turbulence on thin elastic plates with arbitrary boundary conditions

NASA Astrophysics Data System (ADS)

van Rees, Wim M.; Mahadevan, L.

2016-11-01

The statistical characteristics of interacting waves are described by the theory of wave turbulence, with the study of deep water gravity wave turbulence serving as a paradigmatic physical example. Here we consider the elastic analog of this problem in the context of flexural waves arising from vibrations of a thin elastic plate. Such flexural waves generate the unique sounds of so-called thunder machines used in orchestras - thin metal plates that make a thunder-like sound when forcefully shaken. Wave turbulence in elastic plates is typically investigated numerically using spectral simulations with periodic boundary conditions, which are not very realistic. We will present the results of numerical simulations of the dynamics of thin elastic plates in physical space, with arbitrary shapes, boundary conditions, anisotropy and inhomogeneity, and show first results on wave turbulence beyond the conventionally studied rectangular plates. Finally, motivated by a possible method to measure ice-sheet thicknesses in the open ocean, we will further discuss the behavior of a vibrating plate when floating on an inviscid fluid.

The Use of Deconstructed Tires as Elastic Elements in Railway Tracks

PubMed Central

Sol-Sánchez, Miguel; Moreno-Navarro, Fernando; Rubio-Gámez, Mª Carmen

2014-01-01

Elastic elements such as rail pads, under sleeper pads and under ballast mats are railway components that allow for a reduction in track deterioration and vibrations. And they are furthermore commonly used to obtain an optimal vertical stiffness of the infrastructure. However, the use of elastomeric materials can increase construction costs and the consumption of raw materials. Thus, the utilization of used tire layers offers an alternative to reuse an abundant waste reducing the cost of elastic elements. In addition, an innovator technique allows deconstructing tire layers without grinding up the material, reducing production costs at the same time that tire properties are remained. This research is focused on the study of the viability of developing elastic components from used tire layers by evaluating the influence of thickness, the resistance capacity of the elements and their behavior in a ballast box. Results indicate the ability of tire pads to manufacture elastic elements (rail pads, under sleeper pads and under ballast mats) to be used in railway tracks. PMID:28788168

Developing the elastic modulus measurement of asphalt concrete using the compressive strength test

NASA Astrophysics Data System (ADS)

Setiawan, Arief; Suparma, Latif Budi; Mulyono, Agus Taufik

2017-11-01

Elastic modulus is a fundamental property of an asphalt mixture. An analytical method of the elastic modulus is needed to determine the thickness of flexible pavement. It has a role as one of the input values on a stress-strain analysis in the finite element method. The aim of this study was to develop the measurement of the elastic modulus by using compressive strength testing. This research used a set of specimen mold tool and Delta Dimensi software to record strain changes occurring in the proving ring of compression machine and the specimens. The elastic modulus of the five types of aggregate gradation and 2 types of asphalt were measured at optimum asphalt content. Asphalt Cement 60/70 and Elastomer Modified Asphalt (EMA) were used as a binder. Manufacturing success indicators of the specimens used void-in-the-mix (VIM) 3-5 % criteria. The success rate of the specimen manufacturing was more than 76%. Thus, the procedure and the compressive strength test equipment could be used for the measurement of the elastic modulus. The aggregate gradation and asphalt types significantly affected the elastic modulus of the asphalt concrete.

Extracting elastic properties of an atomically thin interfacial layer by time-domain analysis of femtosecond acoustics

NASA Astrophysics Data System (ADS)

Chen, H.-Y.; Huang, Y.-R.; Shih, H.-Y.; Chen, M.-J.; Sheu, J.-K.; Sun, C.-K.

2017-11-01

Modern devices adopting denser designs and complex 3D structures have created much more interfaces than before, where atomically thin interfacial layers could form. However, fundamental information such as the elastic property of the interfacial layers is hard to measure. The elastic property of the interfacial layer is of great importance in both thermal management and nano-engineering of modern devices. Appropriate techniques to probe the elastic properties of interfacial layers as thin as only several atoms are thus critically needed. In this work, we demonstrated the feasibility of utilizing the time-resolved femtosecond acoustics technique to extract the elastic properties and mass density of a 1.85-nm-thick interfacial layer, with the aid of transmission electron microscopy. We believe that this femtosecond acoustics approach will provide a strategy to measure the absolute elastic properties of atomically thin interfacial layers.

Effect of deposition temperature on morphological, magnetic and elastic properties of ultrathin Co49Pt51 films

NASA Astrophysics Data System (ADS)

Si Abdallah, F.; Chérif, S. M.; Bouamama, Kh.; Roussigné, Y.; Hsu, J.-H.

2018-03-01

Morphological, magnetic and elastic properties of 5 nm-thick Co49Pt51 films, sputtered on glass substrates, with 20 nm-thick Ta (seed) and Pt (buffer) layers were studied as function of the deposition temperature Td ranging between room temperature and 350° C. Atomic and magnetic force microscopy, vibrating sample magnetometer and Brillouin light scattering techniques were used to investigate the root mean square (RMS) roughness, the magnetic domain configuration, the coercive field (Hc), the perpendicular magnetic anisotropy (PMA), and the dynamic magnetic and elastic properties of the films with Td. The results show that surface uniformity was enhanced since the RMS roughness decreases with Td while magnetic domains typical of films with high PMA are observed. Hc and PMA are found to sensibly increase with Td. The dynamic magnetization behavior is characterized by magnetic modes related with the co-existence of hard and soft magnetic areas within the samples. The elastic properties of the stack were first analyzed by means of a model describing the main variation of the elastic wave frequencies within the frame of weighted average thickness, density, Young's modulus and Poisson coefficient of all the layers constituting the stacks. However, while Hc and PMA keep increasing with Td, a more precise experimental analysis of the mechanical behavior shows that the group velocity starts increasing and finally decreases with Td, suggesting that knowledge of the influence of Td on the mechanical properties of each individual layer composing the stack is required to obtain a more accurate analysis.

Adiabatic bulk modulus of elasticity for 2D liquid dusty plasmas

NASA Astrophysics Data System (ADS)

Feng, Yan; Huang, Dong; Li, Wei

2018-05-01

From the recently obtained equation of state (EOS) for two-dimensional (2D) liquid dusty plasmas, their various physical quantities have been derived analytically, such as the specific heat CV, the Grüneisen parameter, the bulk modulus of elasticity, and the isothermal compressibility. Here, the coefficient of volumetric thermal expansion αV and the relative pressure coefficient αP of 2D liquid dusty plasmas are derived from their EOS. Using the obtained CV, αV, and αP, the analytical expression of their heat capacity under constant-pressure conditions CP is obtained. Thus, the heat capacity ratio, expressed as CP/CV , is analytically achieved. Then the adiabatic bulk modulus of elasticity is derived, so that the adiabatic sound speeds are obtained. These obtained results are compared with previous findings using a different approach.

Amputee socks: Sock thickness changes with normal use.

PubMed

Cagle, John C; D'Silva, Krittika J; Hafner, Brian J; Harrison, Daniel S; Sanders, Joan E

2016-06-01

Prosthetic socks are expected to decrease in thickness and have reduced volume accommodation with normal use. It is unknown, however, to what degree they reduce in thickness over time. The goal of this study was to determine a correlation between the age of a prosthetic sock (defined as the out-of-package time) and the resulting change in thickness under standardized weight-bearing and non-weight-bearing conditions. Experimental, mechanical assessment. Used prosthetic socks were donated by donors with transtibial amputation. Sock thickness was measured on a custom instrument under conditions representative of normal use. Stress-thickness response was compared to that of equivalent new socks to quantify the effects of use on sock performance. Sock thickness changed non-linearly over time. On average, socks were 75% ± 17% of their initial thickness after 1 month, while socks older than 1 month were 72% ± 18% of their initial thickness. The elasticity of socks did not change with age. The volume accommodation provided by used socks cannot be reliably predicted by ply or age. Direct measurement of total sock thickness may provide meaningful insight to quantify prosthetic users' socket fit and guide volume accommodation recommendations. The mean difference in thickness between 3-ply and 5-ply used socks was equal to the standard deviation of each ply group (0.3mm). Therefore, it is possible that a 3-ply sock worn for as a little as 1 month could have a greater thickness than a 5-ply sock worn for a month. © The International Society for Prosthetics and Orthotics 2015.

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

NASA Astrophysics Data System (ADS)

Gula, I. A.; Samsonov, A. M.

2017-12-01

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.

Biomechanical implications of cortical elastic properties of the macaque mandible.

PubMed

Dechow, Paul C; Panagiotopoulou, Olga; Gharpure, Poorva

2017-10-01

Knowledge of the variation in the elastic properties of mandibular cortical bone is essential for modeling bone function. Our aim was to characterize the elastic properties of rhesus macaque mandibular cortical bone and compare these to the elastic properties from mandibles of dentate humans and baboons. Thirty cylindrical samples were harvested from each of six adult female rhesus monkey mandibles. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived from ultrasound velocity measurements. Further velocity measurements with longitudinal and transverse ultrasonic transducers along with measurements of bone density were used to compute three-dimensional cortical elastic properties using equations based on Hooke's law. Results showed regional variations in the elastic properties of macaque mandibular cortical bone that have both similarities and differences with that of humans and baboons. So far, the biological and structural basis of these differences is poorly understood. Copyright © 2017 Elsevier GmbH. All rights reserved.

Investigation of PDMS based bi-layer elasticity via interpretation of apparent Young's modulus.

PubMed

Sarrazin, Baptiste; Brossard, Rémy; Guenoun, Patrick; Malloggi, Florent

2016-02-21

As the need of new methods for the investigation of thin films on various kinds of substrates becomes greater, a novel approach based on AFM nanoindentation is explored. Substrates of polydimethylsiloxane (PDMS) coated by a layer of hard material are probed with an AFM tip in order to obtain the force profile as a function of the indentation. The equivalent elasticity of those composite systems is interpreted using a new numerical approach, the Coated Half-Space Indentation Model of Elastic Response (CHIMER), in order to extract the thicknesses of the upper layer. Two kinds of coating are investigated. First, chitosan films of known thicknesses between 30 and 200 nm were probed in order to test the model. A second type of samples is produced by oxygen plasma oxidation of the PDMS substrate, which results in the growth of a relatively homogeneous oxide layer. The local nature of this protocol enables measurements at long oxidation time, where the apparition of cracks prevents other kinds of measurements.

Ultrasound Elasticity Imaging Predicts Therapeutic Outcomes of Patients With Crohn's Disease Treated With Anti-Tumour Necrosis Factor Antibodies.

PubMed

Orlando, Stefania; Fraquelli, Mirella; Coletta, Marina; Branchi, Federica; Magarotto, Andrea; Conti, Clara Benedetta; Mazza, Stefano; Conte, Dario; Basilisco, Guido; Caprioli, Flavio

2018-01-05

Ultrasound elasticity imaging is a non-invasive technique developed to evaluate fibrosis. Measuring tissue strain by ultrasound elasticity imaging can reliably detect severe ileal fibrosis in patients with Crohn's disease [CD]. We have hypothesised that a more severe range of fibrosis might influence the therapeutic response to anti-tumour necrosis factor [TNF] treatment. The aim of this study was to assess the ability of ultrasound elasticity imaging to predict the therapeutic outcome for CD patients. Consecutive patients with ileal/ileocolonic CD, starting anti-TNF treatment, were enrolled for the study. These patients underwent bowel ultrasound and ultrasound elasticity imaging at baseline and at 14 and 52 weeks after anti-TNF treatment. Bowel wall stiffness was quantified by calculating the strain ratio between the mesenteric tissue and the bowel wall. Strain ratio ≥ 2 was used to identify severe ileal fibrosis. Transmural healing at 14 and 52 weeks was defined as bowel wall thickness ≤ 3 mm. Thirty patients with CD were enrolled. Five patients underwent surgery for bowel obstruction. The frequency of surgeries was significantly greater in patients with a strain ratio ≥ 2 at baseline [p = 0.003]. A significant reduction of the bowel thickness was observed after 14 and 52 weeks of anti-TNF treatment [p < 0.005]. A significant inverse correlation was observed between the strain ratio values at baseline and the thickness variations following anti-TNF therapy [p = 0.007]; 27% of patients achieved transmural healing at 14 weeks. The baseline strain ratio was significantly lower in patients with transmural healing [p < 0.05]. This study shows that ultrasound elasticity imaging predicts therapeutic outcomes for CD patients treated with anti-TNF. Copyright © 2017 European Crohn’s and Colitis Organisation (ECCO). Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oup.com

Prediction of brain maturity based on cortical thickness at different spatial resolutions.

PubMed

Khundrakpam, Budhachandra S; Tohka, Jussi; Evans, Alan C

2015-05-01

Several studies using magnetic resonance imaging (MRI) scans have shown developmental trajectories of cortical thickness. Cognitive milestones happen concurrently with these structural changes, and a delay in such changes has been implicated in developmental disorders such as attention-deficit/hyperactivity disorder (ADHD). Accurate estimation of individuals' brain maturity, therefore, is critical in establishing a baseline for normal brain development against which neurodevelopmental disorders can be assessed. In this study, cortical thickness derived from structural magnetic resonance imaging (MRI) scans of a large longitudinal dataset of normally growing children and adolescents (n=308), were used to build a highly accurate predictive model for estimating chronological age (cross-validated correlation up to R=0.84). Unlike previous studies which used kernelized approach in building prediction models, we used an elastic net penalized linear regression model capable of producing a spatially sparse, yet accurate predictive model of chronological age. Upon investigating different scales of cortical parcellation from 78 to 10,240 brain parcels, we observed that the accuracy in estimated age improved with increased spatial scale of brain parcellation, with the best estimations obtained for spatial resolutions consisting of 2560 and 10,240 brain parcels. The top predictors of brain maturity were found in highly localized sensorimotor and association areas. The results of our study demonstrate that cortical thickness can be used to estimate individuals' brain maturity with high accuracy, and the estimated ages relate to functional and behavioural measures, underscoring the relevance and scope of the study in the understanding of biological maturity. Copyright © 2015 Elsevier Inc. All rights reserved.

Differential cross sections in a thick brane world scenario

NASA Astrophysics Data System (ADS)

Pedraza, Omar; Arceo, R.; López, L. A.; Cerón, V. E.

2018-04-01

The elastic differential cross section is calculated at low energies for the elements He and Ne using an effective 4D electromagnetic potential coming from the contribution of the massive Kaluza-Klein modes of the 5D vector field in a thick brane scenario. The length scale is adjusted in the potential to compare with known experimental data and to set bounds for the parameter of the model.

Numerical Analysis of the Elastic Properties of 3D Needled Carbon/Carbon Composites

NASA Astrophysics Data System (ADS)

Tan, Y.; Yan, Y.; Li, X.; Guo, F.

2017-09-01

Based on the observation of microstructures of 3D needled carbon/carbon (C/C) composites, a model of their representative volume element (RVE) considering the true distribution of fibers is established. Using the theories of mesoscopic mechanics and introducing periodic boundary conditions for displacements, their elastic properties, with account of porosity, are determined by finite-element methods. Quasi-static tensile tests were carried out, and the numerical predictions were found to be in good agreement with test results. This means that the RVE model of 3D needled C/C composites can predict their elastic properties efficiently. The effects of needling density, radius of needled fibers, and thickness ratio of a short-cut fiber web and a weftless ply on the elastic constants of the composites are analyzed.

Least-squares reverse time migration in elastic media

NASA Astrophysics Data System (ADS)

Ren, Zhiming; Liu, Yang; Sen, Mrinal K.

2017-02-01

Elastic reverse time migration (RTM) can yield accurate subsurface information (e.g. PP and PS reflectivity) by imaging the multicomponent seismic data. However, the existing RTM methods are still insufficient to provide satisfactory results because of the finite recording aperture, limited bandwidth and imperfect illumination. Besides, the P- and S-wave separation and the polarity reversal correction are indispensable in conventional elastic RTM. Here, we propose an iterative elastic least-squares RTM (LSRTM) method, in which the imaging accuracy is improved gradually with iteration. We first use the Born approximation to formulate the elastic de-migration operator, and employ the Lagrange multiplier method to derive the adjoint equations and gradients with respect to reflectivity. Then, an efficient inversion workflow (only four forward computations needed in each iteration) is introduced to update the reflectivity. Synthetic and field data examples reveal that the proposed LSRTM method can obtain higher-quality images than the conventional elastic RTM. We also analyse the influence of model parametrizations and misfit functions in elastic LSRTM. We observe that Lamé parameters, velocity and impedance parametrizations have similar and plausible migration results when the structures of different models are correlated. For an uncorrelated subsurface model, velocity and impedance parametrizations produce fewer artefacts caused by parameter crosstalk than the Lamé coefficient parametrization. Correlation- and convolution-type misfit functions are effective when amplitude errors are involved and the source wavelet is unknown, respectively. Finally, we discuss the dependence of elastic LSRTM on migration velocities and its antinoise ability. Imaging results determine that the new elastic LSRTM method performs well as long as the low-frequency components of migration velocities are correct. The quality of images of elastic LSRTM degrades with increasing noise.

Hypo-Elastic Model for Lung Parenchyma

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

Freed, Alan D.; Einstein, Daniel R.

2012-03-01

A simple elastic isotropic constitutive model for the spongy tissue in lung is derived from the theory of hypoelasticity. The model is shown to exhibit a pressure dependent behavior that has been interpreted by some as indicating extensional anisotropy. In contrast, we show that this behavior arises natural from an analysis of isotropic hypoelastic invariants, and is a likely result of non-linearity, not anisotropy. The response of the model is determined analytically for several boundary value problems used for material characterization. These responses give insight into both the material behavior as well as admissible bounds on parameters. The model ismore » characterized against published experimental data for dog lung. Future work includes non-elastic model behavior.« less

Pressure Dependences of Elastic Constants of AMg6 Aluminum-Magnesium Alloy and n-AMg6/C60 Nanocomposite Alloy

NASA Astrophysics Data System (ADS)

Prokhorov, V. M.; Gromnitskaya, E. L.

2018-04-01

The ultrasonic study results for dependence of the elastic wave velocities and second-order elasticity coefficients of the polycrystalline aluminum alloy AMg6 and its nanocomposite n-AMg6/C60 on hydrostatic pressure up to 1.6 GPa have been described. The ultrasonic research has been carried out using a highpressure ultrasonic piezometer based on the piston-cylinder device. The pressure derivatives of the secondorder elastic constants of these materials established in the present study have been compared with the results of the third-order elastic constants measurements of the test alloys using the Thurston-Brugger method. Involving available literature data, we determined the relationships between the pressure derivatives of the second-order elastic constants of the AMg6 alloy and the Mg-content and nanostructuring.

Instabilities in dynamic anti-plane sliding of an elastic layer on a dissimilar elastic half-space

NASA Astrophysics Data System (ADS)

Kunnath, R.

2012-12-01

The stability of dynamic anti-plane sliding at an interface between an elastic layer and an elastic half-space with dissimilar elastic properties is studied. Friction at the interface is assumed to follow a rate- and state-dependent law, with a positive instantaneous dependence on slip velocity and a rate weakening behavior in the steady state. The perturbations are of the form exp(ikx+pt), where k is the wavenumber, x is the coordinate along the interface, p is the time response to the perturbation and t is time. The results of the stability analysis are shown in Figs. 1 and 2 with the velocity weakening parameter b/a=5, shear wave speed ratio cs'/cs=1.2, shear modulus ratio μ'/μ=1.2 and non-dimensional layer thickness H=100. The normalized instability growth rate and normalized phase velocity are plotted as a function of wavenumber. Fig.1 is for a non-dimensional unperturbed slip velocity ɛ=5 (rapid sliding) while Fig. 2 is for ɛ=0.05 (slow sliding). The results show the destabilization of interfacial waves. For slow sliding, destabilization of interfacial waves is still seen, indicating that the quasi-static approximation to slow sliding is not valid. This is in agreement with the result of Ranjith (Int. J. Solids and Struct., 2009, 46, 3086-3092) who predicted an instability of long-wavelength Love waves in slow sliding.

Development of a child head analytical dynamic model considering cranial nonuniform thickness and curvature - Applying to children aged 0-1 years old.

PubMed

Li, Zhigang; Ji, Cheng; Wang, Lishu

2018-07-01

Although analytical models have been used to quickly predict head response under impact condition, the existing models generally took the head as regular shell with uniform thickness which cannot account for the actual head geometry with varied cranial thickness and curvature at different locations. The objective of this study is to develop and validate an analytical model incorporating actual cranial thickness and curvature for child aged 0-1YO and investigate their effects on child head dynamic responses at different head locations. To develop the new analytical model, the child head was simplified into an irregular fluid-filled shell with non-uniform thickness and the cranial thickness and curvature at different locations were automatically obtained from CT scans using a procedure developed in this study. The implicit equation of maximum impact force was derived as a function of elastic modulus, thickness and radius of curvature of cranium. The proposed analytical model are compared with cadaver test data of children aged 0-1 years old and it is shown to be accurate in predicting head injury metrics. According to this model, obvious difference in injury metrics were observed among subjects with the same age, but different cranial thickness and curvature; and the injury metrics at forehead location are significant higher than those at other locations due to large thickness it owns. The proposed model shows good biofidelity and can be used in quickly predicting the dynamics response at any location of head for child younger than 1 YO. Copyright © 2018 Elsevier B.V. All rights reserved.

Mechanism of Rock Burst Occurrence in Specially Thick Coal Seam with Rock Parting

NASA Astrophysics Data System (ADS)

Wang, Jian-chao; Jiang, Fu-xing; Meng, Xiang-jun; Wang, Xu-you; Zhu, Si-tao; Feng, Yu

2016-05-01

Specially thick coal seam with complex construction, such as rock parting and alternative soft and hard coal, is called specially thick coal seam with rock parting (STCSRP), which easily leads to rock burst during mining. Based on the stress distribution of rock parting zone, this study investigated the mechanism, engineering discriminant conditions, prevention methods, and risk evaluation method of rock burst occurrence in STCSRP through setting up a mechanical model. The main conclusions of this study are as follows. (1) When the mining face moves closer to the rock parting zone, the original non-uniform stress of the rock parting zone and the advancing stress of the mining face are combined to intensify gradually the shearing action of coal near the mining face. When the shearing action reaches a certain degree, rock burst easily occurs near the mining face. (2) Rock burst occurrence in STCSRP is positively associated with mining depth, advancing stress concentration factor of the mining face, thickness of rock parting, bursting liability of coal, thickness ratio of rock parting to coal seam, and difference of elastic modulus between rock parting and coal, whereas negatively associated with shear strength. (3) Technologies of large-diameter drilling, coal seam water injection, and deep hole blasting can reduce advancing stress concentration factor, thickness of rock parting, and difference of elastic modulus between rock parting and coal to lower the risk of rock burst in STCSRP. (4) The research result was applied to evaluate and control the risk of rock burst occurrence in STCSRP.

Derivation of Nonlinear Wave Equation for Flexural Motions of AN Elastic Beam Travelling in AN Air-Filled Tube

NASA Astrophysics Data System (ADS)

Sugimoto, N.; Kugo, K.; Watanabe, Y.

2002-07-01

Asymptotic analysis is carried out to derive a nonlinear wave equation for flexural motions of an elastic beam of circular cross-section travelling along the centre-axis of an air-filled, circular tube placed coaxially. Both the beam and tube are assumed to be long enough for end-effects to be ignored and the aerodynamic loading on the lateral surface of the beam is considered. Assuming a compressible inviscid fluid, the velocity potential of the air is sought systematically in the form of power series in terms of the ratios of the tube radius to a wavelength and of a typical deflection to the radius. Evaluating the pressure force acting on the lateral surface of the beam, the aerodynamic loading including the effects of finite deflection as well as of air's compressibility and axial curvature of the beam are obtained. Although the nonlinearity arises from the kinematical condition on the beam surface, it may be attributed to the presence of the tube wall. With the aerodynamic loading thus obtained, a nonlinear wave equation is derived, whereas linear theory is assumed for the flexural motions of the beam. Some discussions are given on the results.

On determining dead layer and detector thicknesses for a position-sensitive silicon detector

NASA Astrophysics Data System (ADS)

Manfredi, J.; Lee, Jenny; Lynch, W. G.; Niu, C. Y.; Tsang, M. B.; Anderson, C.; Barney, J.; Brown, K. W.; Chajecki, Z.; Chan, K. P.; Chen, G.; Estee, J.; Li, Z.; Pruitt, C.; Rogers, A. M.; Sanetullaev, A.; Setiawan, H.; Showalter, R.; Tsang, C. Y.; Winkelbauer, J. R.; Xiao, Z.; Xu, Z.

2018-04-01

In this work, two particular properties of the position-sensitive, thick silicon detectors (known as the "E" detectors) in the High Resolution Array (HiRA) are investigated: the thickness of the dead layer on the front of the detector, and the overall thickness of the detector itself. The dead layer thickness for each E detector in HiRA is extracted using a measurement of alpha particles emitted from a 212Pb pin source placed close to the detector surface. This procedure also allows for energy calibrations of the E detectors, which are otherwise inaccessible for alpha source calibration as each one is sandwiched between two other detectors. The E detector thickness is obtained from a combination of elastically scattered protons and an energy-loss calculation method. Results from these analyses agree with values provided by the manufacturer.

Derivation of the out-of-plane behaviour of an English bond masonry wall through homogenization strategies

NASA Astrophysics Data System (ADS)

Silva, Luís Carlos; Milani, Gabriele; Lourenço, Paulo B.

2017-11-01

Two finite element homogenized-based strategies are presented for the out-of-plane behaviour characterization of an English bond masonry wall. A finite element micro-modelling approach using Cauchy stresses and first order movements are assumed for both strategies. The material nonlinearity is lumped on joints interfaces and bricks are considered elastic. Nevertheless, the first model is based on a Plane-stress assumption, in which the out-of-plane quantities are derived through on-thickness wall integration considering a Kirchhoff-plate theory. The second model is a tridimensional one, in which the homogenized out-of-plane quantities can be directly derived after solving the boundary value problem. The comparison is conducted by assessing the obtained out-of-plane bending- and torsion-curvature diagrams. A good agreement is found for the present study case.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

Variations in local elastic modulus along the length of the aorta as observed by use of a scanning haptic microscope (SHM).

PubMed

Moriwaki, Takeshi; Oie, Tomonori; Takamizawa, Keiichi; Murayama, Yoshinobu; Fukuda, Toru; Omata, Sadao; Kanda, Keiichi; Nakayama, Yasuhide

2011-12-01

Variations in microscopic elastic structures along the entire length of canine aorta were evaluated by use of a scanning haptic microscope (SHM). The total aorta from the aortic arch to the abdominal aorta was divided into 6 approximately equal segments. After embedding the aorta in agar, it was cut into horizontal circumferential segments to obtain disk-like agar portions containing ring-like samples of aorta with flat surfaces (thickness, approximately 1 mm). The elastic modulus and topography of the samples under no-load conditions were simultaneously measured along the entire thickness of the wall by SHM by using a probe with a diameter of 5 μm and a spatial resolution of 2 μm at a rate of 0.3 s/point. The elastic modulus of the wall was the highest on the side of the luminal surface and decreased gradually toward the adventitial side. This tendency was similar to that of the change in the elastin fiber content. During the evaluation of the mid-portion of each tunica media segment, the highest elastic modulus (40.8 ± 3.5 kPa) was identified at the thoracic section of the aorta that had the highest density of elastic fibers. Under no-load conditions, portions of the aorta with high elastin density have a high elastic modulus.

Postbuckling of magneto-electro-elastic CNT-MT composite nanotubes resting on a nonlinear elastic medium in a non-uniform thermal environment

NASA Astrophysics Data System (ADS)

Kamali, M.; Shamsi, M.; Saidi, A. R.

2018-03-01

As a first endeavor, the effect of nonlinear elastic foundation on the postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanotubes is investigated. The composite nanotube is affected by a non-uniform thermal environment. A typical MEE composite nanotube consists of microtubules (MTs) and carbon nanotubes (CNTs) with a MEE cylindrical nanoshell for smart control. It is assumed that the nanoscale layers of the system are coupled by a polymer matrix or filament network depending on the application. In addition to thermal loads, magneto-electro-mechanical loads are applied to the composite nanostructure. Length scale effects are taken into account using the nonlocal elasticity theory. The principle of virtual work and von Karman's relations are used to derive the nonlinear governing differential equations of MEE CNT-MT nanotubes. Using Galerkin's method, nonlinear critical buckling loads are determined. Various types of non-uniform temperature distribution in the radial direction are considered. Finally, the effects of various parameters such as the nonlinear constant of elastic medium, thermal loading factor and small scale coefficient on the postbuckling of MEE CNT-MT nanotubes are studied.

Local Elastic Constants for Epoxy-Nanotube Composites from Molecular Dynamics Simulation

NASA Technical Reports Server (NTRS)

Frankland, S. J. V.; Gates, T. S.

2007-01-01

A method from molecular dynamics simulation is developed for determining local elastic constants of an epoxy/nanotube composite. The local values of C11, C33, K12, and K13 elastic constants are calculated for an epoxy/nanotube composite as a function of radial distance from the nanotube. While the results possess a significant amount of statistical uncertainty resulting from both the numerical analysis and the molecular fluctuations during the simulation, the following observations can be made. If the size of the region around the nanotube is increased from shells of 1 to 6 in thickness, then the scatter in the data reduces enough to observe trends. All the elastic constants determined are at a minimum 20 from the center of the nanotube. The C11, C33, and K12 follow similar trends as a function of radial distance from the nanotube. The K13 decreases greater distances from the nanotube and becomes negative which may be a symptom of the statistical averaging.

Laser-ultrasound spectroscopy apparatus and method with detection of shear resonances for measuring anisotropy, thickness, and other properties

DOEpatents

Levesque, Daniel; Moreau, Andre; Dubois, Marc; Monchalin, Jean-Pierre; Bussiere, Jean; Lord, Martin; Padioleau, Christian

2000-01-01

Apparatus and method for detecting shear resonances includes structure and steps for applying a radiation pulse from a pulsed source of radiation to an object to generate elastic waves therein, optically detecting the elastic waves generated in the object, and analyzing the elastic waves optically detected in the object. These shear resonances, alone or in combination with other information, may be used in the present invention to improve thickness measurement accuracy and to determine geometrical, microstructural, and physical properties of the object. At least one shear resonance in the object is detected with the elastic waves optically detected in the object. Preferably, laser-ultrasound spectroscopy is utilized to detect the shear resonances.

Gurtin-Murdoch surface elasticity theory revisit: An orbital-free density functional theory perspective

NASA Astrophysics Data System (ADS)

Zhu, Yichao; Wei, Yihai; Guo, Xu

2017-12-01

In the present paper, the well-established Gurtin-Murdoch theory of surface elasticity (Gurtin and Murdoch, 1975, 1978) is revisited from an orbital-free density functional theory (OFDFT) perspective by taking the boundary layer into consideration. Our analysis indicates that firstly, the quantities introduced in the Gurtin-Murdoch theory of surface elasticity can all find their explicit expressions in the derived OFDFT-based theoretical model. Secondly, the derived expression for surface energy density captures a competition between the surface normal derivatives of the electron density and the electrostatic potential, which well rationalises the onset of signed elastic constants that are observed both experimentally and computationally. Thirdly, the established model naturally yields an inversely linear relationship between the materials surface stiffness and its size, which conforms to relevant findings in literature. Since the proposed OFDFT-based model is established under arbitrarily imposed boundary condition of electron density, electrostatic potential and external load, it also has the potential of being used to investigate the electro-mechanical behaviour of nanoscale materials manifesting surface effect.

Damping of short gravity-capillary waves due to oil derivatives film on the water surface

NASA Astrophysics Data System (ADS)

Sergievskaya, Irina; Ermakov, Stanislav; Lazareva, Tatyana

2016-10-01

In this paper new results of laboratory studies of damping of gravity-capillary waves on the water surface covered by kerosene are presented and compared with our previous analysis of characteristics of crude oil and diesel fuel films. Investigations of kerosene films were carried out in a wide range values of film thicknesses (from some hundreds millimetres to a few millimetres) and in a wide range of surface wave frequencies (from 10 to 27 Hz). The selected frequency range corresponds to the operating wavelengths of microwave, X- to Ka-band radars typically used for the ocean remote sensing. The studied range of film thickness covers typical thicknesses of routine spills in the ocean. It is obtained that characteristics of waves, measured in the presence of oil derivatives films differ from those for crude oil films, in particular, because the volume viscosity of oil derivatives and crude oil is strongly different. To retrieve parameters of kerosene films from the experimental data the surface wave damping was analyzed theoretically in the frame of a model of two-layer fluid. The films are assumed to be soluble, so the elasticity on the upper and lower boundaries is considered as a function of wave frequency. Physical parameters of oil derivative films were estimated when tuning the film parameters to fit theory and experiment. Comparison between wave damping due to crude oil, kerosene and diesel fuel films have shown some capabilities of distinguishing of oil films from remote sensing of short surface waves.

Predicting gravity and sediment thickness in Afghanistan

NASA Astrophysics Data System (ADS)

Jung, W.; Brozena, J.; Peters, M.

2013-02-01

wavelength 132 km which is approximately equivalent to the reported safe degree and order 250 of GOCO02S at 34º N) combined airborne free-air anomalies. The rms difference between the two data sets was 12.4 mGal. The observed admittance in the western Afghanistan mountains appears to be best fit to a theoretical elastic plate compensation model (with an effective elastic thickness of 5 km and crustal thickness of 22 km) where the ratio between surface load and subsurface load is equal.

Influence of different surfactants on the physicochemical properties of elastic liposomes.

PubMed

Barbosa, R M; Severino, P; Preté, P S C; Santana, M H A

2017-05-01

Elastic liposomes are capable to improve drug transport through the skin by acting as penetration enhancers due to the high fluidity and elasticity of the liposome membranes. Therefore, elastic liposomes were prepared and characterized to facilitate the transdermal transport of bioactive molecules. Liposomes consisted of dimyristoylphosphatidylcholine (DMPC) as the structural component, with different surfactants derived from lauric acid as elastic components: C 12 E 5 (polyoxyethylene-5-lauryl ether), PEG4L (polyethyleneglycol-4-lauryl ester), PEG4DL (polyethylene glycol-4-dilauryl ester), PEG8L (polyethylene glycol-8-lauryl ester) and PEG8DL (polyethylene glycol-8-dilauryl ester). The elastic liposomes were characterized in terms of their phospholipid content, mean diameter, size distribution, elasticity and stability during storage, as well as their ability to incorporate surfactant and permeate through 50 nm pore size membranes. The results showed that the phospholipid phase transition temperature, the fluidity of the lipid bilayer resulting from incorporation of the surfactant and the preservation of particle integrity were factors determining the performance of the elastic liposomes in permeating through nanoporous membranes. The best results were obtained using DMPC combined with the surfactants PEG8L or PEG8DL. The findings demonstrate the potential of using elastic liposomes for transdermal administration of drugs.

Thickness measurement by two-sided step-heating thermal imaging

NASA Astrophysics Data System (ADS)

Li, Xiaoli; Tao, Ning; Sun, J. G.; Zhang, Cunlin; Zhao, Yuejin

2018-01-01

Infrared thermal imaging is a promising nondestructive technique for thickness prediction. However, it is usually thought to be only appropriate for testing the thickness of thin objects or near-surface structures. In this study, we present a new two-sided step-heating thermal imaging method which employed a low-cost portable halogen lamp as the heating source and verified it with two stainless steel step wedges with thicknesses ranging from 5 mm to 24 mm. We first derived the one-dimensional step-heating thermography theory with the consideration of warm-up time of the lamp, and then applied the nonlinear regression method to fit the experimental data by the derived function to determine the thickness. After evaluating the reliability and accuracy of the experimental results, we concluded that this method is capable of testing thick objects. In addition, we provided the criterions for both the required data length and the applicable thickness range of the testing material. It is evident that this method will broaden the thermal imaging application for thickness measurement.

Determining elastic moduli of materials in pavement systems by surface deflection data : a feasibility study.

DOT National Transportation Integrated Search

1975-01-01

The determination of the elastic, or Young's, modulus, E, of the materials in each layer in an n-layered pavement system given the number, order, thicknesses, and Poisson's ratios of the layers, and the surface load and deflection data, is not possib...

Theoretical investigations on structural, elastic and electronic properties of thallium halides

NASA Astrophysics Data System (ADS)

Singh, Rishi Pal; Singh, Rajendra Kumar; Rajagopalan, Mathrubutham

2011-04-01

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.

Single-Crystal Elasticity of Iron-Bearing Bridgemanite in the Lower Mantle

NASA Astrophysics Data System (ADS)

Yang, J.; Lin, J. F.; Okuchi, T.; Tomioka, N.

2014-12-01

Bridgemanite is believed to be the most abundant mineral in the Earth's lower mantle. Knowing its elasticity is thus critical to our understanding of the lower-mantle seismology, geochemistry, and geophysics. Although single-crystal elasticity and elastic anisotropy of bridgemanite under high P-T have been reported theoretically, experimental results on the single-crystal elasticity of bridgemanite remain very limited[1, 2]. Published experimental results have been limited to ambient conditions due to technical challenges in high-pressure measurements to permit derivations of all nine elastic constants (C11, C22, C33, C44, C55, C66, C12, C23 and C13) of the crystal. A thorough understanding of the elastic properties of bridgemanite at relevant lower mantle conditions, as well as the effects of iron, is essentially needed to interpret seismic observations and to construct a reliable mineralogical and geochemical model. In order to solve all individual elastic constants of bridgemanite at high pressures via Christoffel's equations, we employed both Brillouin Light Scattering (BLS) which is sensitive to shear wave velocities (Vs) up to megabars, and Impulsive Stimulated Light Scattering (ISS) which is sensitive to compressional wave velocities (VP) at lower mantle pressures. The BLS and ISS allowed us to measure VP and VS sound velocities as a function of the azimuthal angle from two orientated single-crystal iron bearing bridgemanite platelets under lower mantle pressures. These experimental results permit the derivations of full elastic constants of single-crystal bridgemanite that are consistent with previous theoretical studies [3, 4]. We will discuss how pressure-temperature, as well as the iron spin/valence states and minor element aluminum, affect the single-crystal elasticity and seismic parameters (e.g. VP and VS anisotropy AVP, AVS) at lower mantle conditions. Within a pyrolite mineralogical model, these results are extrapolated using a thermoelastic model

Elastic torsional buckling of thin-walled composite cylinders

NASA Technical Reports Server (NTRS)

Marlowe, D. E.; Sushinsky, G. F.; Dexter, H. B.

1974-01-01

The elastic torsional buckling strength has been determined experimentally for thin-walled cylinders fabricated with glass/epoxy, boron/epoxy, and graphite/epoxy composite materials and composite-reinforced aluminum and titanium. Cylinders have been tested with several unidirectional-ply orientations and several cross-ply layups. Specimens were designed with diameter-to-thickness ratios of approximately 150 and 300 and in two lengths of 10 in. and 20 in. The results of these tests were compared with the buckling strengths predicted by the torsional buckling analysis of Chao.

Governing equations for 1D opto-mechanical vibrations of elastic cubical micro-resonators

NASA Astrophysics Data System (ADS)

Sobhani, Hassan; Zohrabi, Mehdi

2018-03-01

In this paper by employing the Lagrangian method, the effect of the radiation pressure on the coupling between the optical and mechanical modes in an elastic cavity is surveyed. The radiation pressure couldn't be considered as an external force because the electromagnetic waves are non-separable part of the elastic media. Due to the deformation of elastic media, the electromagnetic waves is modified as a result of the element velocity. To consider the electromagnetic evolution, it is preferred to employ the Lagrangian method instead of the second Newton's law. Here, using an elastic frame, governing equations on opto-mechanical oscillations in an elastic media are derived. In a specific case, by comparing the results to the other methods, it shown that this method is more accurate because the exchange of electromagnetic waves by regarding the movement of the elastic media due to deform is considered.

Analysis of Agreement of Retinal-Layer Thickness Measures Derived from the Segmentation of Horizontal and Vertical Spectralis OCT Macular Scans.

PubMed

Gonzalez Caldito, Natalia; Antony, Bhavna; He, Yufan; Lang, Andrew; Nguyen, James; Rothman, Alissa; Ogbuokiri, Esther; Avornu, Ama; Balcer, Laura; Frohman, Elliot; Frohman, Teresa C; Bhargava, Pavan; Prince, Jerry; Calabresi, Peter A; Saidha, Shiv

2018-03-01

Optical coherence tomography (OCT) is a reliable method used to quantify discrete layers of the retina. Spectralis OCT is a device used for this purpose. Spectralis OCT macular scan imaging acquisition can be obtained on either the horizontal or vertical plane. The vertical protocol has been proposed as favorable, due to postulated reduction in confound of Henle's fibers on segmentation-derived metrics. Yet, agreement of the segmentation measures of horizontal and vertical macular scans remains unexplored. Our aim was to determine this agreement. Horizontal and vertical macular scans on Spectralis OCT were acquired in 20 healthy controls (HCs) and 20 multiple sclerosis (MS) patients. All scans were segmented using Heidelberg software and a Johns Hopkins University (JHU)-developed method. Agreement was analyzed using Bland-Altman analyses and intra-class correlation coefficients (ICCs). Using both segmentation techniques, mean differences (agreement at the cohort level) in the thicknesses of all macular layers derived from both acquisition protocols in MS patients and HCs were narrow (<1 µm), while the limits of agreement (LOA) (agreement at the individual level) were wider. Using JHU segmentation mean differences (and LOA) for the macular retinal nerve fiber layer (RNFL) and ganglion cell layer + inner plexiform layer (GCIP) in MS were 0.21 µm (-1.57-1.99 µm) and -0.36 µm (-1.44-1.37 µm), respectively. OCT segmentation measures of discrete retinal-layer thicknesses derived from both vertical and horizontal protocols on Spectralis OCT agree excellently at the cohort level (narrow mean differences), but only moderately at the individual level (wide LOA). This suggests patients scanned using either protocol should continue to be scanned with the same protocol. However, due to excellent agreement at the cohort level, measures derived from both acquisitions can be pooled for outcome purposes in clinical trials.

Third harmonic ac susceptibility of superconductors with finite thickness

NASA Astrophysics Data System (ADS)

Qin, M. J.; Ong, C. K.

Third harmonic ac susceptibility of superconducting strips with finite thickness in perpendicularly applied magnetic field Ha = H0 sin(ω t) have been calculated. The flux creep effect is taken into account by using a power-law electric field E( j) = Ec( j/ jc) n. Results for different thicknesses and creep exponents n have been derived and compared to the results derived from the Bean critical state model.

Ab initio elastic tensor of cubic Ti0.5Al0.5N alloys: Dependence of elastic constants on size and shape of the supercell model and their convergence

NASA Astrophysics Data System (ADS)

Tasnádi, Ferenc; Odén, M.; Abrikosov, Igor A.

2012-04-01

In this study we discuss the performance of the special quasirandom structure (SQS) method in predicting the elastic properties of B1 (rocksalt) Ti0.5Al0.5N alloy. We use a symmetry-based projection technique, which gives the closest cubic approximate of the elastic tensor and allows us to align the SQSs of different shapes and sizes for a comparison in modeling elastic tensors. We show that the derived closest cubic approximate of the elastic tensor converges faster with respect to SQS size than the elastic tensor itself. That establishes a less demanding computational strategy to achieve convergence for the elastic constants. We determine the cubic elastic constants (Cij) and Zener's type elastic anisotropy (A) of Ti0.5Al0.5N. Optimal supercells, which capture accurately both the configurational disorder and cubic symmetry of elastic tensor, result in C11=447 GPa, C12=158 GPa, and C44=203 GPa with 3% of error and A=1.40 with 6% of error. In addition, we establish the general importance of selecting proper SQS with symmetry arguments to reliably model elasticity of alloys. We suggest the calculation of nine elastic tensor elements: C11, C22, C33, C12, C13, C23, C44, C55, and C66, to analyze the performance of SQSs and predict elastic constants of cubic alloys. The described methodology is general enough to be extended for alloys with other symmetry at arbitrary composition.

Propagation of acoustic-gravity waves in arctic zones with elastic ice-sheets

NASA Astrophysics Data System (ADS)

Kadri, Usama; Abdolali, Ali; Kirby, James T.

2017-04-01

We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation, as postulated by Refs. [1, 3]. References [1] U. Kadri, 2016. Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones. Advances in Acoustics and Vibration, 2016, Article ID 8076108, 7 pages http://dx.doi.org/10.1155/2016/8076108 [2] A. Abdolali, J. T. Kirby and G. Bellotti, 2015, Depth-integrated equation for hydro-acoustic waves with bottom damping, J. Fluid Mech., 766, R1 doi:10.1017/jfm.2015.37 [3] U. Kadri, 2014. Deep ocean water transportation by acoustic?gravity waves. J. Geophys. Res. Oceans, 119, doi:10.1002/ 2014JC010234

Quantitative Estimation of Seismic Velocity Changes Using Time-Lapse Seismic Data and Elastic-Wave Sensitivity Approach

NASA Astrophysics Data System (ADS)

Denli, H.; Huang, L.

2008-12-01

Quantitative monitoring of reservoir property changes is essential for safe geologic carbon sequestration. Time-lapse seismic surveys have the potential to effectively monitor fluid migration in the reservoir that causes geophysical property changes such as density, and P- and S-wave velocities. We introduce a novel method for quantitative estimation of seismic velocity changes using time-lapse seismic data. The method employs elastic sensitivity wavefields, which are the derivatives of elastic wavefield with respect to density, P- and S-wave velocities of a target region. We derive the elastic sensitivity equations from analytical differentiations of the elastic-wave equations with respect to seismic-wave velocities. The sensitivity equations are coupled with the wave equations in a way that elastic waves arriving in a target reservoir behave as a secondary source to sensitivity fields. We use a staggered-grid finite-difference scheme with perfectly-matched layers absorbing boundary conditions to simultaneously solve the elastic-wave equations and the elastic sensitivity equations. By elastic-wave sensitivities, a linear relationship between relative seismic velocity changes in the reservoir and time-lapse seismic data at receiver locations can be derived, which leads to an over-determined system of equations. We solve this system of equations using a least- square method for each receiver to obtain P- and S-wave velocity changes. We validate the method using both surface and VSP synthetic time-lapse seismic data for a multi-layered model and the elastic Marmousi model. Then we apply it to the time-lapse field VSP data acquired at the Aneth oil field in Utah. A total of 10.5K tons of CO2 was injected into the oil reservoir between the two VSP surveys for enhanced oil recovery. The synthetic and field data studies show that our new method can quantitatively estimate changes in seismic velocities within a reservoir due to CO2 injection/migration.

Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells

NASA Astrophysics Data System (ADS)

Marchuk, A. V.; Gnedash, S. V.; Levkovskii, S. A.

2017-03-01

Two approaches to studying the free and forced axisymmetric vibrations of cylindrical shell are proposed. They are based on the three-dimensional theory of elasticity and division of the original cylindrical shell with concentric cross-sectional circles into several coaxial cylindrical shells. One approach uses linear polynomials to approximate functions defined in plan and across the thickness. The other approach also uses linear polynomials to approximate functions defined in plan, but their variation with thickness is described by the analytical solution of a system of differential equations. Both approaches have approximation and arithmetic errors. When determining the natural frequencies by the semi-analytical finite-element method in combination with the divide and conqure method, it is convenient to find the initial frequencies by the finite-element method. The behavior of the shell during free and forced vibrations is analyzed in the case where the loading area is half the shell thickness

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

NASA Astrophysics Data System (ADS)

McGee, O. G.; Kim, J. W.

2010-02-01

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of " edge functions" that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1- c/ a), and the notch angle is defined as (360°- α). For a very small notch angle (1° or less), the notch may be regarded as a "sharp radial crack." Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°- α), depths (1- c/ a), and thickness ratios ( a/ h for plates and h/ a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and

Elastic Properties of Pore-Spanning Apical Cell Membranes Derived from MDCK II Cells.

PubMed

Nehls, Stefan; Janshoff, Andreas

2017-10-17

The mechanical response of adherent, polarized cells to indentation is frequently attributed to the presence of an endogenous actin cortex attached to the inner leaflet of the plasma membrane. Here, we scrutinized the elastic properties of apical membranes separated from living cells and attached to a porous mesh in the absence of intracellular factors originating from the cytosol, organelles, the substrate, neighbors, and the nucleus. We found that a tension-based model describes the data very well providing essentially the prestress of the shell generated by adhesion of the apical membrane patches to the pore rim and the apparent area compressibility modulus, an intrinsic elastic modulus modulated by the surface excess stored in membrane reservoirs. Removal of membrane-associated proteins by proteases decreases the area compressibility modulus, whereas fixation and cross-linking of proteins with glutaraldehyde increases it. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Formulas for the elastic constants of plates with integral waffle-like stiffening

NASA Technical Reports Server (NTRS)

Dow, Norris R; Libove, Charles; Hubka, Ralph E

1954-01-01

Formulas are derived for the fifteen elastic constants associated with bending, stretching, twisting, and shearing of plates with closely spaced integral ribbing in a variety of configurations and proportions. In the derivation the plates are considered, conceptually, as more uniform orthotropic plates somewhat on the order of plywood. The constants, which include the effectiveness of the ribs for resisting deformations other than bending and stretching in their longitudinal directions, are defined in terms of four coefficients, and theoretical and experimental methods for the evaluation of these coefficients are discussed. Four of the more important elastic constants are predicted by these formulas and are compared with test results. Good correlation is obtained. (author)

The effects of cortical bone thickness and trabecular bone strength on noninvasive measures of the implant primary stability using synthetic bone models.

PubMed

Hsu, Jui-Ting; Fuh, Lih-Jyh; Tu, Ming-Gene; Li, Yu-Fen; Chen, Kuan-Ting; Huang, Heng-Li

2013-04-01

This study investigated how the primary stability of a dental implant as measured by the insertion torque value (ITV), Periotest value (PTV), and implant stability quotient (ISQ) is affected by varying thicknesses of cortical bone and strengths of trabecular bone using synthetic bone models. Four synthetic cortical shells (with thicknesses of 0, 1, 2, and 3 mm) were attached to four cellular rigid polyurethane foams (with elastic moduli of 137, 47.5, 23, and 12.4 MPa) and one open-cell rigid polyurethane foam which mimic the osteoporotic bone (with an elastic modulus 6.5 MPa), to represent the jawbones with various cortical bone thicknesses and strengths of trabecular bone. A total of 60 bone specimens accompanied with implants was examined by a torque meter, Osstell resonance frequency analyzer, and Periotest electronic device. All data were statistically analyzed by two-way analysis of variance. In addition, second-order nonlinear regression was utilized to assess the correlations of the primary implant stability with the four cortex thicknesses and five strengths of trabecular bone. ITV, ISQ, and PTV differed significantly (p < .05) and were strongly correlated with the thickness of cortical bone (R(2) > 0.9) and the elastic modulus of trabecular bone (R(2) = 0.74-0.99). The initial stability at the time of implant placement is influenced by both the cortical bone thickness and the strength of trabecular bone; however, these factors are mostly nonlinearly correlated with ITV, PTV, and ISQ. Using ITV and PTV seems more suitable for identifying the primary implant stability in osteoporotic bone with a thin cortex. © 2011 Wiley Periodicals, Inc.

Internal resonance of an elastic body levitated above high-Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Kokuzawa, T.; Toshihiko, S.; Yoshizawa, M.

2010-06-01

In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.

Torsion of a Cosserat elastic bar with square cross section: theory and experiment

NASA Astrophysics Data System (ADS)

Drugan, W. J.; Lakes, R. S.

2018-04-01

An approximate analytical solution for the displacement and microrotation vector fields is derived for pure torsion of a prismatic bar with square cross section comprised of homogeneous, isotropic linear Cosserat elastic material. This is accomplished by analytical simplification coupled with use of the principle of minimum potential energy together with polynomial representations for the desired field components. Explicit approximate expressions are derived for cross section warp and for applied torque versus angle of twist of the bar. These show that torsional rigidity exceeds the classical elasticity value, the difference being larger for slender bars, and that cross section warp is less than the classical amount. Experimental measurements on two sets of 3D printed square cross section polymeric bars, each set having a different microstructure and four different cross section sizes, revealed size effects not captured by classical elasticity but consistent with the present analysis for physically sensible values of the Cosserat moduli. The warp can allow inference of Cosserat elastic constants independently of any sensitivity the material may have to dilatation gradients; warp also facilitates inference of Cosserat constants that are difficult to obtain via size effects.

Interfacial profiles in fluid/liquid systems: a description based on the storing of elastic energy.

PubMed

Castellanos-Suárez, Aly J; Toro-Mendoza, Jhoan; García-Sucre, Máximo

2011-06-01

An analytical expression for the interfacial energy is found by solving a Poisson equation and assuming a Boltzmann distribution of volume elements forming the fluid/liquid system. Interfacial phenomena are treated as a result of the response of a liquid when it makes contact with other fluid phase, in order to reach thermal and mechanical equilibrium. This model gives a quantitative description of the interface, obtaining values for its molar, force and energy density profiles. Also, our model allows the determination of the proportion of the fluids present in the interfacial zone, the values of interfacial tension and thickness. In the case of water+n-alkanes systems, the tensions are in agreement with the behavior shown by the experimental data. Finally, the values for interfacial thickness predicted from molar density profiles are lower than the range of influence of the elastic energy and elastic field. Copyright © 2011 Elsevier Inc. All rights reserved.

Elastic properties of single-walled carbon nanotube thin film by nanoindentation test.

PubMed

Tang, Xingling; El-Hami, Abdelkhalak; El-Hami, Khalil; Eid, Mohamed; Si, Chaorun

2017-09-12

This paper carries out a preliminary study for the elastic properties of single walled carbon nanotube (SWCNT) thin film. The SWCNT thin films (~250 nm) are prepared by a simple and cost effective method of spin-coating technology. Nanoindentation test with a Berkovich indenter is used to determine the hardness and elastic modulus of the SWCNT thin film. It is important to note that the elastic properties of SWCNT film are indirectly derived from the information of load and displacement of the indenter under certain assumptions, deviation of the 'test value' is inevitable. In this regard, uncertainty analysis is an effective process in guarantying the validity of the material properties. This paper carries out uncertainty estimation for the tested elastic properties of SWCNT film by nanoindentation. Experimental results and uncertainty analysis indicates that nanoindentation test could be an effective and reliable method in determine the elastic properties of SWCNT thin film. Moreover, the obtained values of hardness and elastic modulus can further benefit the design of SWCNT thin film based components.

Serum Factors from Pseudoxanthoma Elasticum Patients Alter Elastic Fiber Formation In Vitro

PubMed Central

Le Saux, Olivier; Bunda, Severa; VanWart, Christopher M.; Douet, Vanessa; Got, Laurence; Martin, Ludovic; Hinek, Aleksander

2017-01-01

Pseudoxanthoma elasticum (PXE) is a heritable disorder mainly characterized by calcified elastic fibers in cutaneous, ocular, and vascular tissues. PXE is caused by mutations in ABCC6, a gene encoding an ABC transporter predominantly expressed in liver and kidneys. The functional relationship between ABCC6 and elastic fiber calcification is unknown. We speculated that ABCC6 deficiency in PXE patients induces a persistent imbalance in circulating metabolite(s), which may impair the synthetic abilities of normal elastoblasts or specifically alter elastic fiber assembly. Therefore, we compared the deposition of elastic fiber proteins in cultures of fibroblasts derived from PXE and unaffected individuals. PXE fibroblasts cultured with normal human serum expressed and deposited increased amounts of proteins, but structurally normal elastic fibers. Interestingly, normal and PXE fibroblasts as well as normal smooth muscle cells deposited abnormal aggregates of elastic fibers when maintained in the presence of serum from PXE patients. The expression of tropoelastin and other elastic fiber-associated genes was not significantly modulated by the presence of PXE serum. These results indicated that certain metabolites present in PXE sera interfered with the normal assembly of elastic fibers in vitro and suggested that PXE is a primary metabolic disorder with secondary connective tissue manifestations. PMID:16543900

Substrate-dependent cell elasticity measured by optical tweezers indentation

NASA Astrophysics Data System (ADS)

Yousafzai, Muhammad S.; Ndoye, Fatou; Coceano, Giovanna; Niemela, Joseph; Bonin, Serena; Scoles, Giacinto; Cojoc, Dan

2016-01-01

In the last decade, cell elasticity has been widely investigated as a potential label free indicator for cellular alteration in different diseases, cancer included. Cell elasticity can be locally measured by pulling membrane tethers, stretching or indenting the cell using optical tweezers. In this paper, we propose a simple approach to perform cell indentation at pN forces by axially moving the cell against a trapped microbead. The elastic modulus is calculated using the Hertz-model. Besides the axial component, the setup also allows us to examine the lateral cell-bead interaction. This technique has been applied to measure the local elasticity of HBL-100 cells, an immortalized human cell line, originally derived from the milk of a woman with no evidence of breast cancer lesions. In addition, we have studied the influence of substrate stiffness on cell elasticity by performing experiments on cells cultured on two substrates, bare and collagen-coated, having different stiffness. The mean value of the cell elastic modulus measured during indentation was 26±9 Pa for the bare substrate, while for the collagen-coated substrate it diminished to 19±7 Pa. The same trend was obtained for the elastic modulus measured during the retraction of the cell: 23±10 Pa and 13±7 Pa, respectively. These results show the cells adapt their stiffness to that of the substrate and demonstrate the potential of this setup for low-force probing of modifications to cell mechanics induced by the surrounding environment (e.g. extracellular matrix or other cells).

Surface folding-induced attraction and motion of particles in a soft elastic gel: cooperative effects of surface tension, elasticity, and gravity.

PubMed

Chakrabarti, Aditi; Chaudhury, Manoj K

2013-12-17

We report some experimental observations regarding a new type of long-range interaction between rigid particles that prevails when they are suspended in an ultrasoft elastic gel. A denser particle submerges itself to a considerable depth inside the gel and becomes elasto-buoyant by balancing its weight against the elastic force exerted by the surrounding medium. By virtue of a large elasto-capillary length, the surface of the gel wraps around the particle and closes to create a line singularity connecting the particle to the free surface of the gel. A substantial amount of tensile strain is thus developed in the gel network parallel to the free surface that penetrates to a significant depth inside the gel. The field of this tensile strain is rather long-range because of a large gravito-elastic correlation length and sufficiently strong to pull two submerged particles into contact. The particles move toward each other with an effective force following an inverse linear distance law. When more monomers or dimers of the particles are released inside the gel, they orient rather freely inside the capsules where they are located and attract each other to form closely packed clusters. Eventually, these clusters themselves interact and coalesce. This is an emergent phenomenon in which gravity, capillarity, and elasticity work in tandem to create a long-range interaction. We also present the results of a related experiment, in which a particle suspended inside a thickness-graded gel moves accompanied by the continuous folding and the relaxation of the gel's surface.

XBAER-derived aerosol optical thickness from OLCI/Sentinel-3 observation

NASA Astrophysics Data System (ADS)

Mei, Linlu; Rozanov, Vladimir; Vountas, Marco; Burrows, John P.; Richter, Andreas

2018-02-01

study, the recently developed AOT retrieval algorithm eXtensible Bremen AErosol Retrieval (XBAER) has been applied to data from the OLCI instrument for the first time to illustrate the feasibility of applying XBAER to the data from this new instrument. The first global retrieval results show similar patterns of aerosol optical thickness, AOT, to those from MODIS and MISR aerosol products. The AOT retrieved from OLCI is validated by comparison with AERONET observations and a correlation coefficient of 0.819 and bias (root mean square) of 0.115 is obtained. The haze episode is well captured by the OLCI-derived AOT product. XBAER is shown to retrieve AOT well from the observations of MERIS and OLCI.

Charge distribution of the neven sulphur isotopes from elastic electron scattering

NASA Astrophysics Data System (ADS)

Rychel, D.; Emrich, H. J.; Miska, H.; Gyufko, R.; Wiedner, C. A.

1983-10-01

Elastic electron scattering experiments on the isotopes 32,34,36S were performed covering a range in momentum transfer q = 0.5-2.6 fm -. The cross sections were analysed with the Fourier-Bessel method yielding model-independent charge distributions and their differences. The extracted rms radii follow approximately the systematics of even-even nuclei; this also holds for the gross features as expressed in dms radii and skin thicknesses.

Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity

NASA Astrophysics Data System (ADS)

Delfani, M. R.; Latifi Shahandashti, M.

2017-09-01

In this paper, within the complete form of Mindlin's second strain gradient theory, the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non-uniform distribution of eigenfields is determined. These eigenfields, in addition to eigenstrain, comprise eigen double and eigen triple strains. After the derivation of a closed-form expression for Green's function associated with the problem, two different cases of non-uniform distribution of the eigenfields are considered as follows: (i) radial distribution, i.e. the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion, and (ii) polynomial distribution, i.e. the distributions of the eigenfields are polynomial functions in the Cartesian coordinates of points. While the obtained solution for the elastic field of the latter case takes the form of an infinite series, the solution to the former case is represented in a closed form. Moreover, Eshelby's tensors associated with the two mentioned cases are obtained.

A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

PubMed Central

Zhou, Y. C.; Holst, Michael; McCammon, J. Andrew

2008-01-01

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules, and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations. We derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field, and establish the existance of an equilibrium configuration using a fixed-point argument, under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small. The results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities, and can be generalized to large elastic deformation caused by high ionic strength, large charges, and strong external fields by using continuation methods. PMID:19461946

Elastic least-squares reverse time migration with velocities and density perturbation

NASA Astrophysics Data System (ADS)

Qu, Yingming; Li, Jinli; Huang, Jianping; Li, Zhenchun

2018-02-01

Elastic least-squares reverse time migration (LSRTM) based on the non-density-perturbation assumption can generate false-migrated interfaces caused by density variations. We perform an elastic LSRTM scheme with density variations for multicomponent seismic data to produce high-quality images in Vp, Vs and ρ components. However, the migrated images may suffer from crosstalk artefacts caused by P- and S-waves coupling in elastic LSRTM no matter what model parametrizations used. We have proposed an elastic LSRTM with density variations method based on wave modes separation to reduce these crosstalk artefacts by using P- and S-wave decoupled elastic velocity-stress equations to derive demigration equations and gradient formulae with respect to Vp, Vs and ρ. Numerical experiments with synthetic data demonstrate the capability and superiority of the proposed method. The imaging results suggest that our method promises imaging results with higher quality and has a faster residual convergence rate. Sensitivity analysis of migration velocity, migration density and stochastic noise verifies the robustness of the proposed method for field data.

Tracking sea ice floes from the Lincoln Sea to Nares Strait and deriving large scale melt from coincident spring and summer (2009) aerial EM thickness surveys

NASA Astrophysics Data System (ADS)

Lange, B. A.; Haas, C.; Beckers, J.; Hendricks, S.

2011-12-01

Satellite observations demonstrate a decreasing summer Arctic sea ice extent over the past ~40 years, as well as a smaller perennial sea ice zone, with a significantly accelerated decline in the last decade. Recent ice extent observations are significantly lower than predicted by any model employed by the Intergovernmental Panel on Climate Change. The disagreement of the modeled and observed results, along with the large variability of model results, can be in part attributed to a lack of consistent and long term sea ice mass balance observations for the High Arctic. This study presents the derivation of large scale (individual floe) seasonal sea ice mass balance in the Lincoln Sea and Nares Strait. Large scale melt estimates are derived by comparing aerial borne electromagnetic induction thickness surveys conducted in spring with surveys conducted in summer 2009. The comparison of coincident floes is ensured by tracking sea ice using ENIVSAT ASAR and MODIS satellite imagery. Only EM thickness survey sections of floes that were surveyed in both spring and summer are analyzed and the resulting modal thicknesses of the distributions, which represent the most abundant ice type, are compared to determine the difference in thickness and therefore total melt (snow+basal ice+surface ice melt). Preliminary analyses demonstrate a bulk (regional ice tracking) seasonal total thickness variability of 1.1m, Lincoln Sea modal thickness 3.7m (April, 2009) and Nares Strait modal thickness 2.6m (August 2009)(Fig1). More detailed floe tracking, in depth analysis of EM surveys and removal of deformed ridged/rafted sea ice (due to inaccuracies over deformed ice) will result in more accurate melt estimates for this region and will be presented. The physical structure of deformed sea ice and the footprint of the EM instrument typically underestimate the total thicknesses observed. Seasonal variations of sea ice properties can add additional uncertainty to the response of the EM

Resolvent estimates in homogenisation of periodic problems of fractional elasticity

NASA Astrophysics Data System (ADS)

Cherednichenko, Kirill; Waurick, Marcus

2018-03-01

We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier-Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces.

Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels with general elastic supports

NASA Astrophysics Data System (ADS)

Xie, Fei; Tang, Jinyuan; Wang, Ailun; Shuai, Cijun; Wang, Qingshan

2018-05-01

In this paper, a unified solution for vibration analysis of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panels with general elastic supports is carried out via using the Ritz method. The excellent accuracy and reliability of the present method are compared with the results of the classical boundary cases found in the literature. New results are given for vibration characteristics of FG-CNTRC cylindrical panels with various boundary conditions. The effects of the elastic restraint parameters, thickness, subtended angle and volume fraction of carbon nanotubes on the free vibration characteristic of the cylindrical panels are also reported.

Effective elastic thickness along the conjugate passive margins of India, Madagascar and Antarctica: A re-evaluation using the Hermite multitaper Bouguer coherence application

NASA Astrophysics Data System (ADS)

Ratheesh-Kumar, R. T.; Xiao, Wenjiao

2018-05-01

Gondwana correlation studies had rationally positioned the western continental margin of India (WCMI) against the eastern continental margin of Madagascar (ECMM), and the eastern continental margin of India (ECMI) against the eastern Antarctica continental margin (EACM). This contribution computes the effective elastic thickness (Te) of the lithospheres of these once-conjugated continental margins using the multitaper Bouguer coherence method. The results reveal significantly low strength values (Te ∼ 2 km) in the central segment of the WCMI that correlate with consistently low Te values (2-3 km) obtained throughout the entire marginal length of the ECMM. This result is consistent with the previous Te estimates of these margins, and confirms the idea that the low-Te segments in the central part of the WCMI and along the ECMM represents paleo-rift inception points of the lithospheric margins that was thermally and mechanically weakened by the combined action of the Marion hotspot and lithospheric extension during the rifting. The uniformly low-Te value (∼2 km) along the EACM indicates a mechanically weak lithospheric margin, probably due to considerable stretching of the lithosphere, considering the fact that this margin remained almost stationary throughout its rift history. In contrast, the ECMI has comparatively high-Te variations (5-11 km) that lack any correlation with the regional tectonic setting. Using gravity forward and inversion applications, we find a leading order of influence of sediment load on the flexural properties of this marginal lithosphere. The study concludes that the thick pile of the Bengal Fan sediments in the ECMI masks and has erased the signal of the original load-induced topography, and its gravity effect has biased the long-wavelength part of the observed gravity signal. The hence uncorrelated flat topography and deep lithospheric flexure together contribute a bias in the flexure modeling, which likely accounts a relatively high Te

On contact problems of elasticity theory

NASA Technical Reports Server (NTRS)

Kalandiya, A. I.

1986-01-01

Certain contact problems are reviewed in the two-dimensional theory of elasticity when round bodies touch without friction along most of the boundary and, therefore, Herz' hypothesis on the smallness of the contact area cannot be used. Fundamental equations were derived coinciding externally with the equation in the theory of a finite-span wing with unkown parameter. These equations are solved using Multhopp's well-known technique, and numerical calculations are performed in specific examples.

Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series

NASA Astrophysics Data System (ADS)

Chanard, Kristel; Fleitout, Luce; Calais, Eric; Rebischung, Paul; Avouac, Jean-Philippe

2018-04-01

We model surface displacements induced by variations in continental water, atmospheric pressure, and nontidal oceanic loading, derived from the Gravity Recovery and Climate Experiment (GRACE) for spherical harmonic degrees two and higher. As they are not observable by GRACE, we use at first the degree-1 spherical harmonic coefficients from Swenson et al. (2008, https://doi.org/10.1029/2007JB005338). We compare the predicted displacements with the position time series of 689 globally distributed continuous Global Navigation Satellite System (GNSS) stations. While GNSS vertical displacements are well explained by the model at a global scale, horizontal displacements are systematically underpredicted and out of phase with GNSS station position time series. We then reestimate the degree 1 deformation field from a comparison between our GRACE-derived model, with no a priori degree 1 loads, and the GNSS observations. We show that this approach reconciles GRACE-derived loading displacements and GNSS station position time series at a global scale, particularly in the horizontal components. Assuming that they reflect surface loading deformation only, our degree-1 estimates can be translated into geocenter motion time series. We also address and assess the impact of systematic errors in GNSS station position time series at the Global Positioning System (GPS) draconitic period and its harmonics on the comparison between GNSS and GRACE-derived annual displacements. Our results confirm that surface mass redistributions observed by GRACE, combined with an elastic spherical and layered Earth model, can be used to provide first-order corrections for loading deformation observed in both horizontal and vertical components of GNSS station position time series.

Relationships among cloud occurrence frequency, overlap, and effective thickness derived from CALIPSO and CloudSat merged cloud vertical profiles

NASA Astrophysics Data System (ADS)

Kato, Seiji; Sun-Mack, Sunny; Miller, Walter F.; Rose, Fred G.; Chen, Yan; Minnis, Patrick; Wielicki, Bruce A.

2010-01-01

A cloud frequency of occurrence matrix is generated using merged cloud vertical profiles derived from the satellite-borne Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and cloud profiling radar. The matrix contains vertical profiles of cloud occurrence frequency as a function of the uppermost cloud top. It is shown that the cloud fraction and uppermost cloud top vertical profiles can be related by a cloud overlap matrix when the correlation length of cloud occurrence, which is interpreted as an effective cloud thickness, is introduced. The underlying assumption in establishing the above relation is that cloud overlap approaches random overlap with increasing distance separating cloud layers and that the probability of deviating from random overlap decreases exponentially with distance. One month of Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) and CloudSat data (July 2006) support these assumptions, although the correlation length sometimes increases with separation distance when the cloud top height is large. The data also show that the correlation length depends on cloud top hight and the maximum occurs when the cloud top height is 8 to 10 km. The cloud correlation length is equivalent to the decorrelation distance introduced by Hogan and Illingworth (2000) when cloud fractions of both layers in a two-cloud layer system are the same. The simple relationships derived in this study can be used to estimate the top-of-atmosphere irradiance difference caused by cloud fraction, uppermost cloud top, and cloud thickness vertical profile differences.

Cracking of a layered medium on an elastic foundation under thermal shock

NASA Technical Reports Server (NTRS)

Rizk, Abd El-Fattah A.; Erdogan, Fazil

1988-01-01

The cladded pressure vessel under thermal shock conditions which is simulated by using two simpler models was studied. The first model (Model 1) assumes that, if the crack size is very small compared to the vessel thickness, the problem can be treated as a semi-infinite elastic medium bonded to a very thin layer of different material. However, if the crack size is of the same order as the vessel thickness, the curvature effects may not be negligible. In this case it is assumed that the relatively thin walled hollow cylinder with cladding can be treated as a composite beam on an elastic foundation (Model 2). In both models, the effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. The calculated results include the transient temperature, thermal stresses in the uncracked medium and stress intensity factors which are presented as a function of time, and the duration of cooling ramp. The stress intensity factors are also presented as a function of the size and the location of the crack. The problem is solved for two bonded materials of different thermal and mechanical properties. The mathematical formulation results in two singular integral equations which are solved numerically. The results are given for two material pairs, namely an austenitic steel layer welded on a ferritic steel substrate, and a ceramic coating on ferritic steel. In the case of the yielded clad, the stress intensity factors for a crack under the clad are determined by using a plastic strip model and are compared with elastic clad results.

Effect of the Coronal Wall Thickness of Dental Implants on the Screw Joint Stability in the Internal Implant-Abutment Connection.

PubMed

Lee, Ji-Hye; Huh, Yoon-Hyuk; Park, Chan-Jin; Cho, Lee-Ra

2016-01-01

To evaluate the effect of implant coronal wall thickness on load-bearing capacity and screw joint stability. Experimental implants were customized after investigation of the thinnest coronal wall thickness of commercially available implant systems with a regular platform diameter. Implants with four coronal wall thicknesses (0.2, 0.3, 0.4, and 0.5 mm) were fabricated. Three sets of tests were performed. The first set was a failure test to evaluate load-bearing capacity and elastic limit. The second and third sets were cyclic and static loading tests. After abutment screw tightening of each implant, vertical cyclic loading of 250 N or static loading from 250 to 800 N was applied. Coronal diameter expansion, axial displacement, and removal torque values of the implants were compared. Repeated measures analysis of variance (ANOVA) was used for statistical analysis (α = .05). Implants with 0.2-mm coronal wall thickness demonstrated significantly low load-bearing capacity and elastic limit (both P < .05). These implants also showed significantly large coronal diameter expansion and axial displacement after screw tightening (both P < .05). Greater vertical load and thinner coronal wall thickness significantly increased coronal diameter expansion of the implant, axial displacement of the abutment, and removal torque loss of the abutment screw (all P < .05). Implant coronal wall thickness of 0.2 mm produces significantly inferior load-bearing capacity and screw joint stability.

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

NASA Astrophysics Data System (ADS)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

Effect of Prestresses on the Dispersion of Quasi-Lamb Waves in the System Consisting of an Ideal Liquid Layer and a Compressible Elastic Layer

NASA Astrophysics Data System (ADS)

Bagno, A. M.

2017-03-01

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer interacting with a layer of an ideal compressible fluid is studied. The three-dimensional equations of linearized elasticity and the assumption of finite strains for the elastic layer and the three-dimensional linearized Euler equations for the fluid are used. The dispersion curves for the quasi-Lamb modes are plotted over a wide frequency range. The effect of prestresses and the thickness of the elastic and liquid layers on the frequency spectrum of normal quasi-Lamb waves is analyzed. The localization properties of the lower quasi-Lamb modes in the elastic-fluid waveguides are studied. The numerical results are presented in the form of graphs and analyzed

Elastic modulus and surface tension of a polyurethane rubber in nanometer thick films

NASA Astrophysics Data System (ADS)

Zhai, Meiyu; McKenna, Gregory

2014-03-01

Estane is a kind of polyurethane with thermodynamically incompatible hard and soft segments. In this study the macro and micro properties of Estane have been characterized and compared. The viscoelastic properties of this material in bulk scale have been determined using dynamic rheometry. Time-temperature superposition was found to be applicable for this material, and a master curve was successfully constructed from the dynamic shear responses of G'(ω) and G''(ω) . Also a novel nano bubble inflation method was used to obtain the creep compliance of the Estane ultrathin films and the results show stiffening in the rubbery region for the Estane over thicknesses ranging from 110nm to 22nm. The dependence of the rubbery stiffening on film thickness is studied and the relative influences of nano confinement and surface tension effect are analyzed using both a direct stress strain analysis and an energy balance method for the membrane. The contributions of surface tension and nano confinement are considered separately. Office of Naval Research under project No.N00014-11-1-0424.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

Motion of a rigid sphere through an elastic tube with a lubrication film

NASA Astrophysics Data System (ADS)

Tani, Marie; Cambau, Thomas; Bico, Jose; Reyssat, Etienne

2017-11-01

The motion of large objects through narrow tubes is a common problem in physiology and more generally in the biological world. We built a model experiment where a rigid sphere is moved inside a narrower elastic tube coated with a lubricating fluid. The friction force is generally lower than in a non-lubricated situation. Interestingly, the force increases with the pulling velocity to the power 1/3, and also depends on the viscosity of the lubricant, the geometry and the mechanical properties of the tube. All our experimental data are well described by a scaling law combining lubrication and elasticity equations. We furthermore measured the thickness of the lubricant film. We present all these results.

Studying the influence of surface effects on vibration behavior of size-dependent cracked FG Timoshenko nanobeam considering nonlocal elasticity and elastic foundation

NASA Astrophysics Data System (ADS)

Ghadiri, Majid; Soltanpour, Mahdi; Yazdi, Ali; Safi, Mohsen

2016-05-01

Free transverse vibration of a size-dependent cracked functionally graded (FG) Timoshenko nanobeam resting on a polymer elastic foundation is investigated in the present study. Also, all of the surface effects: surface density, surface elasticity and residual surface tension are studied. Moreover, satisfying the balance condition between the nanobeam and its surfaces was discussed. According to the power-law distribution, it is supposed that the material properties of the FG nanobeam are varying continuously across the thickness. Considering the small-scale effect, the Eringen's nonlocal theory is used; accounting the effect of polymer elastic foundation, the Winkler model is proposed. For this purpose, the equations of motion of the FG Timoshenko nanobeam and boundary conditions are obtained using Hamilton's principle. To find the analytical solutions for equations of motion of the FG nanobeam, the separation of variables method is employed. Two cases of boundary conditions, i.e., simply supported-simply supported (SS) and clamped-clamped (CC) are investigated in the present work. Numerical results are demonstrating a good agreement between the results of the present study and some available cases in the literature. The emphasis of the present study is on investigating the effect of various parameters such as crack severity, crack position, gradient index, mode number, nonlocal parameter, elastic foundation parameter and nanobeam length. It is clearly revealed that the vibrational behavior of a FG nanobeam is depending significantly on these effects. Also, these numerical results can be serving as benchmarks for future studies of FG nanobeams.

Influence of surface roughness and waviness on film thickness and pressure distribution in elastohydrodynamic contacts

NASA Technical Reports Server (NTRS)

Chow, L. S. H.; Cheng, H. S.

1976-01-01

The Christensen theory of a stochastic model for hydrodynamic lubrication of rough surfaces was extended to elastohydrodynamic lubrication between two rollers. Solutions for the reduced pressure at the entrance as a function of the ratio of the average nominal film thickness to the rms surface roughness, were obtained numerically. Results were obtained for purely transverse as well as purely longitudinal surface roughness for cases with or without slip. The reduced pressure was shown to decrease slightly by considering longitudinal surface roughness. The same approach was used to study the effect of surface roughness on lubrication between rigid rollers and lubrication of an infinitely wide slider bearing. Using the flow balance concept, the perturbed Reynolds equation, was derived and solved for the perturbed pressure distribution. In addition, Cheng's numerical scheme was modified to incorporate a single two-dimensional elastic asperity on the stationary surface. The perturbed pressures obtained by these three different models were compared.

FEM simulation of the die compaction of pharmaceutical products: influence of visco-elastic phenomena and comparison with experiments.

PubMed

Diarra, Harona; Mazel, Vincent; Busignies, Virginie; Tchoreloff, Pierre

2013-09-10

This work studies the influence of visco-elastic behavior in the finite element method (FEM) modeling of die compaction of pharmaceutical products and how such a visco-elastic behavior may improve the agreement between experimental and simulated compression curves. The modeling of the process was conducted on a pharmaceutical excipient, microcrystalline cellulose (MCC), by using Drucker-Prager cap model coupled with creep behavior in Abaqus(®) software. The experimental data were obtained on a compaction simulator (STYLCAM 200R). The elastic deformation of the press was determined by performing experimental tests on a calibration disk and was introduced in the simulation. Numerical optimization was performed to characterize creep parameters. The use of creep behavior in the simulations clearly improved the agreement between the numerical and experimental compression curves (stresses, thickness), mainly during the unloading part of the compaction cycle. For the first time, it was possible to reproduce numerically the fact that the minimum tablet thickness is not obtained at the maximum compression stress. This study proves that creep behavior must be taken into account when modeling the compaction of pharmaceutical products using FEM methods. Copyright © 2013 Elsevier B.V. All rights reserved.

Unusual Stiffening and Elastic Response of Polyisobutylene Nanometric Thin Films

NASA Astrophysics Data System (ADS)

Yoon, Heedong; Wigham, Caleb; McKenna, Gregory

The TTU bubble inflation technique was used to study the elastic response and unusual stiffening behavior of nanometirc polyisobutylene (PIB) films. Mechanical properties and surface tension of PIB films were measured through the strain-stress response for film thicknesses ranging from 13 nm to 126 nm. The tests were performed at room temperature, far above the glass transition temperature of PIB. It is found that the stiffening increases with decreasing film thickness, while the surface tension is independent of the film thickness. Similar to the prior bubble inflation measurements in polymeric thin films, the thickness dependence of the stiffening followed a power law behavior in this case of Ds h1.5. These results are consistent with the Ngai et al proposition that rubbery stiffening is related to the separation of the α relaxation and Rouse modes. In addition, we compare stiffening index (S) with fragility (m) based on our prior observation that the S follows a linear behavior with dynamic m. Unlike other polymeric materials seen in prior bubble inflation measurements, the S of PIB does not follow the linear behavior with m.

Micromechanics-based magneto-elastic constitutive modeling of particulate composites

NASA Astrophysics Data System (ADS)

Yin, Huiming

Modified Green's functions are derived for three situations: a magnetic field caused by a local magnetization, a displacement field caused by a local body force and a displacement field caused by a local prescribed eigenstrain. Based on these functions, an explicit solution is derived for two magnetic particles embedded in the infinite medium under external magnetic and mechanical loading. A general solution for numerable magnetic particles embedded in an infinite domain is then provided in integral form. Two-phase composites containing spherical magnetic particles of the same size are considered for three kinds of microstructures. With chain-structured composites, particle interactions in the same chain are considered and a transversely isotropic effective elasticity is obtained. For periodic composites, an eight-particle interaction model is developed and provides a cubic symmetric effective elasticity. In the random composite, pair-wise particle interactions are integrated from all possible positions and an isotropic effective property is reached. This method is further extended to functionally graded composites. Magneto-mechanical behavior is studied for the chain-structured composite and the random composite. Effective magnetic permeability, effective magnetostriction and field-dependent effective elasticity are investigated. It is seen that the chain-structured composite is more sensitive to the magnetic field than the random composite; a composite consisting of only 5% of chain-structured particles can provide a larger magnetostriction and a larger change of effective elasticity than an equivalent composite consisting of 30% of random dispersed particles. Moreover, the effective shear modulus of the chain-structured composite rapidly increases with the magnetic field, while that for the random composite decreases. An effective hyperelastic constitutive model is further developed for a magnetostrictive particle-filled elastomer, which is sampled by using a

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2011-01-01

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

Evaluation of carotid intima-media thickness and carotid arterial stiffness in children with adenotonsillar hypertrophy.

PubMed

Çiftel, Murat; Demir, Berrin; Kozan, Günay; Yılmaz, Osman; Kahveci, Hasan; Kılıç, Ömer

2016-02-01

Adenotonsillar hypertrophy can produce cardiopulmonary disease in children. However, it is unclear whether adenotonsillar hypertrophy causes atherosclerosis. This study evaluated carotid intimamedia thickness and carotid arterial stiffness in children with adenotonsillar hypertrophy. The study included 40 children with adenotonsillar hypertrophy (age: 5-10 years) and 36 healthy children with similar age and body mass index. Systolic blood pressure, diastolic blood pressure, and pulse pressure were measured in all subjects. Carotid intima-media thickness, carotid arterial systolic diameter, and carotid arterial diastolic diameter were measured using a high-resolution ultrasound device. Based on these measurements, carotid arterial strain, carotid artery distensibility, beta stiffness index, and elasticity modulus were calculated. Carotid intima-media thickness was greater in children with adenotonsillar hypertrophy (0.36±0.05 mm vs. 0.34±0.04 mm, P=0.02) compared to healthy controls. Beta stiffness index (3.01±1.22 vs. 2.98±0.98, P=0.85), elasticity modulus (231.39±99.23 vs. 226.46±83.20, P=0.88), carotid arterial strain (0.17±0.06 vs. 0.17±0.04, P=0.95), and carotid artery distensibility (13.14±3.88 vs. 12.92±3.84, P=0.75) were similar between children with adenotonsillar hypertrophy and the healthy controls. The present study revealed increased carotid intima-media thickness in children with adenotonsillar hypertrophy. The risk of subclinical atherosclerosis may be higher in children with adenotonsillar hypertrophy.

Blocky inversion of multichannel elastic impedance for elastic parameters

NASA Astrophysics Data System (ADS)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

Model-based cartilage thickness measurement in the submillimeter range

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

Streekstra, G. J.; Strackee, S. D.; Maas, M.

2007-09-15

Current methods of image-based thickness measurement in thin sheet structures utilize second derivative zero crossings to locate the layer boundaries. It is generally acknowledged that the nonzero width of the point spread function (PSF) limits the accuracy of this measurement procedure. We propose a model-based method that strongly reduces PSF-induced bias by incorporating the PSF into the thickness estimation method. We estimated the bias in thickness measurements in simulated thin sheet images as obtained from second derivative zero crossings. To gain insight into the range of sheet thickness where our method is expected to yield improved results, sheet thickness wasmore » varied between 0.15 and 1.2 mm with an assumed PSF as present in the high-resolution modes of current computed tomography (CT) scanners [full width at half maximum (FWHM) 0.5-0.8 mm]. Our model-based method was evaluated in practice by measuring layer thickness from CT images of a phantom mimicking two parallel cartilage layers in an arthrography procedure. CT arthrography images of cadaver wrists were also evaluated, and thickness estimates were compared to those obtained from high-resolution anatomical sections that served as a reference. The thickness estimates from the simulated images reveal that the method based on second derivative zero crossings shows considerable bias for layers in the submillimeter range. This bias is negligible for sheet thickness larger than 1 mm, where the size of the sheet is more than twice the FWHM of the PSF but can be as large as 0.2 mm for a 0.5 mm sheet. The results of the phantom experiments show that the bias is effectively reduced by our method. The deviations from the true thickness, due to random fluctuations induced by quantum noise in the CT images, are of the order of 3% for a standard wrist imaging protocol. In the wrist the submillimeter thickness estimates from the CT arthrography images correspond within 10% to those estimated from the

Axial buckling and transverse vibration of ultrathin nanowires: low symmetry and surface elastic effect

NASA Astrophysics Data System (ADS)

Lei, Xiao; Narsu, B.; Yun, Guohong; Li, Jiangang; Yao, Haiyan

2016-05-01

Surface effects play a deterministic role in the physical and mechanical properties of nanosized materials and structures. In this paper, we present a self-consistent theoretical scheme for describing the elasticity of nanowires. The natural frequency and the critical compression force of axial buckling are obtained analytically, taking into consideration the influences of lower symmetry, additional elastic parameters, surface reconstruction, surface elasticity, and residual surface stress. Applications of the present theory to elastic systems for the  <1 0 0 >  axially oriented Si and Cu nanowires and Ag  <1 1 0 >  axially oriented nanowires yield good agreement with experimental data and calculated results. The larger positive value of the new elastic parameter c12α taken into account for Si  <1 0 0 >  oriented nanowires drives the curves of natural frequency and critical compression force versus thickness towards the results obtained from density functional theory simulation. Negative surface stress decreases the critical load for axial buckling, thus making the nanowires very easy to bend into various structures. The present study is envisaged to provide useful insights for the design and application of nanowire-based devices.

Resonance line polarization and the Hanle effect in optically thick media. I - Formulation for the two-level atom

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, E.; Bommier, V.; Sahal-Brechot, S.

1990-08-01

A general formalism is presented to describe resonance line polarization for a two-level atom in an optically thick, three-dimensional medium embedded in an arbitrary varying magnetic field and irradiated by an arbitrary radiation field. The magnetic field is supposed sufficiently small to induce a Zeeman splitting much smaller than the typical line width. By neglecting atomic polarization in the lower level and stimulated emission, an integral equation is derived for the multipole moments of the density matrix of the upper level. This equation shows how the multipole moments at any assigned point of the medium are coupled to the multipole moments relative at a different point as a consequence of the propagation of polarized radiation between the two points. The equation also accounts for the effect of the magnetic field, described by a kernel locally connecting multipole moments of the same rank, and for the role of inelastic and elastic (or depolarizing) collisions. After having given its formal derivation for the general case, the integral equation is particularized to the one-dimensional and two-dimensional cases. For the one-dimensional case of a plane parallel atmosphere, neglecting both the magnetic field and depolarizing collisions, the equation here derived reduces to a previous one given by Rees (1978).

Supersonic flow past oscillating airfoils including nonlinear thickness effects

NASA Technical Reports Server (NTRS)

Van Dyke, Milton D

1954-01-01

A solution to second order in thickness is derived for harmonically oscillating two-dimensional airfoils in supersonic flow. For slow oscillations of an arbitrary profile, the result is found as a series including the third power of frequency. For arbitrary frequencies, the method of solution for any specific profile is indicated, and the explicit solution derived for a single wedge. Nonlinear thickness effects are found generally to reduce the torsional damping, and so enlarge the range of Mach numbers within which torsional instability is possible.

Elastic constants for superplastically formed/diffusion-bonded corrugated sandwich core

NASA Technical Reports Server (NTRS)

Ko, W. L.

1980-01-01

Formulas and associated graphs for evaluating the effective elastic constants for a superplastically formed/diffusion bonded (SPF/DB) corrugated sandwich core, are presented. A comparison of structural stiffnesses of the sandwich core and a honeycomb core under conditions of equal sandwich core density was made. The stiffness in the thickness direction of the optimum SPF/DB corrugated core (that is, triangular truss core) is lower than that of the honeycomb core, and that the former has higher transverse shear stiffness than the latter.

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Atomistic calculations of interface elastic properties in noncoherent metallic bilayers

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

Mi Changwen; Jun, Sukky; Kouris, Demitris A.

2008-02-15

The paper describes theoretical and computational studies associated with the interface elastic properties of noncoherent metallic bicrystals. Analytical forms of interface energy, interface stresses, and interface elastic constants are derived in terms of interatomic potential functions. Embedded-atom method potentials are then incorporated into the model to compute these excess thermodynamics variables, using energy minimization in a parallel computing environment. The proposed model is validated by calculating surface thermodynamic variables and comparing them with preexisting data. Next, the interface elastic properties of several fcc-fcc bicrystals are computed. The excess energies and stresses of interfaces are smaller than those on free surfacesmore » of the same crystal orientations. In addition, no negative values of interface stresses are observed. Current results can be applied to various heterogeneous materials where interfaces assume a prominent role in the systems' mechanical behavior.« less

Active Vibration Control of Elastic Beam by Means of Shape Memory Alloy Layers

NASA Technical Reports Server (NTRS)

Chen, Q.; Levy, C.

1996-01-01

The mathematical model of a flexible beam covered with shape memory alloy (SMA) layers is presented. The SMA layers are used as actuators, which are capable of changing their elastic modulus and recovery stress, thus changing the natural frequency of, and adjusting the excitation to, the vibrating beam. The frequency factor variation as a function of SMA Young's modulus, SMA layer thickness and beam thickness is discussed. Also control of the beam employing an optimal linear control law is evaluated. The control results indicate how the system reacts to various levels of excitation input through the non-homogeneous recovery shear term of the governing differential equation.

Elastic rebound following the Kocaeli earthquake, Turkey, recorded using synthetic aperture radar interferometry

USGS Publications Warehouse

Mayer, Larry; Lu, Zhong

2001-01-01

A basic model incorporating satellite synthetic aperture radar (SAR) interferometry of the fault rupture zone that formed during the Kocaeli earthquake of August 17, 1999, documents the elastic rebound that resulted from the concomitant elastic strain release along the North Anatolian fault. For pure strike-slip faults, the elastic rebound function derived from SAR interferometry is directly invertible from the distribution of elastic strain on the fault at criticality, just before the critical shear stress was exceeded and the fault ruptured. The Kocaeli earthquake, which was accompanied by as much as ∼5 m of surface displacement, distributed strain ∼110 km around the fault prior to faulting, although most of it was concentrated in a narrower and asymmetric 10-km-wide zone on either side of the fault. The use of SAR interferometry to document the distribution of elastic strain at the critical condition for faulting is clearly a valuable tool, both for scientific investigation and for the effective management of earthquake hazard.

Ab-initio study of electronic structure and elastic properties of ZrC

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

Mund, H. S., E-mail: hmoond@gmail.com; Ahuja, B. L.

2016-05-23

The electronic and elastic properties of ZrC have been investigated using the linear combination of atomic orbitals method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within generalized gradient approximation. We have computed energy bands, density of states, elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, lattice parameters and pressure derivative of the bulk modulus by calculating ground state energy of the rock salt structure type ZrC.

Energy Bounds for a Compressed Elastic Film on a Substrate

NASA Astrophysics Data System (ADS)

Bourne, David P.; Conti, Sergio; Müller, Stefan

2017-04-01

We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimisation into a free boundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, {σ }, and a measure of the bonding strength between the film and substrate, {γ }. We prove upper bounds on the minimum energy of the form {σ }^a {γ }^b and find that there are four different parameter regimes corresponding to different values of a and b and to different folding patterns of the film. In some cases, the upper bounds are attained by self-similar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds.

Anomalous elasticity, fluctuations and disorder in elastic membranes

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Radzihovsky, Leo

2018-05-01

Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky, 1992; 1993). The experimental realization atom-thin graphene sheets (Novoselov et al., 2004) have driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic "membrane" embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d → ∞, (ii) D → 4, and (iii) D = d. Focusing on the critical "flat" phase, for a homogeneous two-dimensional (D = 2) membrane embedded in three dimensions (d = 3), we predict its universal roughness exponent ζ = 0 . 590, length-scale dependent elastic moduli exponents η = 0 . 821 and ηu = 0 . 358, and an anomalous Poisson ratio, σ = - 1 / 3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ‧ = 0 . 775 ,η‧ = 0 . 449, ηu‧ = 1 . 101 and a Poisson ratio σ‧ = - 1 / 3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a "phantom" sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν = 0 . 732 and η = 0

Stresses and elastic constants of crystalline sodium, from molecular dynamics

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

Schiferl, S.K.

1985-02-01

The stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340K. The total adiabatic potential of a system of sodium atoms is represented by pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the resultsmore » to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. 45 refs., 10 figs., 4 tabs.« less

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates.

PubMed

Mehrkash, Milad; Azhari, Mojtaba; Mirdamadi, Hamid Reza

2014-01-01

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates. Copyright © 2013 Elsevier B.V. All rights reserved.

Mechanical evaluation of the resistance and elastance of post-burn scars after topical treatment with tretinoin

PubMed Central

Dematte, Maria Fernanda; Gemperli, Rolf; Salles, Alessandra Grassi; Dolhnikoff, Marisa; Lanças, Tatiana; Saldiva, Paulo Hilário Nascimento; Ferreira, Marcus Castro

2011-01-01

OBJECTIVE: After burn injuries, scarred skin lacks elasticity, especially in hypertrophic scars. Topical treatment with tretinoin can improve the appearance and quality of the skin (i.e., texture, distensibility, color, and hydration). The objective of this prospective study was to examine the effects of treatment with 0.05% tretinoin for one year on the biomechanical behavior and histological changes undergone by facial skin with post-burn scarring. Setting: Tertiary, Institutional. METHOD: Fifteen female patients who had suffered partial thickness burns with more than two years of evolution were selected. Skin biopsies were obtained initially and after one year of treatment. The resistance and elastance of these skin biopsies were measured using a mechanical oscillation analysis system. The density of collagen fibers, elastic fibers, and versican were determined using immunohistochemical analysis. RESULTS: Tretinoin treatment significantly lowered skin resistance and elastance, which is a result that indicates higher distensibility of the skin. However, tretinoin treatment did not significantly affect the density of collagen fibers, elastic fibers, or versican. CONCLUSION: Topical tretinoin treatment alters the mechanical behavior of post-burn scarred skin by improving its distensibility and thus leads to improved quality of life for patients. PMID:22086527

Mechanical evaluation of the resistance and elastance of post-burn scars after topical treatment with tretinoin.

PubMed

Dematte, Maria Fernanda; Gemperli, Rolf; Salles, Alessandra Grassi; Dolhnikoff, Marisa; Lanças, Tatiana; Saldiva, Paulo Hilário Nascimento; Ferreira, Marcus Castro

2011-01-01

After burn injuries, scarred skin lacks elasticity, especially in hypertrophic scars. Topical treatment with tretinoin can improve the appearance and quality of the skin (i.e., texture, distensibility, color, and hydration). The objective of this prospective study was to examine the effects of treatment with 0.05% tretinoin for one year on the biomechanical behavior and histological changes undergone by facial skin with post-burn scarring. Tertiary, Institutional. Fifteen female patients who had suffered partial thickness burns with more than two years of evolution were selected. Skin biopsies were obtained initially and after one year of treatment. The resistance and elastance of these skin biopsies were measured using a mechanical oscillation analysis system. The density of collagen fibers, elastic fibers, and versican were determined using immunohistochemical analysis. Tretinoin treatment significantly lowered skin resistance and elastance, which is a result that indicates higher distensibility of the skin. However, tretinoin treatment did not significantly affect the density of collagen fibers, elastic fibers, or versican. Topical tretinoin treatment alters the mechanical behavior of post-burn scarred skin by improving its distensibility and thus leads to improved quality of life for patients.

Elastic Response of Crimped Collagen Fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils have a three-dimensional structure at the micrometer scale that we approximate as a helical spring. The symmetry of this waveform allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendineae

High-Temperature Elasticity of Topaz: A Resonant Ultrasound Spectroscopic study

NASA Astrophysics Data System (ADS)

Tennakoon, S.; Peng, Y.; Andreu, L.; Rivera, F.; Mookherjee, M.; Manthilake, G.; Speziale, S.

2017-12-01

Topaz (Al2SiO4(F,OH)2) is a hydrous aluminosilicate mineral stable in the hydrated sediments in subduction zone settings and could transport water into the Earth's interior. To constrain the amount of water subducted, it is important to have a better understanding of the elastic constants of hydrous phases and compare them with the geophysical observations. In this study, we explored the full elastic moduli tensor for a single crystal topaz using Resonant Ultrasound Spectroscopy. We determined the full elastic moduli tensor at ambient conditions (1 bar and 297 K), with the principal components- C11, C22, and C33 are 279, 352 and 288 GPa respectively, the off-diagonal components- C­12, C13, and C23 are 124, 72, and 82 GPa respectively, and the shear components- C44, C55, and C66 are 111, 134, and 130 GPa respectively. The compressional (AVP) and shear (AVS) anisotropy for topaz are 13 and 14 % respectively. The aggregate bulk (K) and shear (G) moduli are 162 and 117 GPa respectively. We determined the elasticity of topaz up to 1000 K. The components of the full elastic moduli tensor show softening at high temperature. Temperature derivatives of sound velocity of topaz, dVP/dT = -3.5 ×10-4 km/s/K and dVS/dT = -2.2 ×10-4 km/s/K are smaller than those for corundum [1], α-quartz [2], and olivine [3]. In contrast, the temperature derivatives of primary and shear sound velocity for topaz is greater than that of pyrope garnet [4]. The elasticity and sound velocity of topaz also vary as a function of chemistry i.e., OH-F contents. Our study demonstrates that the effect of composition (xOH) on the velocity is more pronounced than that of temperature.Acknowledgement: This study is supported by US NSF awards EAR-1634422. Reference: [1] Goto, T. et al.,1989, J. Geophys. Res., 94, 7588; [2] Ohno, I. et al., 2006, Phys. Chem. Miner., 33, 1-9; [3] Isaak, D. G., 1992, J. Geophys. Res. Solid Earth, 97, 1871-1885; [4] Sinogeikin, S. V., Bass, J. D., 2002, Earth Planet. Sci. Lett

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments.

PubMed

Lee, Jia-Jye; Rao, Satish; Kaushik, Gaurav; Azeloglu, Evren U; Costa, Kevin D

2018-06-05

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of

Moho depth and equivalent elastic thickness of the lithosphere over the Vema Channel: A new evidence of an aborted ridge

NASA Astrophysics Data System (ADS)

Constantino, Renata Regina; Costa, Iago Sousa Lima; Hackspacher, Peter Christian; de Souza, Iata Anderson

2018-03-01

We investigate the Vema Channel in terms of spatial variations of the elastic thickness (Te) in the frame of the thin plate flexure model using the convolutive method. The modeling of the Moho in terms of the thin plate flexure model is done by a least squares approximation of the Moho obtained from gravity inversion. The flexure is calculated by the convolution of the crustal load with the point-load flexure response curves. The RMS difference between the gravity and flexure Moho surfaces is minimized by varying the Te by inverse modeling. The result is a solution of the flexed crust that is in best agreement with the long-wavelength component of the gravity field. The flexure Moho depths vary between 12 and 18 km and agree well with those obtained from gravity inversion. The spatial variations of Te range from 2 to 30 km and have a good correlation with the geological interpretation for an aborted ridge near Vema Channel, called in this paper as the Vema Aborted Ridge (VAR). The occurring of seamounts appears to be correlated to a weak and deformed region. Attempts of crustal breakup are marked by high Te values (30 km) while lower values (3-12 km) are found for the suggested aborted ridge. The VAR is on Isochron of 93 Ma and shows symmetrical older along both sides of its axis. Asymmetric magnetic anomalies are found over the ridge and may be related to upper-extended continental crust broken by the Vema.

Constraining Lithospheric Stress on Mars From Mars Global Surveyor (MGS) Topography, Gravity, and Crustal Thickness

NASA Astrophysics Data System (ADS)

Dimitrova, L. L.; Holt, W. E.; Haines, A. J.

2004-12-01

The quantification of lithospheric dynamics on Mars is of fundamental importance to the understanding of Martian geologic history and surface morphology. The global stress field associated with gravitational potential energy differences (GPE) constitutes a significant fraction of the total stress field. We have obtained 0.25 × 0.25 degree data sets of MOLA topography and crustal thickness from Zuber et al 2000. We calculate the GPE associated with the topography by vertically integrating density to a given lithospheric depth using either Airy isostasy assumptions or the crustal thickness model of Zuber et al 2000. Using a finite-element thin sheet method we solve the full 3-D force-balance equations for stress magnitudes and orientations within the lithosphere associated with the horizontal gradients in GPE. We assume ρ crust = 2900~ kg m-3, ~ρ mantle = 3500~ kg m-3, ~g = 3.7~ ms-2 and various lithospheric thicknesses. We explore both viscous and elastic rheologies. It is interesting to note that our solutions depend on the rheology only through the ratio of shear and bulk moduli for the elastic case or the shear and bulk viscosities for the viscous case. Finally, we also calculate the expected style and orientation of the associated elastic strain. To first order, all stress field solutions are consistent with a tectonically inactive region relaxing due to excess or deficit of mass. Thus topographic highs e.g., Tharsis Mons, Olympus Mons, and Alba Patera, are in deviatoric extension, while topographic lows e.g., Valles Marineras and impact basins, are in deviatoric compression. At short wavelengths, however, features are regionally supported and differences in the stress field solutions occur between the Airy isostasy and the crustal thickness models. For example, several lowlands e.g., Isidis and Argyre Planitae, are in deviatoric extension in the crustal thickness model. Increasing the lithospheric depth increases the magnitudes of stresses but does not

Nanoindentation study of electrodeposited Ag thin coating: An inverse calculation of anisotropic elastic-plastic properties

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

Cheng, Guang; Sun, Xin; Wang, Yuxin

A new inverse method was proposed to calculate the anisotropic elastic-plastic properties (flow stress) of thin electrodeposited Ag coating utilizing nanoindentation tests, previously reported inverse method for isotropic materials and three-dimensional (3-D) finite element analyses (FEA). Indentation depth was ~4% of coating thickness (~10 μm) to avoid substrate effect and different indentation responses were observed in the longitudinal (L) and the transverse (T) directions. The estimated elastic-plastic properties were obtained in the newly developed inverse method by matching the predicted indentation responses in the L and T directions with experimental measurements considering indentation size effect (ISE). The results were validatedmore » with tensile flow curves measured from free-standing (FS) Ag film. The current method can be utilized to characterize the anisotropic elastic-plastic properties of coatings and to provide the constitutive properties for coating performance evaluations.« less

Elastic hydrogel substrate supports robust expansion of murine myoblasts and enhances their engraftment

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

Ding, Ke, E-mail: dk1118@yeah.net; Yang, Zhong; Xu, Jian-zhong, E-mail: xjzspine@163.com

The application of satellite cell-derived myoblasts in regenerative medicine has been restricted by the rapid loss of stemness during in vitro cell expansion using traditional culture systems. However, studies published in the past decade have highlighted the influence of substrate elasticity on stem cell fate and revealed that culture on a soft hydrogel substrate can promote self-renewal and prolong the regenerative potential of muscle stem cells. Whether hydrogel substrates have similar effects after long-term robust expansion remains to be determined. Herein we prepared an elastic chitosan/beta-glycerophosphate/collagen hydrogel mimicking the soft microenvironment of muscle tissues for use as the substrate formore » satellite cell culture and investigated its influence on long-term cell expansion. After 20 passages in culture, satellite cell-derived myoblasts cultured on our hydrogel substrate exhibited significant improvements in proliferation capability, cell viability, colony forming frequency, and potential for myogenic differentiation compared to those cultured on a routine rigid culture surface. Immunochemical staining and western blot analysis both confirmed that myoblasts cultured on the hydrogel substrate expressed higher levels of several differentiation-related markers, including Pax7, Pax3, and SSEA-1, and a lower level of MyoD compared to myoblasts cultured on rigid culture plates (all p<0.05). After transplantation into the tibialis anterior of nude mice, myoblasts that had been cultured on the hydrogel substrate demonstrated a significantly greater engraftment efficacy than those cultured on the traditional surface. Collectively, these results indicate that the elastic hydrogel substrate supported robust expansion of murine myoblasts and enhanced their engraftment in vivo. - Highlights: • An elastic hydrogel was designed to mimic the pliable muscle tissue microenvironment. • Myoblasts retained their stemness in long-term culture on the

Thickness-shear mode quartz crystal resonators in viscoelastic fluid media

NASA Astrophysics Data System (ADS)

Arnau, A.; Jiménez, Y.; Sogorb, T.

2000-10-01

An extended Butterworth-Van Dyke (EBVD) model to characterize a thickness-shear mode quartz crystal resonator in a semi-infinite viscoelastic medium is derived by means of analysis of the lumped elements model described by Cernosek et al. [R. W. Cernosek, S. J. Martin, A. R. Hillman, and H. L. Bandey, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1399 (1998)]. The EBVD model parameters are related to the viscoelastic properties of the medium. A capacitance added to the motional branch of the EBVD model has to be included when the elastic properties of the fluid are considered. From this model, an explicit expression for the frequency shift of a quartz crystal sensor in viscoelastic media is obtained. By combining the expressions for shifts in the motional series resonant frequency and in the motional resistance, a simple equation that relates only one unknown (the loss factor of the fluid) to those measurable quantities, and two simple explicit expressions for determining the viscoelastic properties of semi-infinite fluid media have been derived. The proposed expression for the parameter Δf/ΔR is compared with the corresponding ratio obtained with data computed from the complete admittance model. Relative errors below 4.5%, 3%, and 1.2% (for the ratios of the load surface mechanical impedance to the quartz shear characteristic impedance of 0.3, 0.25, and 0.1, respectively), are obtained in the range of the cases analyzed. Experimental data from the literature are used to validate the model.

The impact of ice I rheology on interior models of Ganymede: The elastic vs. the visco-elastic case

NASA Astrophysics Data System (ADS)

Steinbrügge, Gregor; Hussmann, Hauke; Sohl, Frank; Oberst, Jürgen

2015-04-01

Many investigations on key processes of icy satellites are driven by the rheological behavior of planetary ices. Future missions to Jupiter's icy moons (e.g. JUICE / Europa clipper) aimed at constraining the thickness of the outer ice shell using radio science and/or laser altimetry will have to address this problem. We investigate for the case of Ganymede under which conditions the ice I viscosity could be constrained by measuring the phase-lag of the tidal response using laser altimetry. In the absence of seismic data, interior structure models are constrained by the satellite's mean density and mean moment-of-inertia factor. One key observable to reduce the ambiguity of the corresponding structural models is the measurement of the dynamic response of the satellite's outer ice shells to tidal forces exerted by Jupiter and characterized by the body tide surface Love numbers h2 and k2. The Love number k2 measures the variation of the gravitational potential due to tidally induced internal redistribution of mass and can be inferred from radio science experiments. The Love number h2 is a measure for the tide-induced radial displacement of the satellite's surface. It is an advantage that Ganymede's surface displacement Love number h2 can be expected to be measured with a high accuracy using laser altimetry (Steinbrügge et al., 2014). However, the determination of the resulting ice thickness further depends on the possible existence of a liquid subsurface water ocean and on the tidally effective rheology of the outer ice shell (Moore and Schubert, 2003). Here, we distinguish between an elastic, visco-elastic or even fluid behavior in the sense of the Maxwell model and alternative rheological models. In the case of Ganymede the fluid case would imply high ice temperatures which are at odds with thermal equilibrium models calculated by Spohn and Schubert (2003). However the visco-elastic case is still possible. Laboratory measurements of ice I (e.g. Sotin et al., 1998

Estimating the own-price elasticity of demand for irrigation water in the Musi catchment of India

NASA Astrophysics Data System (ADS)

Davidson, Brian; Hellegers, Petra

2011-10-01

SummaryAs irrigation water is an input into a production process, its demand must be 'derived'. According to theory, a derived demand schedule should be downward sloping and dependent on the outputs produced from it, the prices of other inputs and the price of the water itself. Problems arise when an attempt is made to estimate the demand for irrigation water and the resulting own-price elasticity of demand, as the uses to which water is put are spatially, temporarily and geographically diverse. Because water is not generally freely traded, what normally passes for an estimate of the own-price elasticity of demand for irrigation water is usually a well argued assumption or an estimate that is derived from a simulation model of a hypothesized producer. Such approaches tend to provide an inadequate explanation of what is an extremely complex and important relationship. An adequate explanation of the relationship between the price and the quantity demanded of water should be one that not only accords with the theoretical expectations, but also accounts for the diversity of products produced from water (which includes the management practices of farmers), the seasons in which it is used and over the region within which it is used. The objective in this article is to present a method of estimating the demand curve for irrigation water. The method uses actual field data which is collated using the Residual Method to determine the value of the marginal product of water deployed over a wide range of crops, seasons and regions. These values of the marginal products, all which must lie of the input demand schedule for water, are then ordered from the highest value to the lowest. Then, the amount of irrigation water used for each product, in each season and in each region is cumulatively summed over the range of uses according to the order of the values of the marginal products. This data, once ordered, is then used to econometrically estimate the demand schedule from which

Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping

NASA Astrophysics Data System (ADS)

Zhao, Jiong; Deng, Qingming; Ly, Thuc Hue; Han, Gang Hee; Sandeep, Gorantla; Rümmeli, Mark H.

2015-11-01

The great application potential for two-dimensional (2D) membranes (MoS2, WSe2, graphene and so on) aroused much effort to understand their fundamental mechanical properties. The out-of-plane bending rigidity is the key factor that controls the membrane morphology under external fields. Herein we provide an easy method to reconstruct the 3D structures of the folded edges of these 2D membranes on the atomic scale, using high-resolution (S)TEM images. After quantitative comparison with continuum mechanics shell model, it is verified that the bending behaviour of the studied 2D materials can be well explained by the linear elastic shell model. And the bending rigidities can thus be derived by fitting with our experimental results. Recall almost only theoretical approaches can access the bending properties of these 2D membranes before, now a new experimental method to measure the bending rigidity of such flexible and atomic thick 2D membranes is proposed.

Lattice model calculation of elastic and thermodynamic properties at high pressure and temperature. [for alkali halides in NaCl lattice

NASA Technical Reports Server (NTRS)

Demarest, H. H., Jr.

1972-01-01

The elastic constants and the entire frequency spectrum were calculated up to high pressure for the alkali halides in the NaCl lattice, based on an assumed functional form of the inter-atomic potential. The quasiharmonic approximation is used to calculate the vibrational contribution to the pressure and the elastic constants at arbitrary temperature. By explicitly accounting for the effect of thermal and zero point motion, the adjustable parameters in the potential are determined to a high degree of accuracy from the elastic constants and their pressure derivatives measured at zero pressure. The calculated Gruneisen parameter, the elastic constants and their pressure derivatives are in good agreement with experimental results up to about 600 K. The model predicts that for some alkali halides the Grunesen parameter may decrease monotonically with pressure, while for others it may increase with pressure, after an initial decrease.

Estimation of critical thickness of Stranski-Krastanow transition in GeSi/Sn/Si system

NASA Astrophysics Data System (ADS)

Lozovoy, K. A.; Pishchagin, A. A.; Kokhanenko, A. P.; Voitsekhovskii, A. V.

2017-11-01

In this paper Stranski-Krastanow growth of Ge x Si1-x epitaxial layers on the Si(001) surface with pre-deposited tin layer with the thickness less than 1 ML is considered. For the calculations of critical thickness of transition from 2D to 3D growth in this paper a theoretical model based on general nucleation theory is used. This model is specified by taking into account dependencies of elastic modulus, lattices mismatch and surface energy of side facet on the composition x, as well as change in the adatoms diffusion coefficient and surface energy of the substrate in the presence of tin. As a result, dependencies of critical thickness of Stranski-Krastanow transition on compositon x and temperature are obtained. The simulated results are in a good agreement with experimentally observed results.

Use of an ultrasonic device for the determination of elastic modulus of dentin.

PubMed

Miyazaki, Masashi; Inage, Hirohiko; Onose, Hideo

2002-03-01

The mechanical properties of dentin substrate are one of the important factors in determining bond strength of dentin bonding systems. The purpose of this study was to determine the elastic modulus of dentin substrate with the use of an ultrasonic device. The dentin disks of about 1 mm thickness were obtaining from freshly extracted human third molars, and the dentin disk was shaped in a rectangular form with a line diamond point. The size and weight of each specimen was measured to calculate the density of the specimen. The ultrasonic equipment employed in this study was composed of a Pulser-Receiver (Model 5900PR, Panametrics), transducers (V155, V156, Panametrics) and an oscilloscope. The measured two-way transit time through the dentin disk was divided by two to account for the down-and-back travel path, and then multiplied by the velocity of sound in the test material. Measuring the longitudinal and share wave sound velocity determine elastic modulus. The mean elastic modulus of horizontally sectioned specimens was 21.8 GPa and 18.5 GPa for the vertically sectioned specimens, and a significant difference was found between the two groups. The ultrasonic method used in this study shows considerable promise for determination of the elastic modulus of the tooth substrate.

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

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

Juan, Pierre -Alexandre; Dingreville, Remi

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to themore » complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.« less

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

DOE PAGES

Juan, Pierre -Alexandre; Dingreville, Remi

2017-09-13

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to themore » complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.« less

Elastic scattering and total reaction cross section of {sup 6}He+{sup 120}Sn

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

Faria, P. N. de; Lichtenthaeler, R.; Pires, K. C. C.

The elastic scattering of {sup 6}He on {sup 120}Sn has been measured at four energies above the Coulomb barrier using the {sup 6}He beam produced at the RIBRAS (Radioactive Ion Beams in Brasil) facility. The elastic angular distributions have been analyzed with the optical model and three- and four-body continuum-discretized coupled-channels calculations. The total reaction cross sections have been derived and compared with other systems of similar masses.

Converging shocks in elastic-plastic solids.

PubMed

Ortega, A López; Lombardini, M; Hill, D J

2011-11-01

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=e(s)(I(1))+e(h)(ρ,ς), where e(s) accounts for shear through the first invariant of the Cauchy-Green tensor, and e(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e(h)=e(h)(ρ), with a power-law dependence e(h) is proportional to ρ(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M is proportional to [log(1/R)](α), independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M is proportional to R(-(s-1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part e(h) is that of an ideal gas, is also tested, recovering the strong-shock limit M is proportional to R(-(s-1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the

Through thick and thin: Structure of the Galactic thick disc from extragalactic surveys

NASA Astrophysics Data System (ADS)

Kordopatis, G.; Hill, V.; Irwin, M.; Gilmore, G.; Wyse, R. F. G.; Tolstoy, E.; de Laverny, P.; Recio-Blanco, A.; Battaglia, G.; Starkenburg, E.

2013-07-01

Context. We aim to understand the accretion history of the Milky Way by exploring the vertical and radial properties of the Galactic thick disc. Aims: We study the chemical and kinematic properties of roughly a thousand spectra of faint magnitude foreground Galactic stars observed serendipitously during extra-galactic surveys in four lines-of-sight: three in the southern Galactic hemisphere (surveys of the Carina, Fornax and Sculptor dwarf spheroidal galaxies) and one in the northern Galactic hemisphere (a survey of the Sextans dwarf spheroidal galaxy). The foreground stars span distances up to ~3 kpc from the Galactic plane and Galactocentric radii up to 11 kpc. Methods: The stellar atmospheric parameters (effective temperature, surface gravity, metallicity) are obtained by an automated parameterisation pipeline and the distances of the stars are then derived by a projection of the atmospheric parameters on a set of theoretical isochrones using a Bayesian approach. The metallicity gradients are estimated for each line-of-sight and compared with predictions from the Besançon model of the Galaxy, in order to test the chemical structure of the thick disc. Finally, we use the radial velocities in each line-of-sight to derive a proxy for either the azimuthal or the vertical component of the orbital velocity of the stars. Results: Only three lines-of-sight have a sufficient number of foreground stars for a robust analysis. Towards Sextans in the Northern Galactic hemisphere and Sculptor in the South, we measure a consistent decrease in mean metallicity with height from the Galactic plane, suggesting a chemically symmetric thick disc. This decrease can either be due to an intrinsic thick disc metallicity gradient, or simply due to a change in the thin disc/thick disc population ratio and no intrinsic metallicity gradients for the thick disc. We favour the latter explanation. In contrast, we find evidence of an unpredicted metal-poor population in the direction of Carina

Extended analytical solutions for effective elastic moduli of cracked porous media

NASA Astrophysics Data System (ADS)

Nguyen, Sy-Tuan; To, Quy Dong; Vu, Minh Ngoc

2017-05-01

Extended solutions are derived, on the basis of the micromechanical methods, for the effective elastic moduli of porous media containing stiff pores and both open and closed cracks. Analytical formulas of the overall bulk and shear moduli are obtained as functions of the elastic moduli of the solid skeleton, porosity and the densities of open and closed cracks families. We show that the obtained results are extensions of the classical widely used Walsh's (JGR, 1965) and Budiansky-O‧Connell's (JGR, 1974) solutions. Parametric sensitivity analysis clarifies the impact of the model parameters on the effective elastic properties. An inverse analysis, using sonic and density data, is considered to quantify the density of both open and closed cracks. It is observed that the density of closed cracks depends strongly on stress condition while the dependence of open cracks on the confining stress is negligible.

Attenuation and Dispersion Analysis in Laboratory Measured Elastic Properties in the Middle East Carbonate Reservoir Rocks

NASA Astrophysics Data System (ADS)

Sharma, R.

2016-12-01

Carbonate rocks are sensitive to circulation of fluid types that leads to diagenetic alterations and therefore to heterogeneity in distribution of porosity and permeability. These heterogeneities in turn, lead to heterogeneity in saturations varying from partial to patchy to uniform. Depending on the interaction between fluids and rock matrix, a weakening or strengthening in shear modulus of carbonate rocks can also develop (Eberli et al., 2003; Adam et al., 2006; Sharma et al., 2009; Sharma et al., 2013). Thus the elastic response over the production life of the carbonate reservoirs can change considerably. Efforts to couple fluid flow with varying seismic properties of these reservoirs are limited in success due to the differences between static elastic properties derived from reservoir simulation and dynamic elastic properties derived from inverted seismic. An additional limitation arises from the assumption that shear modulus does not change with fluid type and saturations. To overcome these limitations, we need to understand the relationships between the static and the dynamic elastic properties using laboratory measurements made at varying pressures, frequencies and with varying saturants. I will present the following results: 1) errors associated with using dynamic (2 - 2000 Hz and 1 MHz) elastic properties data for static ( 0 Hz) reservoir properties, 2) shear modulus variation in carbonates upon saturation with varying saturants The results will enable us to estimate, 1) distribution of stress-strain relations in reservoir rocks and 2) modulus dispersion to correct seismic-derived moduli as inputs for reservoir simulators. The results are critical to estimate, 1) modulus dispersion correction and 2) occurrence and amount of shear modulus variation with fluid change vital for rock stability analysis

Interface crack in a nonhomogeneous elastic medium

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1988-01-01

The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

NASA Astrophysics Data System (ADS)

Wei, Lai; Zeng, Jing; Chi, Maoru; Wang, Jianbin

2017-09-01

In particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel-rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid-flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel-rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.

An Obstacle Problem for Conical Deformations of Thin Elastic Sheets

NASA Astrophysics Data System (ADS)

Figalli, Alessio; Mooney, Connor

2018-05-01

A developable cone ("d-cone") is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance {ɛ}. Starting from a nonlinear model depending on the thickness h > 0 of the sheet, we prove a {Γ} -convergence result as {h → 0} to a fourth-order obstacle problem for curves in {S^2}. We then describe the exact shape of minimizers of the limit problem when {ɛ} is small. In particular, we rigorously justify previous results in the physics literature.

Elastic constants of hcp 4He: Path-integral Monte Carlo results versus experiment

NASA Astrophysics Data System (ADS)

Ardila, Luis Aldemar Peña; Vitiello, Silvio A.; de Koning, Maurice

2011-09-01

The elastic constants of hcp 4He are computed using the path-integral Monte Carlo (PIMC) method. The stiffness coefficients are obtained by imposing different distortions to a periodic cell containing 180 atoms, followed by measurement of the elements of the corresponding stress tensor. For this purpose an appropriate path-integral expression for the stress tensor observable is derived and implemented into the pimc++ package. In addition to allowing the determination of the elastic stiffness constants, this development also opens the way to an explicit atomistic determination of the Peierls stress for dislocation motion using the PIMC technique. A comparison of the results to available experimental data shows an overall good agreement of the density dependence of the elastic constants, with the single exception of C13. Additional calculations for the bcc phase, on the other hand, show good agreement for all elastic constants.

QUANTITATIVE NON-DESTRUCTIVE EVALUATION (QNDE) OF THE ELASTIC MODULI OF POROUS TIAL ALLOYS

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

Yeheskel, O.

2008-02-28

The elastic moduli of {gamma}-TiA1 were studied in porous samples consolidated by various techniques e.g. cold isostatic pressing (CIP), pressure-less sintering, or hot isostatic pressing (HIP). Porosity linearly affects the dynamic elastic moduli of samples. The results indicate that the sound wave velocities and the elastic moduli affected by the processing route and depend not only on the attained density but also on the consolidation temperature. In this paper we show that there is linear correlation between the shear and the longitudinal sound velocities in porous TiA1. This opens the way to use a single sound velocity as a toolmore » for quantitative non-destructive evaluation (QNDE) of porous TiA1 alloys. Here we demonstrate the applicability of an equation derived from the elastic theory and used previously for porous cubic metals.« less

Inverse finite element methods for extracting elastic-poroviscoelastic properties of cartilage and other soft tissues from indentation

NASA Astrophysics Data System (ADS)

Namani, Ravi

Mechanical properties are essential for understanding diseases that afflict various soft tissues, such as osteoarthritic cartilage and hypertension which alters cardiovascular arteries. Although the linear elastic modulus is routinely measured for hard materials, standard methods are not available for extracting the nonlinear elastic, linear elastic and time-dependent properties of soft tissues. Consequently, the focus of this work is to develop indentation methods for soft biological tissues; since analytical solutions are not available for the general context, finite element simulations are used. First, parametric studies of finite indentation of hyperelastic layers are performed to examine if indentation has the potential to identify nonlinear elastic behavior. To answer this, spherical, flat-ended conical and cylindrical tips are examined and the influence of thickness is exploited. Also the influence of the specimen/substrate boundary condition (slip or non-slip) is clarified. Second, a new inverse method---the hyperelastic extraction algorithm (HPE)---was developed to extract two nonlinear elastic parameters from the indentation force-depth data, which is the basic measurement in an indentation test. The accuracy of the extracted parameters and the influence of noise in measurements on this accuracy were obtained. This showed that the standard Berkovitch tip could only extract one parameter with sufficient accuracy, since the indentation force-depth curve has limited sensitivity to both nonlinear elastic parameters. Third, indentation methods for testing tissues from small animals were explored. New methods for flat-ended conical tips are derived. These account for practical test issues like the difficulty in locating the surface or soft specimens. Also, finite element simulations are explored to elucidate the influence of specimen curvature on the indentation force-depth curve. Fourth, the influence of inhomogeneity and material anisotropy on the extracted

Method for computing energy release rate using the elastic work factor approach

NASA Astrophysics Data System (ADS)

Rhee, K. Y.; Ernst, H. A.

1992-01-01

The elastic work factor eta(el) concept was applied to composite structures for the calculation of total energy release rate by using a single specimen. Cracked lap shear specimens with four different unidirectional fiber orientation were used to examine the dependence of eta(el) on the material properties. Also, three different thickness ratios (lap/strap) were used to determine how geometric conditions affect eta(el). The eta(el) values were calculated in two different ways: compliance method and crack closure method. The results show that the two methods produce comparable eta(el) values and, while eta(el) is affected significantly by geometric conditions, it is reasonably independent of material properties for the given geometry. The results also showed that the elastic work factor can be used to calculate total energy release rate using a single specimen.

Thick shell tectonics on one-plate planets - Applications to Mars

NASA Technical Reports Server (NTRS)

Banerdt, W. B.; Saunders, R. S.; Phillips, R. J.; Sleep, N. H.

1982-01-01

Using the zero frequency equations of a self-gravitating elastic spherical shell overlying a strengthless fluid, a theory for stress distribution in thick lithospheric shells on one-plate planets is developed. For both the compensated and flexural modes, stress distributions in lithospheres are reviewed. For compensated modes, surface stresses depend only on surface topography, whereas for flexural modes it is shown that, for long wavelengths, stress trajectories are mainly dependent on the lithospheric lateral density distribution and not on elastic properties. Computational analyses are performed for Mars, and it is found that isostatically compensated models correctly predict the graben structure in the immediate Tharsis region and a flexural loading model is satisfactory in explaining the graben in the regions surrounding Tharsis. A three-stage model for the evolution of Tharsis is hypothesized: isostasy with north-south graben formation on Tharsis, followed by flexural loading and radial graben formation on the perimeter of Tharsis, followed by a last stage of loading with little or no regional deformation.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections. Part 1; Electron-Hydrogen Elastic Scattering

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2001-01-01

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Guided elastic waves in a pre-stressed compressible interlayer

PubMed

Sotiropoulos

2000-03-01

The propagation of guided elastic waves in a pre-stressed elastic compressible layer embedded in a different compressible material is examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer and host material. The underlying stress condition in the two materials is characterized by equibiaxial in-plane deformations with common principal axes of strain, one of the axes being perpendicular to the layering. Both materials have arbitrary strain energy functions. The dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency, material parameters and stress parameters. Combinations of these parameters are also defined for which guided waves cannot propagate.

The asymptotic homogenization elasticity tensor properties for composites with material discontinuities

NASA Astrophysics Data System (ADS)

Penta, Raimondo; Gerisch, Alf

2017-01-01

The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents' elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite's interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents' elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies ( Hill's condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young's and shear moduli) and Poisson's ratio at increasing (up to

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Surface instability of an imperfectly bonded thin elastic film under surface van der Waals forces

NASA Astrophysics Data System (ADS)

Wang, Xu; Jing, Rong

2017-02-01

This paper studies surface instability of a thin elastic film imperfectly bonded to a rigid substrate interacting with a rigid contactor through van der Waals forces under plane strain conditions. The film-substrate interface is modeled as a linear spring with vanishing thickness described in terms of the normal and tangential interface parameters. Depending on the ratio of the two imperfect interface parameters, the critical value of the Poisson's ratio for the occurrence of surface wrinkling in the absence of surface energy can be greater than, equal to, or smaller than 0.25, which is the critical Poisson's ratio for a perfect film-substrate interface. The critical surface energy for the inhibition of the surface wrinkling is also obtained. Finally, we propose a very simple and effective method to study the surface instability of a multilayered elastic film with imperfect interfaces interacting with a rigid contactor or with another multilayered elastic film (or a multilayered simply supported plate) with imperfect interfaces.

Thickness-shear and thickness-twist modes in an AT-cut quartz acoustic wave filter.

PubMed

Zhao, Zinan; Qian, Zhenghua; Wang, Bin; Yang, Jiashi

2015-04-01

We studied thickness-shear and thickness-twist vibrations of a monolithic, two-pole crystal filter made from a plate of AT-cut quartz. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded quartz plates were employed which are valid for both the fundamental and the overtone modes. Exact solutions for the free vibration resonant frequencies and modes were obtained from the equations. For a structurally symmetric filter, the modes can be separated into symmetric and antisymmetric ones. Trapped modes with vibrations mainly under the electrodes were found. The effect of the distance between the two pairs of electrodes was examined. Copyright © 2015 Elsevier B.V. All rights reserved.

Motion of an elastic capsule in a square microfluidic channel.

PubMed

Kuriakose, S; Dimitrakopoulos, P

2011-07-01

In the present study we investigate computationally the steady-state motion of an elastic capsule along the centerline of a square microfluidic channel and compare it with that in a cylindrical tube. In particular, we consider a slightly over-inflated elastic capsule made of a strain-hardening membrane with comparable shearing and area-dilatation resistance. Under the conditions studied in this paper (i.e., small, moderate, and large capsules at low and moderate flow rates), the capsule motion in a square channel is similar to and thus governed by the same scaling laws with the capsule motion in a cylindrical tube, even though in the channel the cross section in the upstream portion of large capsules is nonaxisymmetric (i.e., square-like with rounded corners). When the hydrodynamic forces on the membrane increase, the capsule develops a pointed downstream edge and a flattened rear (possibly with a negative curvature) so that the restoring tension forces are increased as also happens with droplets. Membrane tensions increase significantly with the capsule size while the area near the downstream tip is the most probable to rupture when a capsule flows in a microchannel. Because the membrane tensions increase with the interfacial deformation, a suitable Landau-Levich-Derjaguin-Bretherton analysis reveals that the lubrication film thickness h for large capsules depends on both the capillary number Ca and the capsule size a; our computations determine the latter dependence to be (in dimensionless form) h ~ a(-2) for the large capsules studied in this work. For small and moderate capsule sizes a, the capsule velocity Ux and additional pressure drop ΔP+ are governed by the same scaling laws as for high-viscosity droplets. The velocity and additional pressure drop of large thick capsules also follow the dynamics of high-viscosity droplets, and are affected by the lubrication film thickness. The motion of our large thick capsules is characterized by a Ux-U ~ h ~ a(-2

Motion of an elastic capsule in a square microfluidic channel

PubMed Central

Kuriakose, S.; Dimitrakopoulos, P.

2013-01-01

In the present study we investigate computationally the steady-state motion of an elastic capsule along the centerline of a square microfluidic channel and compare it with that in a cylindrical tube. In particular, we consider a slightly over-inflated elastic capsule made of a strain-hardening membrane with comparable shearing and area-dilatation resistance. Under the conditions studied in this paper (i.e. small, moderate and large capsules at low and moderate flow rates), the capsule motion in a square channel is similar to, and thus governed by the same scaling laws with the capsule motion in a cylindrical tube, even though in the channel the cross-section in the upstream portion of large capsules is non-axisymmetric (i.e. square-like with rounded corners). When the hydrodynamic forces on the membrane increase, the capsule develops a pointed downstream edge and a flattened rear (possibly with a negative curvature) so that the restoring tension forces are increased as also happens with droplets. Membrane tensions increase significantly with the capsule size while the area near the downstream tip is the most probable to rupture when a capsule flows in a microchannel. Because the membrane tensions increase with the interfacial deformation, a suitable Landau-Levich-Derjaguin-Bretherton analysis reveals that the lubrication film thickness h for large capsules depends on both the capillary number Ca and the capsule size a; our computations determine the latter dependence to be (in dimensionless form) h ~ a−2 for the large capsules studied in this work. For small and moderate capsule sizes a, the capsule velocity Ux and additional pressure drop ΔP+ are governed by the same scaling laws as for high-viscosity droplets. The velocity and additional pressure drop of large thick capsules also follow the dynamics of high-viscosity droplets, and are affected by the lubrication film thickness. The motion of our large thick capsules is characterized by a Ux−u~h~a−2

Elasticity reconstruction: Beyond the assumption of local homogeneity

NASA Astrophysics Data System (ADS)

Sinkus, Ralph; Daire, Jean-Luc; Van Beers, Bernard E.; Vilgrain, Valerie

2010-07-01

Elasticity imaging is a novel domain which is currently gaining significant interest in the medical field. Most inversion techniques are based on the homogeneity assumption, i.e. the local spatial derivatives of the complex-shear modulus are ignored. This analysis presents an analytic approach in order to overcome this limitation, i.e. first order spatial derivatives of the real-part of the complex-shear modulus are taken into account. Resulting distributions in a gauged breast lesion phantom agree very well with the theoretical expectations. An in-vivo example of a cholangiocarcinoma demonstrates that the new approach provides maps of the viscoelastic properties which agree much better with expectations from anatomy.

General analytical approach for sound transmission loss analysis through a thick metamaterial plate

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

Oudich, Mourad; Zhou, Xiaoming; Badreddine Assouar, M., E-mail: Badreddine.Assouar@univ-lorraine.fr

We report theoretically and numerically on the sound transmission loss performance through a thick plate-type acoustic metamaterial made of spring-mass resonators attached to the surface of a homogeneous elastic plate. Two general analytical approaches based on plane wave expansion were developed to calculate both the sound transmission loss through the metamaterial plate (thick and thin) and its band structure. The first one can be applied to thick plate systems to study the sound transmission for any normal or oblique incident sound pressure. The second approach gives the metamaterial dispersion behavior to describe the vibrational motions of the plate, which helpsmore » to understand the physics behind sound radiation through air by the structure. Computed results show that high sound transmission loss up to 72 dB at 2 kHz is reached with a thick metamaterial plate while only 23 dB can be obtained for a simple homogeneous plate with the same thickness. Such plate-type acoustic metamaterial can be a very effective solution for high performance sound insulation and structural vibration shielding in the very low-frequency range.« less

Single-Crystal Elastic Constants of Yttria (Y2O3) Measured to High Temperatures

NASA Technical Reports Server (NTRS)

Sayir, Ali; Palko, James W.; Kriven, Waltraud M.; Sinogeikin, Sergey V.; Bass, Jay D.

2001-01-01

Yttria, or yttrium sesquioxide (Y2O3), has been considered for use in nuclear applications and has gained interest relatively recently for use in infrared optics. Single crystals of yttria have been grown successfully at the NASA Glenn Research Center using a laser-heated float zone technique in a fiber and rod. Such samples allow measurement of the single-crystal elastic properties, and these measurements provide useful property data for the design of components using single crystals. They also yield information as to what degree the elastic properties of yttria ceramics are a result of the intrinsic properties of the yttria crystal in comparison to characteristics that may depend on processing, such as microstructure and intergranular phases, which are common in sintered yttria. The single-crystal elastic moduli are valuable for designing such optical components. In particular, the temperature derivatives of elastic moduli allow the dimensional changes due to heating under physical constraints, as well as acoustic excitation, to be determined. The single-crystal elastic moduli of yttria were measured by Brillouin spectroscopy up to 1200 C. The room-temperature values obtained were C(sub 11) = 223.6 + 0.6 GPa, C(sub 44) = 74.6 + 0.5 GPa, and C(sub 12) = 112.4 + 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli were K = 149.5 + 1.0 GPa and G(sub VRH) = 66.3 + 0.8 GPa, respectively. Linear least-squares regressions to the variation of bulk and shear moduli with temperature resulted in derivatives of dK/dT = -17 + 2 MPa/C and dG(sub VRH)/dT = -8 + 2 MPa/ C. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

DOE PAGES

Juan, Pierre -Alexandre; Dingreville, Remi

2016-10-31

Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

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

Juan, Pierre -Alexandre; Dingreville, Remi

Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive “interferences” aremore » directly affected by the interface structure and its elastic response. Furthermore, this general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.« less

Elastic model for crimped collagen fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

Monitoring ice thickness and elastic properties from the measurement of leaky guided waves: A laboratory experiment.

PubMed

Moreau, Ludovic; Lachaud, Cédric; Théry, Romain; Predoi, Mihai V; Marsan, David; Larose, Eric; Weiss, Jérôme; Montagnat, Maurine

2017-11-01

The decline of Arctic sea ice extent is one of the most spectacular signatures of global warming, and studies converge to show that this decline has been accelerating over the last four decades, with a rate that is not reproduced by climate models. To improve these models, relying on comprehensive and accurate field data is essential. While sea ice extent and concentration are accurately monitored from microwave imagery, an accurate measure of its thickness is still lacking. Moreover, measuring observables related to the mechanical behavior of the ice (such as Young's modulus, Poisson's ratio, etc.) could provide better insights in the understanding of sea ice decline, by completing current knowledge so far acquired mostly from radar and sonar data. This paper aims at demonstrating on the laboratory scale that these can all be estimated simultaneously by measuring seismic waves guided in the ice layer. The experiment consisted of leaving a water tank in a cold room in order to grow an ice layer at its surface. While its thickness was increasing, ultrasonic guided waves were generated with a piezoelectric source, and measurements were subsequently inverted to infer the thickness and mechanical properties of the ice with very good accuracy.

Influence of chemistry, interfacial width, and non-isothermal conditions on spatially heterogeneous activated relaxation and elasticity in glass-forming free standing films

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

Mirigian, Stephen; Schweizer, Kenneth S.

Here, we employ the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation to study several questions in free standing thin films of glass-forming molecular and polymer liquids. The influence of non-universal chemical aspects on dynamical confinement effects is found to be relatively weak, but with the caveat that for the systems examined, the bulk ECNLE polymer theory does not predict widely varying fragilities. Allowing the film model to have a realistic vapor interfacial width significantly enhances the reduction of the film-averaged glass transition temperature, T g, in a manner that depends on whether a dynamic or pseudo-thermodynamic averagingmore » of the spatial mobility gradient is adopted. The nature of film thickness effects on the spatial profiles of the alpha relaxation time and elastic modulus is studied under non-isothermal conditions and contrasted with the corresponding isothermal behavior. Modest differences are found if a film-thickness dependent T g is defined in a dynamical manner. But, adopting a pseudo-thermodynamic measure of T g leads to a qualitatively new form of the alpha relaxation time gradient where highly mobile layers near the film surface coexist with strongly vitrified regions in the film interior. Consequently, the film-averaged shear modulus can increase with decreasing film thickness, despite the T g reduction and presence of a mobile surface layer. Such a behavior stands in qualitative contrast to the predicted mechanical softening under isothermal conditions. Spatial gradients of the elastic modulus are studied as a function of temperature, film thickness, probing frequency, and experimental protocol, and a rich behavior is found.« less

Influence of chemistry, interfacial width, and non-isothermal conditions on spatially heterogeneous activated relaxation and elasticity in glass-forming free standing films

DOE PAGES

Mirigian, Stephen; Schweizer, Kenneth S.

2017-02-02

Here, we employ the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated relaxation to study several questions in free standing thin films of glass-forming molecular and polymer liquids. The influence of non-universal chemical aspects on dynamical confinement effects is found to be relatively weak, but with the caveat that for the systems examined, the bulk ECNLE polymer theory does not predict widely varying fragilities. Allowing the film model to have a realistic vapor interfacial width significantly enhances the reduction of the film-averaged glass transition temperature, T g, in a manner that depends on whether a dynamic or pseudo-thermodynamic averagingmore » of the spatial mobility gradient is adopted. The nature of film thickness effects on the spatial profiles of the alpha relaxation time and elastic modulus is studied under non-isothermal conditions and contrasted with the corresponding isothermal behavior. Modest differences are found if a film-thickness dependent T g is defined in a dynamical manner. But, adopting a pseudo-thermodynamic measure of T g leads to a qualitatively new form of the alpha relaxation time gradient where highly mobile layers near the film surface coexist with strongly vitrified regions in the film interior. Consequently, the film-averaged shear modulus can increase with decreasing film thickness, despite the T g reduction and presence of a mobile surface layer. Such a behavior stands in qualitative contrast to the predicted mechanical softening under isothermal conditions. Spatial gradients of the elastic modulus are studied as a function of temperature, film thickness, probing frequency, and experimental protocol, and a rich behavior is found.« less

Theoretical requirements for broadband perfect absorption of acoustic waves by ultra-thin elastic meta-films

PubMed Central

Duan, Yuetao; Luo, Jie; Wang, Guanghao; Hang, Zhi Hong; Hou, Bo; Li, Jensen; Sheng, Ping; Lai, Yun

2015-01-01

We derive and numerically demonstrate that perfect absorption of elastic waves can be achieved in two types of ultra-thin elastic meta-films: one requires a large value of almost pure imaginary effective mass density and a free space boundary, while the other requires a small value of almost pure imaginary effective modulus and a hard wall boundary. When the pure imaginary density or modulus exhibits certain frequency dispersions, the perfect absorption effect becomes broadband, even in the low frequency regime. Through a model analysis, we find that such almost pure imaginary effective mass density with required dispersion for perfect absorption can be achieved by elastic metamaterials with large damping. Our work provides a feasible approach to realize broadband perfect absorption of elastic waves in ultra-thin films. PMID:26184117

Finite Element Modeling of Elastic Volume Changes in Fluid Inclusions: Comparison with Experiment

NASA Astrophysics Data System (ADS)

Burnley, P. C.; Bruhn, D.; Schmidt, C.

2003-12-01

Inclusions within mineral grains in rocks of all types are widely studied because they contain information about either the environment of formation of the mineral grain or conditions since. Understanding the mechanics of the inclusion-host system caused by differences in thermal expansion and compressibility is often essential for interpreting measurements made on the inclusion. We are studying the mechanics of inclusions by comparing elastic volume changes and deformation of synthetic pure water inclusions in quartz with finite element models of the individual inclusions. Synthetic fluid inclusions are ideal for such a study because the mechanical boundary conditions as well as the resulting deformation are either known or can be determined from the homogenization temperature and equation of state of the fluid. The experiments for this study were conducted using a hydrothermal diamond anvil cell with water as the pressure medium. The homogenization temperature of the inclusions was used to determine the inclusion volume at various confining pressures. The confining pressure was obtained from the homogenization or the ice I liquidus temperature of the pressure medium. After the experiment the homogenization temperature of the inclusion at 1 atm confining pressure was re-determined to confirm that the deformation of the inclusions was completely elastic. The inclusion shape for each model was determined from optical photomicrographs. The thickness of the synthetic fluid inclusions is consistently about 1 micron. We used a commercially available engineering package, MSC MARC/Mentat, to create and analyze two-dimensional and three-dimensional finite element models of the inclusions. The inclusions are assumed to have at least one mirror plane (parallel to the plane of the photograph) permitting a portion of the inclusion to be modeled. We assume a linear elastic response for the quartz host and have used both isotropic and anisotropic elastic moduli. Within the

Asymptotic self-restabilization of a continuous elastic structure

NASA Astrophysics Data System (ADS)

Bosi, F.; Misseroni, D.; Dal Corso, F.; Neukirch, S.; Bigoni, D.

2016-12-01

A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.

Extending double modulation: combinatorial rules for identifying the modulations necessary for determining elasticities in metabolic pathways.

PubMed

Giersch, C; Cornish-Bowden, A

1996-10-07

The double modulation method for determining the elasticities of pathway enzymes, originally devised by Kacser & Burns (Biochem. Soc. Trans. 7, 1149-1160, 1979), is extended to pathways of complex topological structure, including branching and feedback loops. An explicit system of linear equations for the unknown elasticities is derived. The constraints imposed on this linear system imply that modulations of more than one enzyme are not necessarily independent. Simple combinatorial rules are described for identifying without using any algebra the set of independent modulations that allow the determination of the elasticities of any enzyme. By repeated application, the minimum numbers of modulations required to determine the elasticities of all enzymes of a given pathway can be determined. The procedure is illustrated with numerous examples.

Developments in GHz-ultrasonic interferometry for elasticity studies in geophysics and materials science: application to diamond

NASA Astrophysics Data System (ADS)

Chang, Y.; Jacobsen, S. D.; Holl, C. M.; Bina, C. R.

2009-12-01

Elastic properties of solids are fundamentally important in Earth and materials science because they govern seismic wave propagation at the geophysical scale, but are controlled at the atomic scale by the nature of interatomic bonding. GHz-ultrasonic interferometry utilizes thin-film piezoelectric transducers driven by pulse modulated, microwave-range carrier frequencies at 0.5-2.0 GHz to measure sound wave travel times in sub-millimeter sized samples (Spetzler et al. 1993). Travel times are determined from the spacing of interference fringes produced by measuring the amplitude of overlapping echoes scanned in frequency (wavelength) from opposite polished faces of single crystals. The ultrasonic signals are near-optical in wavelength at 5-20 km/s in high-modulus materials, allowing study of samples as small as a few tens of micrometers in thickness, including micro-crystals loaded in diamond-anvil cells at high pressures and temperatures. Following Jacobsen et al. (2004), both longitudinal and shear-wave measurements are possible. Although relative changes in travel time on compression or heating are measured with standard deviation of about 0.02 nanoseconds out of 20-200 ns (depending on sample thickness), the absolute accuracy of ultrasonic measurements at standard conditions, required to anchor high P-T measurements, has been limited by our ability to measure sample thickness mechanically at STP, with only 1-2 micrometer accuracy out of 20-200 μm for typical samples. Thus, we have recently installed a commercial heterodyne optical interferometer to determine ultrasonic sample lengths at STP conditions. Using a double-pass laser interferometer we achieve λ/4 fundamental optical resolution with λ/128 (about 5 nm) system resolution through software-based interpolation. By adding real-time corrections for air temperature, humidity, and pressure applied to the laser wavelength, we achieve high accuracy with standard deviations of about 0.02 micrometers in the

Mechanical Model Analysis for Quantitative Evaluation of Liver Fibrosis Based on Ultrasound Tissue Elasticity Imaging

NASA Astrophysics Data System (ADS)

Shiina, Tsuyoshi; Maki, Tomonori; Yamakawa, Makoto; Mitake, Tsuyoshi; Kudo, Masatoshi; Fujimoto, Kenji

2012-07-01

Precise evaluation of the stage of chronic hepatitis C with respect to fibrosis has become an important issue to prevent the occurrence of cirrhosis and to initiate appropriate therapeutic intervention such as viral eradication using interferon. Ultrasound tissue elasticity imaging, i.e., elastography can visualize tissue hardness/softness, and its clinical usefulness has been studied to detect and evaluate tumors. We have recently reported that the texture of elasticity image changes as fibrosis progresses. To evaluate fibrosis progression quantitatively on the basis of ultrasound tissue elasticity imaging, we introduced a mechanical model of fibrosis progression and simulated the process by which hepatic fibrosis affects elasticity images and compared the results with those clinical data analysis. As a result, it was confirmed that even in diffuse diseases like chronic hepatitis, the patterns of elasticity images are related to fibrous structural changes caused by hepatic disease and can be used to derive features for quantitative evaluation of fibrosis stage.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

A highly aromatic and sulfonated ionomer for high elastic modulus ionic polymer membrane micro-actuators

NASA Astrophysics Data System (ADS)

Hatipoglu, Gokhan; Liu, Yang; Zhao, Ran; Yoonessi, Mitra; Tigelaar, Dean M.; Tadigadapa, Srinivas; Zhang, Q. M.

2012-05-01

A high modulus, sulfonated ionomer synthesized from 4,6-bis(4-hydroxyphenyl)-N,N-diphenyl-1,3,5-triazin-2-amine and 4,4‧-biphenol with bis(4-fluorophenyl)sulfone (DPA-PS:BP) is investigated for ionic polymer actuators. The uniqueness of DPA-PS:BP is that it can have a high ionic liquid (IL) uptake and consequently generates a high intrinsic strain response, which is >1.1% under 1.6 V while maintaining a high elastic modulus (i.e. 600 MPa for 65 vol% IL uptake). Moreover, such a high modulus of the active ionomer, originating from the highly aromatic backbone and side-chain-free structure, allows for the fabrication of free-standing thin film micro-actuators (down to 5 µm thickness) via the solution cast method and focused-ion-beam milling, which exhibits a much higher bending actuation, i.e. 43 µm tip displacement and 180 kPa blocking stress for a 200 µm long and 5 µm thick cantilever actuator, compared with the ionic actuators based on traditional ionomers such as Nafion, which has a much lower elastic modulus (50 MPa) and actuation strain.

Interlaminar Stresses by Refined Beam Theories and the Sinc Method Based on Interpolation of Highest Derivative

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Kapania, Rakesh K.; Tessler, Alexander

2010-01-01

Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory.

Proton elastic scattering from tin isotopes at 295 MeV and systematic change of neutron density distributions

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

Terashima, S.; Sakaguchi, H.; Takeda, H.

Cross sections and analyzing powers for proton elastic scattering from {sup 116,118,120,122,124}Sn at 295 MeV have been measured for a momentum transfer of up to about 3.5 fm{sup -1} to deduce systematic changes of the neutron density distribution. We tuned the relativistic Love-Franey interaction to explain the proton elastic scattering of a nucleus whose density distribution is well known. Then, we applied this interaction to deduce the neutron density distributions of tin isotopes. The result of our analysis shows the clear systematic behavior of a gradual increase in the neutron skin thickness of tin isotopes with mass number.

Effect of Thermal Gradient on Vibration of Non-uniform Visco-elastic Rectangular Plate

NASA Astrophysics Data System (ADS)

Khanna, Anupam; Kaur, Narinder

2016-04-01

Here, a theoretical model is presented to analyze the effect of bilinear temperature variations on vibration of non-homogeneous visco-elastic rectangular plate with non-uniform thickness. Non-uniformity in thickness of the plate is assumed linear in one direction. Since plate's material is considered as non-homogeneous, authors characterized non-homogeneity in poisson ratio and density of the plate's material exponentially in x-direction. Plate is supposed to be clamped at the ends. Deflection for first two modes of vibration is calculated by using Rayleigh-Ritz technique and tabulated for various values of plate's parameters i.e. taper constant, aspect ratio, non-homogeneity constants and thermal gradient. Comparison of present findings with existing literature is also provided in tabular and graphical manner.

Influence of colorant and film thickness on thermal aging characteristics of oxo-biodegradable plastic bags

NASA Astrophysics Data System (ADS)

Leuterio, Giselle Lou D.; Pajarito, Bryan B.; Domingo, Carla Marie C.; Lim, Anna Patricia G.

2016-05-01

Functional, lightweight, strong and cheap plastic bags incorporated with pro-oxidants undergo accelerated degradation under exposure to heat and oxygen. This work investigated the effect of colorant and film thickness on thermal aging characteristics of commercial oxo-biodegradable plastic bag films at 70 °C. Degradation is monitored through changes in infrared absorption, weight, and tensile properties of thermally aged films. The presence of carbonyl band in infrared spectrum after 672 h of thermal aging supports the degradation behavior of exposed films. Results show that incorporation of colorant and increasing thickness exhibit low maximum weight uptake. Titanium dioxide as white colorant in films lowers the susceptibility of films to oxygen uptake but enhances physical degradation. Higher amount of pro-oxidant loading also contributes to faster degradation. Opaque films are characterized by low tensile strength and high elastic modulus. Decreasing the thickness contributes to lower tensile strength of films. Thermally aged films with colorant and low thickness promote enhanced degradation.

Sex Ratio Elasticity Influences the Selection of Sex Ratio Strategy.

PubMed

Wang, Yaqiang; Wang, Ruiwu; Li, Yaotang; Sam Ma, Zhanshan

2016-12-23

There are three sex ratio strategies (SRS) in nature-male-biased sex ratio, female-biased sex ratio and, equal sex ratio. It was R. A. Fisher who first explained why most species in nature display a sex ratio of ½. Consequent SRS theories such as Hamilton's local mate competition (LMC) and Clark's local resource competition (LRC) separately explained the observed deviations from the seemingly universal 1:1 ratio. However, to the best of our knowledge, there is not yet a unified theory that accounts for the mechanisms of the three SRS. Here, we introduce the price elasticity theory in economics to define sex ratio elasticity (SRE), and present an analytical model that derives three SRSs based on the following assumption: simultaneously existing competitions for both resources A and resources B influence the level of SRE in both sexes differently. Consequently, it is the difference (between two sexes) in the level of their sex ratio elasticity that leads to three different SRS. Our analytical results demonstrate that the elasticity-based model not only reveals a highly plausible mechanism that explains the evolution of SRS in nature, but also offers a novel framework for unifying two major classical theories (i.e., LMC &LRC) in the field of SRS research.

Sex Ratio Elasticity Influences the Selection of Sex Ratio Strategy

NASA Astrophysics Data System (ADS)

Wang, Yaqiang; Wang, Ruiwu; Li, Yaotang; (Sam) Ma, Zhanshan

2016-12-01

There are three sex ratio strategies (SRS) in nature—male-biased sex ratio, female-biased sex ratio and, equal sex ratio. It was R. A. Fisher who first explained why most species in nature display a sex ratio of ½. Consequent SRS theories such as Hamilton’s local mate competition (LMC) and Clark’s local resource competition (LRC) separately explained the observed deviations from the seemingly universal 1:1 ratio. However, to the best of our knowledge, there is not yet a unified theory that accounts for the mechanisms of the three SRS. Here, we introduce the price elasticity theory in economics to define sex ratio elasticity (SRE), and present an analytical model that derives three SRSs based on the following assumption: simultaneously existing competitions for both resources A and resources B influence the level of SRE in both sexes differently. Consequently, it is the difference (between two sexes) in the level of their sex ratio elasticity that leads to three different SRS. Our analytical results demonstrate that the elasticity-based model not only reveals a highly plausible mechanism that explains the evolution of SRS in nature, but also offers a novel framework for unifying two major classical theories (i.e., LMC & LRC) in the field of SRS research.

Elastic electron scattering from formamide

NASA Astrophysics Data System (ADS)

Buk, M. V.; Bardela, F. P.; da Silva, L. A.; Iga, I.; Homem, M. G. P.

2018-05-01

Differential cross sections for elastic electron scattering by formamide (NH2CHO) were measured in the 30–800 eV and 10°–120° ranges. The angular distribution of scattered electrons was obtained using a crossed electron beam-molecular beam geometry. The relative flow technique was applied to normalize our data. Integral and momentum-transfer cross sections were derived from the measured differential cross sections. Theoretical results in the framework of the independent-atom model at the static-exchange-polarization plus absorption level of approximation are also given. The present measured and calculated results are compared with those available in the literature showing a generally good agreement.

Understanding the Earth's Mantle Through Advanced Elasticity Measurements

NASA Astrophysics Data System (ADS)

Marquardt, Hauke; Schulze, Kirsten; Kurnosov, Alexander; Buchen, Johannes; Frost, Daniel; Boffa Ballaran, Tiziana; Marquardt, Katharina; Kawazoe, Takaaki

2017-04-01

Constraints on the inner structure, chemical and mineralogical composition as well as dynamics of Earth's mantle can be derived through comparison of laboratory elasticity data to seismological observables. A quantitative knowledge of the elastic properties of mantle minerals, and their variations with chemical composition, at pressure and temperature conditions of Earth's mantle is key to construct reliable synthetic mineral physics-based seismic velocity models to be compared to seismic observables. We will discuss results of single-crystal elasticity measurements on Earth mantle minerals that have been conducted using the combined Brillouin scattering and x-ray diffraction (XRD) system at BGI Bayreuth in combination with advanced sample preparation using the focused ion beam (FIB) technique [1] that allows for tailoring sizes and shapes of tiny single-crystals. In our experiments, multiple FIB-prepared single-crystals were loaded in a single sample chamber of a resistively-heated diamond-anvil cell (DAC). The possiblity to measure simultaneously acoustic wave velocities and density (unit-cell parameters) in the DAC in combination with the multi-sample approach facilitates direct quantification of the effects of chemical substitution on the elasticity and seismic wave velocities at non-ambient conditions. Our experimental approach eliminates uncertainties arising from the combination of data collected under (potentially) different conditions in several DAC runs, in different laboratories and/or from using different pressure-temperature sensors. We will present our recent experiments on the elasticity of single-crystal Fe-Al-bearing bridgmanite in the lower mantle and discuss implications for the composition and oxidation state of Earth's lower mantle. We will further discuss our laboratory data on the effects of 'water' and iron on the seismic wave velocities of ringwoodite in Earth's transition zone and outline implications for mapping 'water' in the transition

Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond

DOE PAGES

Hmiel, A.; Winey, J. M.; Gupta, Y. M.; ...

2016-05-23

Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elasticmore » constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Lastly, our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.« less

Rayleigh-Taylor instability in accelerated elastic-solid slabs

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-12-01

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ2, shear modulus G , and thickness h , placed over a semi-infinite ideal fluid of density ρ1<ρ2 . It extends previous results for Atwood number AT=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998), 10.1007/s000330050121] to arbitrary values of AT and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ2g h /G ≤2 (1 -AT) /AT .

Time-frequency analysis of acoustic scattering from elastic objects

NASA Astrophysics Data System (ADS)

Yen, Nai-Chyuan; Dragonette, Louis R.; Numrich, Susan K.

1990-06-01

A time-frequency analysis of acoustic scattering from elastic objects was carried out using the time-frequency representation based on a modified version of the Wigner distribution function (WDF) algorithm. A simple and efficient processing algorithm was developed, which provides meaningful interpretation of the scattering physics. The time and frequency representation derived from the WDF algorithm was further reduced to a display which is a skeleton plot, called a vein diagram, that depicts the essential features of the form function. The physical parameters of the scatterer are then extracted from this diagram with the proper interpretation of the scattering phenomena. Several examples, based on data obtained from numerically simulated models and laboratory measurements for elastic spheres and shells, are used to illustrate the capability and proficiency of the algorithm.

The impact of lateral variations in lithospheric thickness on glacial isostatic adjustment in West Antarctica

NASA Astrophysics Data System (ADS)

Nield, Grace A.; Whitehouse, Pippa L.; van der Wal, Wouter; Blank, Bas; O'Donnell, John Paul; Stuart, Graham W.

2018-04-01

Differences in predictions of Glacial Isostatic Adjustment (GIA) for Antarctica persist due to uncertainties in deglacial history and Earth rheology. The Earth models adopted in many GIA studies are defined by parameters that vary in the radial direction only and represent a global average Earth structure (referred to as 1D Earth models). Over-simplifying actual Earth structure leads to bias in model predictions in regions where Earth parameters differ significantly from the global average, such as West Antarctica. We investigate the impact of lateral variations in lithospheric thickness on GIA in Antarctica by carrying out two experiments that use different rheological approaches to define 3D Earth models that include spatial variations in lithospheric thickness. The first experiment defines an elastic lithosphere with spatial variations in thickness inferred from seismic studies. We compare the results from this 3D model with results derived from a 1D Earth model that has a uniform lithospheric thickness defined as the average of the 3D lithospheric thickness. Irrespective of deglacial history and sub-lithospheric mantle viscosity, we find higher gradients of present-day uplift rates (i.e. higher amplitude and shorter wavelength) in West Antarctica when using the 3D models, due to the thinner-than-1D-average lithosphere prevalent in this region. The second experiment uses seismically-inferred temperature as input to a power-law rheology thereby allowing the lithosphere to have a viscosity structure. Modelling the lithosphere with a power-law rheology results in behaviour that is equivalent to a thinner-lithosphere model, and it leads to higher amplitude and shorter wavelength deformation compared with the first experiment. We conclude that neglecting spatial variations in lithospheric thickness in GIA models will result in predictions of peak uplift and subsidence that are biased low in West Antarctica. This has important implications for ice-sheet modelling

Effect of channel coupling on the elastic scattering of lithium isotopes

NASA Astrophysics Data System (ADS)

Furumoto, T.; Suhara, T.; Itagaki, N.

2018-04-01

Herein, we investigated the channel coupling (CC) effect on the elastic scatterings of lithium (Li) isotopes (A =6 -9) for 12C and 28Si targets at E /A =50 -60 MeV. The wave functions of the Li isotopes were obtained using the stochastic multi-configuration mixing method based on the microscopic-cluster model. The proton radii of the 7Li, 8Li, and 9Li nuclei became smaller as the number of valence neutrons increased. The valence neutrons in the 8Li and 9Li nuclei exhibited a glue-like behavior, thereby attracting the α and t clusters. Based on the transition densities derived from these microscopic wave functions, the elastic-scattering cross section was calculated using a microscopic coupled-channel method with a complex G -matrix interaction. The existing experimental data for the elastic scatterings of the Li isotopes and 10Be nuclei were well reproduced. The Li isotope elastic cross sections were demonstrated for the 12C and 28Si targets at E /A =53 MeV. The glue-like effect of the valence neutrons on the Li isotope was clearly demonstrated by the CC effect on elastic scattering. Finally, we realize that the valence neutrons stabilized the bindings of the core parts and the CC effect related to core excitation was indeed reduced.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Patterns through elastic instabilities, from thin sheets to twisted ribbons

NASA Astrophysics Data System (ADS)

Damman, Pascal

Sheets embedded in a given shape by external forces store the exerted work in elastic deformations. For pure tensile forces, the work is stored as stretching energy. When the forces are compressive, several ways to store the exerted work, combining stretching and bending deformations can be explored. For large deflections, the ratio of bending, Eh3ζ2 /L4 and stretching, Ehζ4 /L4 energies, suggests that strain-free solutions should be favored for thin sheets, provided ζ2 >>h2 (where E , ζ , Land h are the elastic modulus, the deflection, a characteristic sheet size and its thickness). For uniaxially constrained sheets deriving from the Elastica, strain-free solutions are obvious, i.e., buckles, folds or wrinkles grow to absorb the stress of compression. In contrast, crumpled sheets exhibit ``origami-like'' solutions usually described as an assembly of flat polygonal facets delimitated by ridges focusing strains are observed. This type of solutions is particularly interesting since a faceted morphology is isometric to the undeformed sheet, except at those narrow ridges. In some cases however, the geometric constraints imposed by the external forces do not allow solutions with negligible strain in the deformed state. For instance, considering a circular sheet on a small drop, so thin that bending becomes negligible, i.e., Eh3 / γL2 << 1 . The capillary tension, γ at the edge forces the sheet to follow the spherical shape of the drop. Depending on the magnitude of the capillary tension with respect to the stretching modulus, such a sheet on a sphere can be in full tension or subjected to azimuthal compression. These spherical solutions could generate a hoop stress of compression within a small strip at the sheet's edge. The mechanical response of the sheet will generate tiny wrinkles decorating the edge to relax the compression stress while keeping its spherical shape. Finally, twisting a paper ribbon under high tension spontaneously produces helicoidal shapes

Scattering of Airy elastic sheets by a cylindrical cavity in a solid.

PubMed

Mitri, F G

2017-11-01

The prediction of the elastic scattering by voids (and cracks) in materials is an important process in structural health monitoring, phononic crystals, metamaterials and non-destructive evaluation/imaging to name a few examples. Earlier analytical theories and numerical computations considered the elastic scattering by voids in plane waves of infinite extent. However, current research suggesting the use of (limited-diffracting, accelerating and self-healing) Airy acoustical-sheet beams for non-destructive evaluation or imaging applications in elastic solids requires the development of an improved analytical formalism to predict the scattering efficiency used as a priori information in quantitative material characterization. Based on the definition of the time-averaged scattered power flow density, an analytical expression for the scattering efficiency of a cylindrical empty cavity (i.e., void) encased in an elastic medium is derived for compressional and normally-polarized shear-wave Airy beams. The multipole expansion method using cylindrical wave functions is utilized. Numerical computations for the scattering energy efficiency factors for compressional and shear waves illustrate the analysis with particular emphasis on the Airy beam parameters and the non-dimensional frequency, for various elastic materials surrounding the cavity. The ratio of the compressional to the shear wave speed stimulates the generation of elastic resonances, which are manifested as a series of peaks in the scattering efficiency plots. The present analysis provides an improved method for the computations of the scattering energy efficiency factors using compressional and shear-wave Airy beams in elastic materials as opposed to plane waves of infinite extent. Copyright © 2017 Elsevier B.V. All rights reserved.

Accuracy improvement in measurement of arterial wall elasticity by applying pulse inversion to phased-tracking method

NASA Astrophysics Data System (ADS)

Miyachi, Yukiya; Arakawa, Mototaka; Kanai, Hiroshi

2018-07-01

In our studies on ultrasonic elasticity assessment, minute change in the thickness of the arterial wall was measured by the phased-tracking method. However, most images in carotid artery examinations contain multiple-reflection noise, making it difficult to evaluate arterial wall elasticity precisely. In the present study, a modified phased-tracking method using the pulse inversion method was examined to reduce the influence of the multiple-reflection noise. Moreover, aliasing in the harmonic components was corrected by the fundamental components. The conventional and proposed methods were applied to a pulsated tube phantom mimicking the arterial wall. For the conventional method, the elasticity was 298 kPa without multiple-reflection noise and 353 kPa with multiple-reflection noise on the posterior wall. That of the proposed method was 302 kPa without multiple-reflection noise and 297 kPa with multiple-reflection noise on the posterior wall. Therefore, the proposed method was very robust against multiple-reflection noise.

Structure and elasticity of serpentine at high-pressure

NASA Astrophysics Data System (ADS)

Mookherjee, Mainak; Stixrude, Lars

2009-03-01

Serpentines occur in the subduction zone settings, both along the slab and within the mantle wedge, they are candidates for transporting water in to the deep earth. Their presence is manifested by serpentine mud volcanoes, high electrical conductivities, magnetic and seismic anomalies. Using theoretical methods, we predict a pressure induced structural transformations in serpentine. The transformations are related to the behavior of the silicate framework and misfit between octahedral and tetrahedral layers. As the structure is compressed, the octahedral layer and tetrahedral layers are compressed at different rates. At 7 GPa, the misfit between the layers vanishes. This causes non-linear pressure dependence of tetrahedral rotational angle. This is also manifested by the onset of anomalous pressure dependence of the elastic constants c11, c33, c12, c13. Beyond 7 GPa, the misfit between the layers grows again reaching extremum at 22 GPa. This is also manifested by discontinuity in average Si-O bond length, volume of tetrahedron and re-orientation of hydroxyl vector. The symmetry of the crystal-structure however, remains unaffected. Evidence of pressure-induced hydrogen bonding is absent in serpentine, as evident from reduction of O-H bond length upon compression. Results of compression for the low-pressure regime ( P < 7 GPa) is well represented by a fourth order Birch-Murnaghan finite strain expression with K0 = 79 GPa, K0' = 12 and K0″ = - 2, where K is the bulk modulus, prime indicates pressure derivatives, and O refers to zero pressure. Our best estimates of K0, K0' and the Grüneisen parameter, γ at 300 K and zero pressure based on our results are: 61 GPa, 17, and 0.77, respectively. At low pressures, serpentine structure is anisotropic with c11 ~ 2.4 × c33. The pressure derivative of elastic constants ( ∂cij/ ∂P) are such, that around 22 GPa c11~ c33. An elastic instability ( c66 < 0) at somewhat higher pressures (> 50 GPa) is also noted. The elastic

Mechanical response of thick laminated beams and plates subject to out-of-plane loading

NASA Technical Reports Server (NTRS)

Hiel, C. C.; Brinson, . F.

1989-01-01

The use of simplified elasticity solutions to determine the mechanical response of thick laminated beams and plates subject to out-of-plane loading is demonstrated. Excellent results were obtained which compare favorably with theoretical, numerical and experimental analyses from other sources. The most important characteristic of the solution methodology presented is that it combines great mathematical precision with simplicity. This symbiosis has been needed for design with advanced composite materials.

Interrelationship between flexoelectricity and strain gradient elasticity in ferroelectric nanofilms: A phase field study

NASA Astrophysics Data System (ADS)

Jiang, Limei; Xu, Xiaofei; Zhou, Yichun

2016-12-01

With the development of the integrated circuit technology and decreasing of the device size, ferroelectric films used in nano ferroelectric devices become thinner and thinner. Along with the downscaling of the ferroelectric film, there is an increasing influence of two strain gradient related terms. One is the strain gradient elasticity and the other one is flexoelectricity. To investigate the interrelationship between flexoelectricity and strain gradient elasticity and their combined effect on the domain structure in ferroelectric nanofilms, a phase field model of flexoelectricity and strain gradient elasticity on the ferroelectric domain evolution is developed based on Mindlin's theory of strain-gradient elasticity. Weak form is derived and implemented in finite element formulations for numerically solving the model equations. The simulation results show that upper bounds for flexoelectric coefficients can be enhanced by increasing strain gradient elasticity coefficients. While a large flexoelectricity that exceeds the upper bound can induce a transition from a ferroelectric state to a modulated/incommensurate state, a large enough strain gradient elasticity may lead to a conversion from an incommensurate state to a ferroelectric state. Strain gradient elasticity and the flexoelectricity have entirely opposite effects on polarization. The observed interrelationship between the strain gradient elasticity and flexoelectricity is rationalized by an analytical solution of the proposed theoretical model. The model proposed in this paper could help us understand the mechanism of phenomena observed in ferroelectric nanofilms under complex electromechanical loads and provide some guides on the practical application of ferroelectric nanofilms.

The Enskog Equation for Confined Elastic Hard Spheres

NASA Astrophysics Data System (ADS)

Maynar, P.; García de Soria, M. I.; Brey, J. Javier

2018-03-01

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

Propagation of Love waves with surface effects in an electrically-shorted piezoelectric nanofilm on a half-space elastic substrate.

PubMed

Zhang, Sijia; Gu, Bin; Zhang, Hongbin; Feng, Xi-Qiao; Pan, Rongying; Alamusi; Hu, Ning

2016-03-01

The propagation of Love waves in the structure consisting of a nanosized piezoelectric film and a semi-infinite elastic substrate is investigated in the present paper with the consideration of surface effects. In our analysis, surface effects are taken into account in terms of the surface elasticity theory and the electrically-shorted conditions are adopted on the free surface of the piezoelectric film and the interface between the film and the substrate. This work focuses on the new features in the dispersion relations of different modes due to surface effects. It is found that with the existence of surface effects, the frequency dispersion of Love waves shows the distinct dependence on the thickness and the surface constants when the film thickness reduces to nanometers. In general, phase velocities of all dispersion modes increase with the decrease of the film thickness and the increase of the surface constants. However, surface effects play different functions in the frequency dispersions of different modes, especially for the first mode dispersion. Moreover, different forms of Love waves are observed in the first mode dispersion, depending on the presence of the surface effects on the surface and the interface. Copyright © 2015 Elsevier B.V. All rights reserved.

Adipose-Derived Mesenchymal Stem Cells in the Regeneration of Vocal Folds: A Study on a Chronic Vocal Fold Scar

PubMed Central

Vassiliki, Kalodimou; Irini, Messini; Nikolaos, Psychalakis; Karampela, Eleftheria; Apostolos, Papalois

2016-01-01

Background. The aim of the study was to assess the histological effects of autologous infusion of adipose-derived stem cells (ADSC) on a chronic vocal fold scar in a rabbit model as compared to an untreated scar as well as in injection of hyaluronic acid. Study Design. Animal experiment. Method. We used 74 New Zealand rabbits. Sixteen of them were used as control/normal group. We created a bilateral vocal fold wound in the remaining 58 rabbits. After 18 months we separated our population into three groups. The first group served as control/scarred group. The second one was injected with hyaluronic acid in the vocal folds, and the third received an autologous adipose-derived stem cell infusion in the scarred vocal folds (ADSC group). We measured the variation of thickness of the lamina propria of the vocal folds and analyzed histopathologic changes in each group after three months. Results. The thickness of the lamina propria was significantly reduced in the group that received the ADSC injection, as compared to the normal/scarred group. The collagen deposition, the hyaluronic acid, the elastin levels, and the organization of elastic fibers tend to return to normal after the injection of ADSC. Conclusions. Autologous injection of adipose-derived stem cells on a vocal fold chronic scar enhanced the healing of the vocal folds and the reduction of the scar tissue, even when compared to other treatments. PMID:26933440

Micro-CT based finite element models for elastic properties of glass-ceramic scaffolds.

PubMed

Tagliabue, Stefano; Rossi, Erica; Baino, Francesco; Vitale-Brovarone, Chiara; Gastaldi, Dario; Vena, Pasquale

2017-01-01

In this study, the mechanical properties of porous glass-ceramic scaffolds are investigated by means of three-dimensional finite element models based on micro-computed tomography (micro-CT) scan data. In particular, the quantitative relationship between the morpho-architectural features of the obtained scaffolds, such as macroscopic porosity and strut thickness, and elastic properties, is sought. The macroscopic elastic properties of the scaffolds have been obtained through numerical homogenization approaches using the mechanical characteristics of the solid walls of the scaffolds (assessed through nanoindentation) as input parameters for the numerical simulations. Anisotropic mechanical properties of the produced scaffolds have also been investigated by defining a suitable anisotropy index. A comparison with morphological data obtained through the micro-CT scans is also presented. The proposed study shows that the produced glass-ceramic scaffolds exhibited a macroscopic porosity ranging between 29% and 97% which corresponds to an average stiffness ranging between 42.4GPa and 36MPa. A quantitative estimation of the isotropy of the macroscopic elastic properties has been performed showing that the samples with higher solid fractions were those closest to an isotropic material. Copyright © 2016 Elsevier Ltd. All rights reserved.

Intra-Ocular Pressure Measurement in a Patient with a Thin, Thick or Abnormal Cornea.

PubMed

Clement, Colin I; Parker, Douglas G A; Goldberg, Ivan

2016-01-01

Accurate measurement of intra-ocular pressure is a fundamental component of the ocular examination. The most common method of measuring IOP is by Goldmann applanation tonometry, the accuracy of which is influenced by the thickness and biomechanical properties of the cornea. Algorithms devised to correct for corneal thickness to estimate IOP oversimplify the effects of corneal biomechanics. The viscous and elastic properties of the cornea influence IOP measurements in unpredictable ways, a finding borne out in studies of patients with inherently abnormal and surgically altered corneal biomechanics. Dynamic contour tonometry, rebound tonometry and the ocular response analyzer provide useful alternatives to GAT in patients with abnormal corneas, such as those who have undergone laser vision correction or keratoplasty. This article reviews the various methods of intra-ocular pressure measurement available to the clinician and the ways in which their utility is influenced by variations in corneal thickness and biomechanics.

Refined elasticity sampling for Monte Carlo-based identification of stabilizing network patterns.

PubMed

Childs, Dorothee; Grimbs, Sergio; Selbig, Joachim

2015-06-15

Structural kinetic modelling (SKM) is a framework to analyse whether a metabolic steady state remains stable under perturbation, without requiring detailed knowledge about individual rate equations. It provides a representation of the system's Jacobian matrix that depends solely on the network structure, steady state measurements, and the elasticities at the steady state. For a measured steady state, stability criteria can be derived by generating a large number of SKMs with randomly sampled elasticities and evaluating the resulting Jacobian matrices. The elasticity space can be analysed statistically in order to detect network positions that contribute significantly to the perturbation response. Here, we extend this approach by examining the kinetic feasibility of the elasticity combinations created during Monte Carlo sampling. Using a set of small example systems, we show that the majority of sampled SKMs would yield negative kinetic parameters if they were translated back into kinetic models. To overcome this problem, a simple criterion is formulated that mitigates such infeasible models. After evaluating the small example pathways, the methodology was used to study two steady states of the neuronal TCA cycle and the intrinsic mechanisms responsible for their stability or instability. The findings of the statistical elasticity analysis confirm that several elasticities are jointly coordinated to control stability and that the main source for potential instabilities are mutations in the enzyme alpha-ketoglutarate dehydrogenase. © The Author 2015. Published by Oxford University Press.

Tailoring Elastic Properties of Silica Aerogels Cross-Linked with Polystyrene

NASA Technical Reports Server (NTRS)

Nguyen, Baochau N.; Meador, Mary Ann B.; Tousley, Marissa E.; Shonkwiler, Brian; McCorkle, Linda; Scheiman, Daniel A.; Palczer, Anna

2009-01-01

The effect of incorporating an organic linking group, 1,6-bis(trimethoxysilyl)hexane (BTMSH), into the underlying silica structure of a styrene cross-linked silica aerogel is examined. Vinyltrimethoxysilane (VTMS) is used to provide a reactive site on the silica backbone for styrene polymerization. Replacement of up to 88 mol 1 of the silicon from tetramethoxyorthosilicate with silicon derived from BTMSH and VTMS during the making of silica gels improves the elastic behavior in some formulations of the crosslinked aerogels, as evidenced by measurement of the recovered length after compression of samples to 251 strain. This is especially true for some higher density formulations, which recover nearly 100% of their length after compression to 251 strain twice. The compressive modulus of the more elastic monoliths ranged from 0.2 to 3 MPa. Although some of these monoliths had greatly reduced surface areas, changing the solvent used to produce the gels from methanol to ethanol increased the surface area in one instance from 6 to 220 sq m2/g with little affect on the modulus, elastic recovery, porosity, or density.

Ab initio study of single-crystalline and polycrystalline elastic properties of Mg-substituted calcite crystals.

PubMed

Zhu, L-F; Friák, M; Lymperakis, L; Titrian, H; Aydin, U; Janus, A M; Fabritius, H-O; Ziegler, A; Nikolov, S; Hemzalová, P; Raabe, D; Neugebauer, J

2013-04-01

We employ ab initio calculations and investigate the single-crystalline elastic properties of (Ca,Mg)CO3 crystals covering the whole range of concentrations from pure calcite CaCO3 to pure magnesite MgCO3. Studying different distributions of Ca and Mg atoms within 30-atom supercells, our theoretical results show that the energetically most favorable configurations are characterized by elastic constants that nearly monotonously increase with the Mg content. Based on the first principles-derived single-crystalline elastic anisotropy, the integral elastic response of (Ca,Mg)CO3 polycrystals is determined employing a mean-field self-consistent homogenization method. As in case of single-crystalline elastic properties, the computed polycrystalline elastic parameters sensitively depend on the chemical composition and show a significant stiffening impact of Mg atoms on calcite crystals in agreement with the experimental findings. Our analysis also shows that it is not advantageous to use a higher-scale two-phase mix of stoichiometric calcite and magnesite instead of substituting Ca atoms by Mg ones on the atomic scale. Such two-phase composites are not significantly thermodynamically favorable and do not provide any strong additional stiffening effect. Copyright © 2013 Elsevier Ltd. All rights reserved.

Diametral tensile strength and film thickness of an experimental dental luting agent derived from castor oil.

PubMed

Carmello, Juliana Cabrini; Fais, Laiza Maria Grassi; Ribeiro, Lígia Nunes de Moraes; Claro Neto, Salvador; Guaglianoni, Dalton Geraldo; Pinelli, Lígia Antunes Pereira

2012-02-01

The need to develop new dental luting agents in order to improve the success of treatments has greatly motivated research. The aim of this study was to evaluate the diametral tensile strength (DTS) and film thickness (FT) of an experimental dental luting agent derived from castor oil (COP) with or without addition of different quantities of filler (calcium carbonate - CaCO3). Eighty specimens were manufactured (DTS N=40; FT N=40) and divided into 4 groups: Pure COP; COP 10%; COP 50% and zinc phosphate (control). The cements were mixed according to the manufacturers' recommendations and submitted to the tests. The DTS test was performed in the MTS 810 testing machine (10 KN, 0.5 mm/min). For FT test, the cements were sandwiched between two glass plates (2 cm²) and a load of 15 kg was applied vertically on the top of the specimen for 10 min. The data were analyzed by means of one-way ANOVA and Tukey's test (α=0.05). The values of DTS (MPa) were: Pure COP- 10.94 ± 1.30; COP 10%- 30.06 ± 0.64; COP 50%- 29.87 ± 0.27; zinc phosphate- 4.88 ± 0.96. The values of FT (µm) were: Pure COP- 31.09 ± 3.16; COP 10%- 17.05 ± 4.83; COP 50%- 13.03 ± 4.83; Zinc Phosphate- 20.00 ± 0.12. One-way ANOVA showed statistically significant differences among the groups (DTS - p=1.01E-40; FT - p=2.4E-10). The experimental dental luting agent with 50% of filler showed the best diametral tensile strength and film thickness.

CYTOTOXICITY OF INTERMAXILLARY ORTHODONTIC ELASTICS OF DIFFERENT COLORS: AN IN VITRO STUDY

PubMed Central

dos Santos, Rogério Lacerda; Pithon, Matheus Melo; Mendes, Gabriella da Silva; Romanos, Maria Teresa Villela; Ruellas, Antônio Carlos de Oliveira

2009-01-01

Objectives: Natural latex does not fall into the category of materials known to be entirely inoffensive. The purpose of this in vitro study was to test the hypothesis that there is no difference in the cytotoxicity between elastics of different colors and those from different manufacturers. Material and Methods: Different latex intraoral elastics of different colors (5/16 = 7.9 mm, mean load) were compared. The sample was divided into 7 groups of 24 elastics each: Group T (TP Orthodontics, natural latex elastics, control); Groups U1, U2, U3, U4, U5 and U6 (Uniden, natural latex elastics and colored elastics, namely, green, pink, yellow, red and purple, respectively). Cytotoxicity assays were performed by using cell culture medium containing epithelioid-type cells (Hep-2 line) derived from human laryngeal carcinoma. The cytotoxicity was evaluated by using the "dye-uptake" test, which was employed at two different moments (0 and 24 h). Data were compared by analysis of variance (ANOVA) and Tukey's test (p<0.05). Results: There was statistically significant difference (p<0.05) between Group T and all other groups (U1, U2, U3, U4, U5 and U6) at 0 and 24 h. No statistically significant difference (p<0.05) was found between Groups U1 and U5, U1 and U6, U2 and U3, U2 and U4, U2 and U5, U2 and U6, U3 and U4, U3 and U5, U3 and U6, U4 and U5, U4 and U6, and U5 and U6 at 0 and 24 h. Conclusions: The TP Orthodontics elastics promoted less cell lysis compared to the Uniden elastics regardless of their color. PMID:19668992

Limitation of Cell Adhesion by the Elasticity of the Extracellular Matrix

PubMed Central

Nicolas, Alice; Safran, Samuel. A.

2006-01-01

Cell/matrix adhesions are modulated by cytoskeletal or external stresses and adapt to the mechanical properties of the extracellular matrix. We propose that this mechanosensitivity arises from the activation of a mechanosensor located within the adhesion itself. We show that this mechanism accounts for the observed directional growth of focal adhesions and the reduction or even cessation of their growth when cells adhere to a soft extracellular matrix. We predict quantitatively that both the elasticity and the thickness of the matrix play a key role in the dynamics of focal adhesions. Two different types of dynamics are expected depending on whether the thickness of the matrix is of order of or much larger than the adhesion size. In the latter situation, we predict that the adhesion region reaches a saturation size that can be tuned by the mechanical properties of the matrix. PMID:16581840

Exact solutions for laminated composite cylindrical shells in cylindrical bending

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1992-01-01

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Investigation of the thickness non-uniformity of the very thin silicon-strip detectors

NASA Astrophysics Data System (ADS)

Liu, Qiang; Ye, Yanlin; Li, Zhihuan; Lin, Chengjian; Jia, Huiming; Ge, Yucheng; Li, Qite; Lou, Jianling; Yang, Xiaofei; Yang, Biao; Feng, Jun; Zang, Hongliang; Chen, Zhiqiang; Liu, Yang; Liu, Wei; Chen, Sidong; Yu, Hanzhou; Li, Jingjing; Zhang, Yun; Yang, Feng; Yang, Lei; Ma, Nanru; Sun, Lijie; Wang, Dongxi

2018-07-01

The properties of some very thin (∼ 20 μm) large-area Single-sided Silicon-Strip Detectors (SSSDs) were investigated by using the 12C-particles elastically scattered from a Au target. In the detection system, each thin SSSD was installed in front of a thick (300 μm or 500 μm) Double-sided Silicon-Strip Detector (DSSD) to form a ΔE - E particle-telescope. The energy calibration of these detectors was realized by varying the beam energy and also by the irradiation from a three-component α-particle source. The thickness distribution each SSSD is precisely determined from the energy loss in the thin layer, which was independently measured by the corresponding DSSD. It is found that, for the SSSD with the nominal thicknesses of ∼ 20 μm, the real thickness may vary by several μm over the active area. The reason for this large non-uniformity still needs to be investigated. For the present application, this non-uniformity could be corrected according to the known pixel-thickness. This correction allows to restore a good particle identification (PID) performance for the entire large-area detector, the importance of which is demonstrated by an example of measuring the cluster-decays of the highly-excited resonant states in 16O.

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Liu, XiQiang

2013-08-01

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scattered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

Bending elasticity of macromolecules: analytic predictions from the wormlike chain model.

PubMed

Polley, Anirban; Samuel, Joseph; Sinha, Supurna

2013-01-01

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behavior of a single molecule. We present analytical formulas for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies of "kinks" and cyclization in short and intermediate length DNA strands.

From viscous to elastic sheets: Dynamics of smectic bubbles

NASA Astrophysics Data System (ADS)

Harth, Kirsten; Trittel, Torsten; van der Meer, Devaraj; Stannarius, Ralf

2015-11-01

Oscillations and rupture of bubbles composed of an inner fluid separated from an outer fluid by a membrane, represent an old but still immensely active field of research. Membrane properties apart from surface tension are often neglected for fluids (e.g. soap bubbles), whereas they govern the dynamics in systems with a rigid membrane (e.g. vesicles). Due to their layered phase structure, smectic liquid crystals can form stable, uniform and easy-to-handle fluid films of immense aspect ratios. Only recently, freely floating bubbles detached from a support could be prepared. We analyze their relaxation from strongly non-spherical shapes and the rupture using high-speed video recordings. Peculiar dynamics intermediate between simple viscous fluid films and an elastic response are observed: Fast oscillations, slowed relaxation and even the reversible formation of wrinkles and extrusions. Bubble rupture deviates qualitatively from previously observed behavior of simple Newtonian and other complex fluids. It becomes retarded by at least two orders of magnitude compared to the predictions of Taylor and Culick. A transition between fluid-like and elastic behavior is seen with increasing thickness. We give experimental results, an intuitive explanation and a novel hydrodynamic description.

Stagger angle dependence of inertial and elastic coupling in bladed disks

NASA Technical Reports Server (NTRS)

Crawley, E. F.; Mokadam, D. R.

1984-01-01

Conditions which necessitate the inclusion of disk and shaft flexibility in the analysis of blade response in rotating blade-disk-shaft systems are derived in terms of nondimensional parameters. A simple semianalytical Rayleigh-Ritz model is derived in which the disk possesses all six rigid body degrees of freedom, which are elastically constrained by the shaft. Inertial coupling by the rigid body motion of the disk on a flexible shaft and out-of-plane elastic coupling due to disk flexure are included. Frequency ratios and mass ratios, which depend on the stagger angle, are determined for three typical rotors: a first stage high-pressure core compressor, a high bypass ratio fan, and an advanced turboprop. The stagger angle controls the degree of coupling in the blade-disk system. In the blade-disk-shaft system, the stagger angle determines whether blade-disk motion couples principally to the out-of-plane or in-plane motion of the disk on the shaft. The Ritz analysis shows excellent agreement with experimental results.

On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms

NASA Astrophysics Data System (ADS)

Mascolo, Ida; Amendola, Ada; Zuccaro, Giulio; Feo, Luciano; Fraternali, Fernando

2018-03-01

The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

Quantified elasticity mapping of ocular tissue using acoustic radiation force optical coherence elastography (Conference Presentation)

NASA Astrophysics Data System (ADS)

Qu, Yueqiao; He, Youmin; Zhang, Yi; Ma, Teng; Zhu, Jiang; Miao, Yusi; Dai, Cuixia; Silverman, Ronald; Humayun, Mark S.; Zhou, Qifa; Chen, Zhongping

2017-02-01

Age-related macular degeneration and keratoconus are two ocular diseases occurring in the posterior and anterior eye, respectively. In both conditions, the mechanical elasticity of the respective tissues changes during the early onset of disease. It is necessary to detect these differences and treat the diseases in their early stages to provide proper treatment. Acoustic radiation force optical coherence elastography is a method of elasticity mapping using confocal ultrasound waves for excitation and Doppler optical coherence tomography for detection. We report on an ARF-OCE system that uses modulated compression wave based excitation signals, and detects the spatial and frequency responses of the tissue. First, all components of the system is synchronized and triggered such that the signal is consistent between frames. Next, phantom studies are performed to validate and calibrate the relationship between the resonance frequency and the Young's modulus. Then the frequency responses of the anterior and posterior eye are detected for porcine and rabbit eyes, and the results correlated to the elasticity. Finally, spatial elastograms are obtained for a porcine retina. Layer segmentation and analysis is performed and correlated to the histology of the retina, where five distinct layers are recognized. The elasticities of the tissue layers will be quantified according to the mean thickness and displacement response for the locations on the retina. This study is a stepping stone to future in-vivo animal studies, where the elastic modulus of the ocular tissue can be quantified and mapped out accordingly.

First observation of a negative elastic constant in intermediate valent TmSe

NASA Astrophysics Data System (ADS)

Boppart, H.; Treindl, A.; Wachter, P.; Roth, S.

1980-08-01

The sound velocities v L, v T 1 and v T 2 have been measured at 15 MHz on Tm 3+0.87Se and Tm 2.8+0.99Se between 300 K and 4.2 K and the elastic constants c ij have been derived. In intermediate valent Tm 2.8+0.99Se c 12 turned out to be negative. This sign is interpreted as being typical for intermediate valent compounds. Also for the first time experimental evidence is given for crystal field effects in Tm 3+0.87Se. Strong elastic nonlinearities are observed in intermediate valent Tm 2.8+0.99Se with uniaxial pressure.

Kernelized Elastic Net Regularization: Generalization Bounds, and Sparse Recovery.

PubMed

Feng, Yunlong; Lv, Shao-Gao; Hang, Hanyuan; Suykens, Johan A K

2016-03-01

Kernelized elastic net regularization (KENReg) is a kernelization of the well-known elastic net regularization (Zou & Hastie, 2005). The kernel in KENReg is not required to be a Mercer kernel since it learns from a kernelized dictionary in the coefficient space. Feng, Yang, Zhao, Lv, and Suykens (2014) showed that KENReg has some nice properties including stability, sparseness, and generalization. In this letter, we continue our study on KENReg by conducting a refined learning theory analysis. This letter makes the following three main contributions. First, we present refined error analysis on the generalization performance of KENReg. The main difficulty of analyzing the generalization error of KENReg lies in characterizing the population version of its empirical target function. We overcome this by introducing a weighted Banach space associated with the elastic net regularization. We are then able to conduct elaborated learning theory analysis and obtain fast convergence rates under proper complexity and regularity assumptions. Second, we study the sparse recovery problem in KENReg with fixed design and show that the kernelization may improve the sparse recovery ability compared to the classical elastic net regularization. Finally, we discuss the interplay among different properties of KENReg that include sparseness, stability, and generalization. We show that the stability of KENReg leads to generalization, and its sparseness confidence can be derived from generalization. Moreover, KENReg is stable and can be simultaneously sparse, which makes it attractive theoretically and practically.

Retrieval of ice thickness from polarimetric SAR data

NASA Technical Reports Server (NTRS)

Kwok, R.; Yueh, S. H.; Nghiem, S. V.; Huynh, D. D.

1993-01-01

We describe a potential procedure for retrieving ice thickness from multi-frequency polarimetric SAR data for thin ice. This procedure includes first masking out the thicker ice types with a simple classifier and then deriving the thickness of the remaining pixels using a model-inversion technique. The technique used to derive ice thickness from polarimetric observations is provided by a numerical estimator or neural network. A three-layer perceptron implemented with the backpropagation algorithm is used in this investigation with several improved aspects for a faster convergence rate and a better accuracy of the neural network. These improvements include weight initialization, normalization of the output range, the selection of offset constant, and a heuristic learning algorithm. The performance of the neural network is demonstrated by using training data generated by a theoretical scattering model for sea ice matched to the database of interest. The training data are comprised of the polarimetric backscattering coefficients of thin ice and the corresponding input ice parameters to the scattering model. The retrieved ice thickness from the theoretical backscattering coefficients is compare with the input ice thickness to the scattering model to illustrate the accuracy of the inversion method. Results indicate that the network convergence rate and accuracy are higher when multi-frequency training sets are presented. In addition, the dominant backscattering coefficients in retrieving ice thickness are found by comparing the behavior of the network trained backscattering data at various incidence angels. After the neural network is trained with the theoretical backscattering data at various incidence anges, the interconnection weights between nodes are saved and applied to the experimental data to be investigated. In this paper, we illustrate the effectiveness of this technique using polarimetric SAR data collected by the JPL DC-8 radar over a sea ice scene.

Optimizing Thermal-Elastic Properties of C/C–SiC Composites Using a Hybrid Approach and PSO Algorithm

PubMed Central

Xu, Yingjie; Gao, Tian

2016-01-01

Carbon fiber-reinforced multi-layered pyrocarbon–silicon carbide matrix (C/C–SiC) composites are widely used in aerospace structures. The complicated spatial architecture and material heterogeneity of C/C–SiC composites constitute the challenge for tailoring their properties. Thus, discovering the intrinsic relations between the properties and the microstructures and sequentially optimizing the microstructures to obtain composites with the best performances becomes the key for practical applications. The objective of this work is to optimize the thermal-elastic properties of unidirectional C/C–SiC composites by controlling the multi-layered matrix thicknesses. A hybrid approach based on micromechanical modeling and back propagation (BP) neural network is proposed to predict the thermal-elastic properties of composites. Then, a particle swarm optimization (PSO) algorithm is interfaced with this hybrid model to achieve the optimal design for minimizing the coefficient of thermal expansion (CTE) of composites with the constraint of elastic modulus. Numerical examples demonstrate the effectiveness of the proposed hybrid model and optimization method. PMID:28773343

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure

PubMed Central

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-01-01

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed. PMID:26099720

Universal elastic-hardening-driven mechanical instability in α-quartz and quartz homeotypes under pressure.

PubMed

Dong, Juncai; Zhu, Hailiang; Chen, Dongliang

2015-06-23

As a fundamental property of pressure-induced amorphization (PIA) in ice and ice-like materials (notably α-quartz), the occurrence of mechanical instability can be related to violation of Born criteria for elasticity. The most outstanding elastic feature of α-quartz before PIA has been experimentally reported to be the linear softening of shear modulus C44, which was proposed to trigger the transition through Born criteria B3. However, by using density-functional theory, we surprisingly found that both C44 and C66 in α-quartz exhibit strong nonlinearity under compression and the Born criteria B3 vanishes dominated by stiffening of C14, instead of by decreasing of C44. Further studies of archetypal quartz homeotypes (GeO2 and AlPO4) repeatedly reproduced the same elastic-hardening-driven mechanical instability, suggesting a universal feature of this family of crystals and challenging the long-standing idea that negative pressure derivatives of individual elastic moduli can be interpreted as the precursor effect to an intrinsic structural instability preceding PIA. The implications of this elastic anomaly in relation to the dispersive softening of the lowest acoustic branch and the possible transformation mechanism were also discussed.

Elastic Moduli of Nanoparticle-Polymer Composite Thin Films via Buckling on Elastomeric Substrates

NASA Astrophysics Data System (ADS)

Yuan, Hongyi; Karim, Alamgir; University of Akron Team

2011-03-01

Polymeric thin films find applications in diverse areas such as coatings, barriers and packaging. The dispersion of nanoparticles into the films was proven to be an effective method to generate tunable properties, particularly mechanical strength. However, there are very few methods for mechanical characterization of the composite thin films with high accuracy. In this study, nanometric polystyrene and polyvinyl alcohol films with uniformly dispersed cobalt and Cloisite nanoparticles at varying concentrations were synthesized via flow-coating and then transferred to crosslinked polydimethylsiloxane (PDMS) flexible substrates. The technique of Strain-Induced Elastic Buckling Instability for Mechanical Measurements (SIEBIMM) was employed to determine the elastic moduli of the films, which were calculated from the buckling patterns generated by applying compressive stresses. Results on moduli of films as a function of the concentrations of nanoparticles and the thicknesses of the composite films will be presented. *Corresponding author: alamgir@uakron.edu

Immunohistochemical study of extracellular matrices and elastic fibers in a human sternoclavicular joint.

PubMed

Shimada, K; Takeshige, N; Moriyama, H; Miyauchi, Y; Shimada, S; Fujimaki, E

1997-12-01

In this study, we clarified the distribution of elastic and oxytalan fibers in a human sternoclavicular joint (SCJ) using a color image system and in extracellular matrices using immunoperoxidase staining. Fine elastic fibers (EFs) were scattered in the fibrous layer of the sternoclavicular disk. This articular disk was composed of a collagenous bundle on the sternum side of the articular disk in the SCJ and cellular components including connective tissue on the clavicular side of the articular disk. The thickness of the disk gradually increased from the inferior to superior portion. Collagen fibers type I, III and V and other extracellular matrices (ECMs) were detected in the hypertrophic zone in the clavicular and sternum side of the SCJ and in the connective tissue of the articulatio condylar. On the cervical surface of the articular disk, cellular activity was higher than on the sternum surface.

Prediction of Layer Thickness in Molten Borax Bath with Genetic Evolutionary Programming

NASA Astrophysics Data System (ADS)

Taylan, Fatih

2011-04-01

In this study, the vanadium carbide coating in molten borax bath process is modeled by evolutionary genetic programming (GEP) with bath composition (borax percentage, ferro vanadium (Fe-V) percentage, boric acid percentage), bath temperature, immersion time, and layer thickness data. Five inputs and one output data exist in the model. The percentage of borax, Fe-V, and boric acid, temperature, and immersion time parameters are used as input data and the layer thickness value is used as output data. For selected bath components, immersion time, and temperature variables, the layer thicknesses are derived from the mathematical expression. The results of the mathematical expressions are compared to that of experimental data; it is determined that the derived mathematical expression has an accuracy of 89%.

Biomimetic, ultrathin and elastic hydrogels regulate human neutrophil extravasation across endothelial-pericyte bilayers.

PubMed

Lauridsen, Holly M; Gonzalez, Anjelica L

2017-01-01

The vascular basement membrane-a thin, elastic layer of extracellular matrix separating and encasing vascular cells-provides biological and mechanical cues to endothelial cells, pericytes, and migrating leukocytes. In contrast, experimental scaffolds typically used to replicate basement membranes are stiff and bio-inert. Here, we present thin, porated polyethylene glycol hydrogels to replicate human vascular basement membranes. Like commercial transwells, our hydrogels are approximately 10μm thick, but like basement membranes, the hydrogels presented here are elastic (E: 50-80kPa) and contain a dense network of small pores. Moreover, the inclusion of bioactive domains introduces receptor-mediated biochemical signaling. We compare elastic hydrogels to common culture substrates (E: >2GPa) for human endothelial cell and pericyte monolayers and bilayers to replicate postcapillary venules in vitro. Our data demonstrate that substrate elasticity facilitates differences in vascular phenotype, supporting expression of vascular markers that are increasingly replicative of venules. Endothelial cells differentially express vascular markers, like EphB4, and leukocyte adhesion molecules, such as ICAM-1, with decreased mechanical stiffness. With porated PEG hydrogels we demonstrate the ability to evaluate and observe leukocyte recruitment across endothelial cell and pericyte monolayers and bilayers, reporting that basement membrane scaffolds can significantly alter the rate of vascular migration in experimental systems. Overall, this study demonstrates the creation and utility of a new and accessible method to recapture the mechanical and biological complexity of human basement membranes in vitro.

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833

Calcium binding to an elastic portion of connectin/titin filaments.

PubMed

Tatsumi, R; Maeda, K; Hattori, A; Takahashi, K

2001-01-01

Alpha-connectin/titin-1 exists as an elastic filament that links a thick filament with the Z-disk, keeping thick filaments centered within the sarcomere during force generation. We have shown that the connectin filament has an affinity for calcium ions and its binding site(s) is restricted to the beta-connectin/titin-2 portion. We now report the localization and the characterization of calcium-binding sites on beta-connectin. Purified beta-connectin was digested by trypsin into 1700- and 400-kDa fragments. which were then subjected to fluorescence calcium-binding assays. The 400-kDa fragment possesses calcium-binding activity; the binding constant was 1.0 x 10(7) M(-1) and the molar ratio of bound calcium ions to the 400-kDa fragment reached a maximum of 12 at a free calcium ion concentration of approximately 1.0 microM. Antibodies against the 400-kDa fragment formed a sharp dense stripe at the boundary of the A and the I bands, indicating that the calcium-binding domain constitutes the N-terminal region of beta-connectin, that is, the elastic portion of connectin filaments. Furthermore, we estimated the N-terminal location of beta-connectin of various origins (n = 26). Myofibrils were treated with a solution containing 0.1 mM CaCl2 and 70 microM leupeptin to split connectin filaments into beta-connectin and a subfragment, and chain weights of these polypeptides were estimated according to their mobility in 2% polyacrylamide slab gels. The subfragment exhibited a similar chain weight of 1200+/-33 kDa (mean+/-SD), while alpha- and beta-connectins were variable in size according to their origin. These results suggest that the apparent length of the 1200-kDa subfragment portion is almost constant in all instances, about 0.34 microm at the slack condition, therefore that the C-terminus of the 1200-kDa subfragment, that is, the N-terminus of the calcium-binding domain, is at the N2 line region of parent filaments in situ. Because the secondary structure of the 400-k

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Folding and faulting of an elastic continuum

NASA Astrophysics Data System (ADS)

Bigoni, Davide; Gourgiotis, Panos A.

2016-03-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called `chevrons') and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures.

Stiffness optimization of non-linear elastic structures

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

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Critical Buckling Pressure in Mouse Carotid Arteries with Altered Elastic Fibers

PubMed Central

Luetkemeyer, Callan M.; James, Rhys H.; Devarakonda, Siva Teja; Le, Victoria P.; Liu, Qin; Han, Hai-Chao; Wagenseil, Jessica E.

2015-01-01

Arteries can buckle axially under applied critical buckling pressure due to a mechanical instability. Buckling can cause arterial tortuosity leading to flow irregularities and stroke. Genetic mutations in elastic fiber proteins are associated with arterial tortuosity in humans and mice, and may be the result of alterations in critical buckling pressure. Hence, the objective of this study is to investigate how genetic defects in elastic fibers affect buckling pressure. We use mouse models of human disease with reduced amounts of elastin (Eln+/−) and with defects in elastic fiber assembly due to the absence of fibulin-5 (Fbln5−/−). We find that Eln+/− arteries have reduced buckling pressure compared to their wild-type controls. Fbln5−/− arteries have similar buckling pressure to wild-type at low axial stretch, but increased buckling pressure at high stretch. We fit material parameters to mechanical test data for Eln+/−, Fbln5−/− and wild-type arteries using Fung and four-fiber strain energy functions. Fitted parameters are used to predict theoretical buckling pressure based on equilibrium of an inflated, buckled, thick-walled cylinder. In general, the theoretical predictions underestimate the buckling pressure at low axial stretch and overestimate the buckling pressure at high stretch. The theoretical predictions with both models replicate the increased buckling pressure at high stretch for Fbln5−/− arteries, but the four-fiber model predictions best match the experimental trends in buckling pressure changes with axial stretch. This study provides experimental and theoretical methods for further investigating the influence of genetic mutations in elastic fibers on buckling behavior and the development of arterial tortuosity. PMID:25771258

Elastic-Plastic Thermal Stress Analysis of a High-Pressure Cryogenic Storage Tank

NASA Technical Reports Server (NTRS)

Barker, J. Mark; Field, Robert E. (Technical Monitor)

2003-01-01

The thermal stresses on a cryogenic storage tank contribute strongly to the state of stress of the tank material and its ability to withstand operational stresses. These thermal stresses also affect the growth of any surface damage that might occur in the tank walls. These stresses are particularly of concern during the initial cooldown period for a new tank placed into service, and during any subsequent thermal cycles. A previous preliminary elastic analysis showed that the thermal stress on the inner wall would reach approximately 1,000MPa (145,000 psi). This stress far exceeds the ASTM specified room temperature values for both yield (170MPa) and ultimate (485 MPa) strength for 304L stainless steel. The present analysis determines the thermal stresses using an elastic-plastic model. The commercial software application ANSYS was used to determine the transient spatial temperature profile and the associated spatial thermal stress profiles in a segment of a thick-walled vessel during a typical cooldown process. A strictly elastic analysis using standard material properties for 304L stainless steel showed that the maximum thermal stress on the inner and outer walls was approximately 960 MPa (tensile) and - 270 MPa (compressive) respectively. These values occurred early in the cooldown process, but at different times, An elastic-plastic analysis showed significantly reducing stress, as expected due to the plastic deformation of the material. The maximum stress for the inner wall was approximately 225 MPa (tensile), while the maximum stress for the outer wall was approximately - 130 MPa (compressive).

Rolling motion of an elastic cylinder induced by elastic strain gradients

NASA Astrophysics Data System (ADS)

Chen, Lei; Chen, Shaohua

2014-10-01

Recent experiment shows that an elastic strain gradient field can be utilized to transport spherical particles on a stretchable substrate by rolling, inspired by which a generalized plane-strain Johnson-Kendall-Roberts model is developed in this paper in order to verify possible rolling of an elastic cylinder adhering on an elastic substrate subject to a strain gradient. With the help of contact mechanics, closed form solutions of interface tractions, stress intensity factors, and corresponding energy release rates in the plane-strain contact model are obtained, based on which a possible rolling motion of an elastic cylinder induced by strain gradients is found and the criterion for the initiation of rolling is established. The theoretical prediction is consistent well with the existing experimental observation. The result should be helpful for understanding biological transport mechanisms through muscle contractions and the design of transport systems with strain gradient.

Contact problem for an elastic reinforcement bonded to an elastic plate

NASA Technical Reports Server (NTRS)

Erdogan, F.; Civelek, M. B.

1974-01-01

The contact problem for a thin elastic reinforcement bonded to an elastic plate is considered. The stiffening layer is treated as an elastic membrane and the base plate is assumed to be an elastic continuum. The bonding between the two materials is assumed to be either one of direct adhesion or through a thin adhesive layer which is treated as a shear spring. The solution for the simple case in which both the stiffener and the base plate are treated as membranes is also given. The contact stress is obtained for a series of numerical examples. In the direct adhesion case the contact stress becomes infinite at the stiffener ends with a typical square root singularity for the continuum model and behaving as a delta function for the membrane model. In the case of bonding through an adhesive layer the contact stress becomes finite and continuous along the entire contact area.

Are rapid changes in brain elasticity possible?

NASA Astrophysics Data System (ADS)

Parker, K. J.

2017-09-01

Elastography of the brain is a topic of clinical and preclinical research, motivated by the potential for viscoelastic measures of the brain to provide sensitive indicators of pathological processes, and to assist in early diagnosis. To date, studies of the normal brain and of those with confirmed neurological disorders have reported a wide range of shear stiffness and shear wave speeds, even within similar categories. A range of factors including the shear wave frequency, and the age of the individual are thought to have a possible influence. However, it may be that short term dynamics within the brain may have an influence on the measured stiffness. This hypothesis is addressed quantitatively using the framework of the microchannel flow model, which derives the tissue stiffness, complex modulus, and shear wave speed as a function of the vascular and fluid network in combination with the elastic matrix that comprise the brain. Transformation rules are applied so that any changes in the fluid channels or the elastic matrix can be mapped to changes in observed elastic properties on a macroscopic scale. The results are preliminary but demonstrate that measureable, time varying changes in brain stiffness are possible simply by accounting for vasodynamic or electrochemical changes in the state of any region of the brain. The value of this preliminary exploration is to identify possible mechanisms and order-of-magnitude changes that may be testable in vivo by specialized protocols.

Elastic and piezoelectric fields around a quantum wire of zincblende heterostructures with interface elasticity effect

NASA Astrophysics Data System (ADS)

Ye, Wei; Liu, Yifei

2018-04-01

This work formulates the solutions to the elastic and piezoelectric fields around a quantum wire (QWR) with interface elasticity effect. Closed-form solutions to the piezoelectric potential field of zincblende QWR/matrix heterostructures grown along [111] crystallographic orientation are found and numerical results of InAs/InP heterostructures are provided as an example. The piezoelectric potential in the matrix depends on the interface elasticity, the radius and stiffness of the QWR. Our results indicate that interface elasticity can significantly alter the elastic and piezoelectric fields near the interface. Additionally, when the elastic property of the QWR is considered to be anisotropic in contrary to the common isotropic assumption, piezoelectric potentials are found to be distinct near the interface, but the deviations are negligible at positions far away from the interface.

Effect of geometry on hydrodynamic film thickness

NASA Technical Reports Server (NTRS)

Brewe, D. E.; Hamrock, B. J.; Taylor, C. M.

1978-01-01

The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

Local sample thickness determination via scanning transmission electron microscopy defocus series.

PubMed

Beyer, A; Straubinger, R; Belz, J; Volz, K

2016-05-01

The usable aperture sizes in (scanning) transmission electron microscopy ((S)TEM) have significantly increased in the past decade due to the introduction of aberration correction. In parallel with the consequent increase of convergence angle the depth of focus has decreased severely and optical sectioning in the STEM became feasible. Here we apply STEM defocus series to derive the local sample thickness of a TEM sample. To this end experimental as well as simulated defocus series of thin Si foils were acquired. The systematic blurring of high resolution high angle annular dark field images is quantified by evaluating the standard deviation of the image intensity for each image of a defocus series. The derived dependencies exhibit a pronounced maximum at the optimum defocus and drop to a background value for higher or lower values. The full width half maximum (FWHM) of the curve is equal to the sample thickness above a minimum thickness given by the size of the used aperture and the chromatic aberration of the microscope. The thicknesses obtained from experimental defocus series applying the proposed method are in good agreement with the values derived from other established methods. The key advantages of this method compared to others are its high spatial resolution and that it does not involve any time consuming simulations. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.

Fracton-Elasticity Duality

NASA Astrophysics Data System (ADS)

Pretko, Michael; Radzihovsky, Leo

2018-05-01

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.