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Journal articles on the topic 'Elastic Stiffness Tensor'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Sayers, Colin M., and Lennert D. den Boer. "Effect of variations in microstructure on clay elastic anisotropy." GEOPHYSICS 85, no. 2 (2020): MR73—MR82. http://dx.doi.org/10.1190/geo2019-0374.1.

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Rock physics provides a crucial link between seismic and reservoir properties, but it requires knowledge of the elastic properties of rock components. Whereas the elastic properties of most rock components are known, the anisotropic elastic properties of clay are not. Scanning electron microscopy studies of clay in shales indicate that individual clay platelets vary in orientation but are aligned locally. We present a simple model of the elastic properties of a region (domain) of locally aligned clay platelets that accounts for the volume fraction, aspect ratio, and elastic-stiffness tensor of

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2

Pereverzev, Andrey, та Tommy Sewell. "Elastic Coefficients of β-HMX as Functions of Pressure and Temperature from Molecular Dynamics". Crystals 10, № 12 (2020): 1123. http://dx.doi.org/10.3390/cryst10121123.

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The isothermal second-order elastic stiffness tensor and isotropic moduli of β-1,3,5,7- tetranitro-1,3,5,7-tetrazoctane (β-HMX) were calculated, using the P21/n space group convention, from molecular dynamics for hydrostatic pressures ranging from 10−4 to 30 GPa and temperatures ranging from 300 to 1100 K using a validated all-atom flexible-molecule force field. The elastic stiffness tensor components were calculated as derivatives of the Cauchy stress tensor components with respect to linear strain components. These derivatives were evaluated numerically by imposing small, prescribed finite s

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3

Dellinger, Joe. "Computing the optimal transversely isotropic approximation of a general elastic tensor." GEOPHYSICS 70, no. 5 (2005): I1—I10. http://dx.doi.org/10.1190/1.2073890.

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Mathematically, 21 stiffnesses arranged in a 6 × 6 symmetric matrix completely describe the elastic properties of any homogeneous anisotropic medium, regardless of symmetry system and orientation. However, it can be difficult in practice to characterize an anisotropic medium's properties merely from casual inspection of its (often experimentally measured) stiffness matrix. For characterization purposes, it is better to decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic (TI) medium (whose properties can be readily understood) plus a g

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4

Srivastava, Ankit, and Sia Nemat-Nasser. "Overall dynamic properties of three-dimensional periodic elastic composites." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2137 (2011): 269–87. http://dx.doi.org/10.1098/rspa.2011.0440.

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This article presents a method for the homogenization of three-dimensional periodic elastic composites. It allows for the evaluation of the averaged overall frequency-dependent dynamic material constitutive tensors relating the averaged dynamic field variable tensors of velocity, strain, stress and linear momentum. Although the form of the dynamic constitutive relation for three-dimensional elastodynamic wave propagation has been known, this is the first time that explicit calculations of the effective parameters (for three dimensions) are presented. We show that for three-dimensional periodic

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5

Sayers, Colin M., and Lennert D. den Boer. "The elastic anisotropy of clay minerals." GEOPHYSICS 81, no. 5 (2016): C193—C203. http://dx.doi.org/10.1190/geo2016-0005.1.

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The layered structure of clay minerals produces large elastic anisotropy due to the presence of strong covalent bonds within layers and weaker electrostatic bonds in between. Technical difficulties associated with small grain size preclude experimental measurement of single-crystal elastic moduli. However, theoretical calculations of the complete elastic tensors of several clay minerals have been reported, using either first-principle calculations based on density functional theory or molecular dynamics. Because of the layered microstructure, the elastic stiffness tensor obtained from such cal

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6

Büscher, Julia, Alessandro Mirone, Michał Stękiel, et al. "Elastic stiffness coefficients of thiourea from thermal diffuse scattering." Journal of Applied Crystallography 54, no. 1 (2021): 287–94. http://dx.doi.org/10.1107/s1600576720016039.

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The complete elastic stiffness tensor of thiourea has been determined from thermal diffuse scattering (TDS) using high-energy photons (100 keV). Comparison with earlier data confirms a very good agreement of the tensor coefficients. In contrast with established methods to obtain elastic stiffness coefficients (e.g. Brillouin spectroscopy, inelastic X-ray or neutron scattering, ultrasound spectroscopy), their determination from TDS is faster, does not require large samples or intricate sample preparation, and is applicable to opaque crystals. Using high-energy photons extends the applicability

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7

Lee, Sangryun, Jinyeop Lee, and Seunghwa Ryu. "Modified Eshelby tensor for an anisotropic matrix with interfacial damage." Mathematics and Mechanics of Solids 24, no. 6 (2018): 1749–62. http://dx.doi.org/10.1177/1081286518805521.

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We derive a simple tensor algebraic expression of the modified Eshelby tensor for a spherical inclusion embedded in an arbitrarily anisotropic matrix in terms of three tensor quantities (the fourth-order identity tensor, the elastic stiffness tensor, and the Eshelby tensor) and two scalar quantities (the inclusion radius and interfacial spring constant), when the interfacial damage is modelled as a linear-spring layer of vanishing thickness. We validate the expression for a triclinic crystal involving 21 independent elastic constants against finite element analysis.

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8

Bayuk, Irina O., Mike Ammerman, and Evgeni M. Chesnokov. "Elastic moduli of anisotropic clay." GEOPHYSICS 72, no. 5 (2007): D107—D117. http://dx.doi.org/10.1190/1.2757624.

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Clay minerals are important components in shales, controlling their elastic properties and anisotropy. The elasticity of crystalline clay minerals differs significantly from that of clay in situ because of the ability of clay particles to bind water. In the ma-jority of published works, only isotropic moduli for in situ clays are reported. However, anisotropy is inherent in the clay elas-ticity. We develop an inversion technique for determination of the stiffness tensor of in situ clay from the shale’s stiffness tensor. As an example, we obtain the stiffness tensor of a “water-clay” composite

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9

Chang, Hua Jian, and Shu Wen Zhan. "A Method to Evaluate the Elastic Properties of Ceramics-Enhanced Composites Undertaking Interfacial Delamination." Key Engineering Materials 336-338 (April 2007): 2513–16. http://dx.doi.org/10.4028/www.scientific.net/kem.336-338.2513.

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A micromechanical approach is developed to investigate the behavior of composite materials, which undergo interfacial delamination. The main objective of this approach is to build a bridge between the intricate theories and the engineering applications. On the basis of the spring-layer model, which is useful to treat the interfacial debonding and sliding, the present paper proposes a convenient method to assess the effects of delamination on the overall properties of composites. By applying the Equivalent Inclusion Method (EIM), two fundamental tensors are derived in the present model, the mod

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10

Voyiadjis, George Z., Chahmi Oucif, Peter I. Kattan, and Timon Rabczuk. "Damage and healing mechanics in plane stress, plane strain, and isotropic elasticity." International Journal of Damage Mechanics 29, no. 8 (2020): 1246–70. http://dx.doi.org/10.1177/1056789520905347.

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The present paper presents a theoretical formulation of different self-healing variables. Healing variables based on the recovery in elastic modulus, shear modulus, Poisson's ratio, and bulk modulus are defined. The formulation is presented in both scalar and tensorial cases. A new healing variable based on elastic stiffness recovery in proposed, which is consistent with the continuum damage-healing mechanics. The evolution of the healing variable calculated based on cross-section as function of the healing variable calculated based on elastic stiffness is presented in both hypotheses of elast

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11

Matsu'ura, Mitsuhiro, and Toshiko Terakawa. "Decomposition of elastic potential energy and a rational metric for aftershock generation." Geophysical Journal International 227, no. 1 (2021): 162–68. http://dx.doi.org/10.1093/gji/ggab206.

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SUMMARY The occurrence of earthquakes can be regarded as shear fracture releasing the elastic potential energy stored in the Earth. The potential energy density of linear elastic forces is generally represented in the quadratic form of strain tensor components with the fourth-order coefficient tensor of elastic stiffness. When the material is isotropic, since the stiffness tensor is expressible as a linear combination of two independent symmetric tensors, we can decompose the elastic potential energy density into two independent parts, namely the volumetric part and the shearing part. By defin

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12

Grechka, Vladimir, and Maria Alejandra Rojas. "On the ambiguity of elasticity measurements in layered rocks." GEOPHYSICS 72, no. 3 (2007): D51—D59. http://dx.doi.org/10.1190/1.2709745.

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Different boundary conditions applied to finite-size, heterogeneous rocks result in different average or apparent elastic stiffnesses. In statics, the apparent stiffness tensors that correspond to the homogeneous stress and homogeneous strain boundary conditions provide the lower and upper bounds for the true or effective stiffness tensor. It appears that similar bounds cannot be established for experiments utilizing wave propagation. We present static and dynamic computations of the apparent properties of stacks of horizontal isotropic layers. The effective stiffness tensors of such media are

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13

Dewangan, Pawan, and Vladimir Grechka. "Inversion of multicomponent, multiazimuth, walkaway VSP data for the stiffness tensor." GEOPHYSICS 68, no. 3 (2003): 1022–31. http://dx.doi.org/10.1190/1.1581073.

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Vertical seismic profiling (VSP), an established technique, can be used for estimating in‐situ anisotropy that might provide valuable information for characterization of reservoir lithology, fractures, and fluids. The P‐wave slowness components, conventionally measured in multiazimuth, walkaway VSP surveys, allow one to reconstruct some portion of the corresponding slowness surface. A major limitation of this technique is that the P‐wave slowness surface alone does not constrain a number of stiffness coefficients that may be crucial for inferring certain rock properties. Those stiffnesses can

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14

SAYERS, COLIN M. "Increasing contribution of grain boundary compliance to polycrystalline ice elasticity as temperature increases." Journal of Glaciology 64, no. 246 (2018): 669–74. http://dx.doi.org/10.1017/jog.2018.56.

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ABSTRACTMeasured elastic stiffnesses of ice polycrystals decrease with increasing temperature due to a decrease in grain boundary stiffness with increasing temperature. In this paper, we represent grain boundaries as imperfectly bonded interfaces, across which traction is continuous, but displacement may be discontinuous. We express the additional compliance due to grain boundaries in terms of a second-rank and a fourth-rank tensor, which quantify the effect on elastic wave velocities of the orientation distribution as well as the normal and shear compliances of the grain boundaries. Measureme

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15

Beloborodov, Roman, Marina Pervukhina, and Maxim Lebedev. "Compaction trends of full stiffness tensor and fluid permeability in artificial shales." Geophysical Journal International 212, no. 3 (2017): 1687–93. http://dx.doi.org/10.1093/gji/ggx510.

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Summary We present a methodology and describe a set-up that allows simultaneous acquisition of all five elastic coefficients of a transversely isotropic (TI) medium and its permeability in the direction parallel to the symmetry axis during mechanical compaction experiments. We apply the approach to synthetic shale samples and investigate the role of composition and applied stress on their elastic and transport properties. Compaction trends for the five elastic coefficients that fully characterize TI anisotropy of artificial shales are obtained for a porosity range from 40 per cent to 15 per ce

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16

Schoenberg, Michael, and Colin M. Sayers. "Seismic anisotropy of fractured rock." GEOPHYSICS 60, no. 1 (1995): 204–11. http://dx.doi.org/10.1190/1.1443748.

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A simple method for including the effects of geologically realistic fractures on the seismic propagation through fractured rocks can be obtained by writing the effective compliance tensor of the fractured rock as the sum of the compliance tensor of the unfractured background rock and the compliance tensors for each set of parallel fractures or aligned fractures. The compliance tensor of each fracture set is derivable from a second rank fracture compliance tensor. For a rotationally symmetric set of fractures, the fracture compliance tensor depends on only two fracture compliances, one controll

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17

Barret, C., and S. Baste. "Effective Elastic Stiffnesses of an Anisotropic Medium Permeated by Tilted Cracks." Journal of Applied Mechanics 66, no. 3 (1999): 680–86. http://dx.doi.org/10.1115/1.2791562.

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This paper is concerned with the relationship between the effective stiffness tensor and the intensity of damage in individual modes for an anisotropic material with tilted cracks. The predictions are compared favorably with the experimentally measured load-induced changes of the 13 stiffnesses of a two-dimensional C/C-SiC ceramic matrix composite subjected to an off-axis solicitation. By taking into account the thickness of the cracks, it is possible to understand the change of the elastic anisotropy of the material and of its inelastic strain.

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18

Kruyt, N. P., and L. Rothenburg. "Micromechanical Definition of the Strain Tensor for Granular Materials." Journal of Applied Mechanics 63, no. 3 (1996): 706–11. http://dx.doi.org/10.1115/1.2823353.

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In order to develop constitutive relations for granular materials from the micromechanical viewpoint, general expressions relating macroscopic stress and strain to contact forces and particle displacements are required. Such an expression for the stress tensor under quasi-static conditions is well established in the literature, but a corresponding expression for the strain tensor has been lacking so far. This paper presents such an expression for two-dimensional assemblies. This expression is verified by computer simulations of biaxial and shear tests. As a demonstration of the use of the deve

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19

Spalthoff, P., W. Wunnike, C. Nauer-Gerhard, H. J. Bunge, and E. Schneider. "Determination of the Elastic Tensor of a Textured Low-Carbon Steel." Textures and Microstructures 21, no. 1 (1993): 3–16. http://dx.doi.org/10.1155/tsm.21.3.

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The components of the elastic stiffness tensor of hot rolled low-carbon steel were determined using an ultrasonic pulse-echo-method. They were also calculated on the basis of X-ray texture measurements using the Hill approximation. The maximum deviation between experimental and calculated values is 3.5%. An influence of the slightly anisotropic grain structure on the elastic anisotropy could not be seen.

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20

Chen, Hongyu, and Donald Baird. "Prediction of Young’s Modulus for Injection Molded Long Fiber Reinforced Thermoplastics." Journal of Composites Science 2, no. 3 (2018): 47. http://dx.doi.org/10.3390/jcs2030047.

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In this article, the elastic properties of long-fiber injection-molded thermoplastics (LFTs) are investigated by micro-mechanical approaches including the Halpin-Tsai (HT) model and the Mori-Tanaka model based on Eshelby’s equivalent inclusion (EMT). In the modeling, the elastic properties are calculated by the fiber content, fiber length, and fiber orientation. Several closure approximations for the fourth-order fiber orientation tensor are evaluated by comparing the as-calculated elastic stiffness with that from the original experimental fourth-order tensor. An empirical model was developed

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21

Bhattacharyya, Saswata, Tae Wook Heo, Kunok Chang, and Long-Qing Chen. "A Spectral Iterative Method for the Computation of Effective Properties Of Elastically Inhomogeneous Polycrystals." Communications in Computational Physics 11, no. 3 (2012): 726–38. http://dx.doi.org/10.4208/cicp.290610.060411a.

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AbstractWe report an efficient phase field formalism to compute the stress distribution in polycrystalline materials with arbitrary elastic inhomogeneity and anisotropy The dependence of elastic stiffness tensor on grain orientation is taken into account, and the elastic equilibrium equation is solved using a spectral iterative perturbation method. We discuss its applications to computing residual stress distribution in systems containing arbitrarily shaped cavities and cracks (with zero elastic modulus) and to determining the effective elastic properties of polycrystals and multilayered compo

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22

Louis, Laurent, Ruarri Day-Stirrat, Ronny Hofmann, Nishank Saxena, and Anja M. Schleicher. "Computation of effective elastic properties of clay from X-ray texture goniometry data." GEOPHYSICS 83, no. 5 (2018): MR245—MR261. http://dx.doi.org/10.1190/geo2017-0581.1.

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We have developed a new method for estimating the contribution of a pure clay fraction (i.e., devoid of organic matter) to the total effective rock stiffness. The method is based on published clay mineral stiffness data and on an original preferred clay mineral orientation data set obtained by X-ray texture goniometry on 56 samples of Kimmeridgian and Devonian age from two North American shale plays. We find that (1) large variability in preferred orientation of clay results in moderate variability in effective clay elastic anisotropy and (2) the effect of variations in the preferred orientati

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23

Kushch, V. I. "Elastic fields and effective stiffness tensor of spheroidal particle composite with imperfect interface." Mechanics of Materials 124 (September 2018): 45–54. http://dx.doi.org/10.1016/j.mechmat.2018.06.001.

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24

Phlip, Thresiamma, C. S. Menon, and K. Indulekha. "Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Trigonal Calcite." E-Journal of Chemistry 2, no. 4 (2005): 207–17. http://dx.doi.org/10.1155/2005/913794.

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The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the fourteen non-vanishing third-order elastic constants of trigonal calcite are obtained. The second-orde

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25

Hu, Yanrong, and George A. McMechan. "Comparison of effective stiffness and compliance for characterizing cracked rocks." GEOPHYSICS 74, no. 2 (2009): D49—D55. http://dx.doi.org/10.1190/1.3073004.

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The noninteraction approximation (NIA) is commonly used for prediction of the anisotropic elastic stiffnesses of cracked rocks. At large crack density, the NIA has a desirable nonlinear stiffness behavior; however, this is inconsistent with the dilute crack assumption. The nonlinear behavior of stiffness predicted by the NIA at high crack density is produced by defining compliance to be a linear function of crack density and then inverting the compliance tensor to stiffness. The linear behavior of compliance is strictly valid only when there is no crack interaction (at low crack density), so t

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26

Philip, Thresiamma, C. S. Menon, and K. Indulekha. "Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Lithium Niobate." E-Journal of Chemistry 3, no. 3 (2006): 122–33. http://dx.doi.org/10.1155/2006/842320.

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The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3(lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3are obtained in the present work. The second and third-order elastic constants are c

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27

Senin, HB, HAA Sidek, and GA Saunders. "Elastic Behaviour of Terbium Metaphosphate Glasses Under High Pressures." Australian Journal of Physics 47, no. 6 (1994): 795. http://dx.doi.org/10.1071/ph940795.

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The elastic and nonlinear acoustic vibrational properties of terbium metaphosphate glasses (Tb2O3)x(P2O5)1?x with x = 0�226,0�247,0�263 and 0�271 (x is the mole fraction) have been determined from measurements of the effects of temperature, hydrostatic pressure, and uniaxial stress on' ultrasonic wave velocity. At temperatures below about 140 K, the elastic stiffness of' (Tb2O3)x(P2O5)1?x glasses becomes anomalously dependent upon temperature, a behaviour usually associated with interactions between acoustic phonons and two-level systems. Except for the (Tb2O3)0�271(P205)0�729 glass, the hydro

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28

Mavko, Gary, and Kaushik Bandyopadhyay. "Approximate fluid substitution for vertical velocities in weakly anisotropic VTI rocks." GEOPHYSICS 74, no. 1 (2009): D1—D6. http://dx.doi.org/10.1190/1.3026552.

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Despite the prevalence of elastic anisotropy in rocks, most models used routinely for wave propagation, imaging, and rock physics assume an isotropic Earth. The main reason for using isotropic approximations is that we seldom measure enough parameters to characterize the stiffness tensor of a rock completely. Fluid substitution is an important example: because of an incomplete knowledge of the stiffness tensor, often we choose isotropic equations over their anisotropic form. Assuming weak anisotropy, we derive an approximate form of the anisotropic fluid-substitution equation for seismic waves

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29

Felício Fuck, Rodrigo, and Ilya Tsvankin. "Analysis of the symmetry of a stressed medium using nonlinear elasticity." GEOPHYSICS 74, no. 5 (2009): WB79—WB87. http://dx.doi.org/10.1190/1.3157251.

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Velocity variations caused by subsurface stress changes play an important role in monitoring compacting reservoirs and in several other applications of seismic methods. A general way to describe stress- or strain-induced velocity fields is by employing the theory of nonlinear elasticity, which operates with third-order elastic (TOE) tensors. These sixth-rank strain-sensitivity tensors, however, are difficult to manipulate because of the large number of terms involved in the algebraic operations. Thus, even evaluation of the anisotropic symmetry of a medium under stress/strain proves to be a ch

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30

POZRIKIDIS, C. "Effect of membrane bending stiffness on the deformation of capsules in simple shear flow." Journal of Fluid Mechanics 440 (August 10, 2001): 269–91. http://dx.doi.org/10.1017/s0022112001004657.

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The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfa

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31

Boitz, Nepomuk, Anton Reshetnikov, and Serge A. Shapiro. "Visualizing effects of anisotropy on seismic moments and their potency-tensor isotropic equivalent." GEOPHYSICS 83, no. 3 (2018): C85—C97. http://dx.doi.org/10.1190/geo2017-0442.1.

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Radiation patterns of earthquakes contain important information on tectonic strain responsible for seismic events. However, elastic anisotropy may significantly impact these patterns. We systematically investigate and visualize the effect of anisotropy on the radiation patterns of microseismic events. For visualization, we use a vertical-transverse-isotropic (VTI) medium. We distinguish between two different effects: the anisotropy in the source and the anisotropy on the propagation path. Source anisotropy mathematically comes from the matrix multiplication of the anisotropic stiffness tensor

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32

Yanase, K., and J. W. Ju. "Effective Elastic Moduli of Spherical Particle Reinforced Composites Containing Imperfect Interfaces." International Journal of Damage Mechanics 21, no. 1 (2011): 97–127. http://dx.doi.org/10.1177/1056789510397076.

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The effective elastic moduli of composite materials are investigated in the presence of imperfect interfaces between the inclusions and the matrix. The primary focus is on the spherical particle reinforced composites. By admitting the displacement jumps at the particle–matrix interface, the modified Eshelby inclusion problem is studied anew. To derive the modified Eshelby tensor, three approximate methods are presented and compared by emphasizing the existence of a unique solution and computational efficiency. Subsequently, the effective elastic stiffness tensor of the composite is formulated

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Ogi, Hirotsugu, Goh Shimoike, Kazuki Takashima, and Masahiko Hirao. "Measurement of elastic-stiffness tensor of an anisotropic thin film by electromagnetic acoustic resonance." Ultrasonics 40, no. 1-8 (2002): 333–36. http://dx.doi.org/10.1016/s0041-624x(02)00116-6.

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34

Kato, R., and J. Hama. "First-principles calculation of the elastic stiffness tensor of aluminium nitride under high pressure." Journal of Physics: Condensed Matter 6, no. 38 (1994): 7617–32. http://dx.doi.org/10.1088/0953-8984/6/38/004.

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35

Benveniste, Y., G. J. Dvorak, and T. Chen. "On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media." Journal of the Mechanics and Physics of Solids 39, no. 7 (1991): 927–46. http://dx.doi.org/10.1016/0022-5096(91)90012-d.

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36

Itin, Yakov. "Irreducible matrix resolution for symmetry classes of elasticity tensors." Mathematics and Mechanics of Solids 25, no. 10 (2020): 1873–95. http://dx.doi.org/10.1177/1081286520913596.

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In linear elasticity, a fourth-order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties elastic constants of a material. The main goal of the current work is to derive a compact matrix representation of the elasticity tensor that correlates with its intrinsic algebraic properties. Such representation can be useful in design of artificial materials. Owing to Voigt, the elasticity tensor is conventionally represented by a (6 × 6) symmetric matrix. In this paper, we construct two alternative matrix representations that conform with the irreducib

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37

Senin, H. B., H. A. A. Sidek, and G. A. Saunders. "Acoustic Vibrational Properties and Fractal Bond Connectivity of Praseodymium Doped Glasses." Australian Journal of Physics 53, no. 6 (2000): 805. http://dx.doi.org/10.1071/ph00066.

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The velocities of longitudinal and shear ultrasonic waves propagated in the (Pr2O3)x(P2O5)1-x glass system, where x is the mole fraction of Pr2O3 and (1 - x) is the mole fraction of P2O5, have been measured as functions of temperature and hydrostatic pressure. The temperature dependencies of the second order elastic stiffness tensor components (SOEC) CS IJ , which have been determined from the velocitydata between 10 and 300 K, show no evidence of phonon mode softening throughout the whole temperature range. The elastic stiffnesses increased monotonically, the usual behaviour associated with t

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Krasnitskii, Stanislav, Anton Trofimov, Enrico Radi, and Igor Sevestianov. "Effect of a rigid toroidal inhomogeneity on the elastic properties of a composite." Mathematics and Mechanics of Solids 24, no. 4 (2018): 1129–46. http://dx.doi.org/10.1177/1081286518773806.

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An analytical solution is obtained for the problem of an infinite elastic medium containing a rigid toroidal inhomogeneity under remotely applied uniform strain. The traction on the torus surface is determined as a function of torus parameters and strain components applied at infinity. The results are utilized to calculate components of the stiffness contribution tensor of the rigid toroidal inhomogeneity that is required for calculation of the overall elastic properties of a material containing multiple toroidal inhomogeneities. The analytical results are verified by comparison with finite el

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39

Theocaris, P. S., and T. P. Philippidis. "True bounds on Poisson's ratios for transversely isotropic solids." Journal of Strain Analysis for Engineering Design 27, no. 1 (1992): 43–44. http://dx.doi.org/10.1243/03093247v271043.

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The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

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40

Ofoegbu, G. I., and J. H. Curran. "Yielding and damage of intact rock." Canadian Geotechnical Journal 28, no. 4 (1991): 503–16. http://dx.doi.org/10.1139/t91-067.

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This paper presents a description of the elastic deformability and strength of intact rock. Structural defects such as microcracks cause the load-bearing capacity and elastic stiffness of rock to decrease, because the imposed load is supported by a diminished fraction of the solid volume. This is accounted for using a continuum damage variable, which describes the effect of cracks on the capacity of rock to support distortional loading. Values of the variable are computed using an incremental evolution law, which describes the effects of confinement and distortional load intensity on cracking.

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Szeptyński, P. "Energy-Based Yield Criteria for Orthotropic Materials, Exhibiting Strength-Differential Effect. Specification for Sheets under Plane Stress State." Archives of Metallurgy and Materials 62, no. 2 (2017): 729–36. http://dx.doi.org/10.1515/amm-2017-0110.

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AbstractA general proposition of an energy-based limit condition for anisotropic materials exhibiting strength-differential effect (SDE) based on spectral decomposition of elasticity tensors and the use of scaling pressure-dependent functions is specified for the case of orthotropic materials. A detailed algorithm (based on classical solutions of cubic equations) for the determination of elastic eigenstates and eigenvalues of the orthotropic stiffness tensor is presented. A yield condition is formulated for both two-dimensional and three-dimensional cases. Explicit formulas based on simple str

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Perreux, Dominique M., and W. Steven Johnson. "A Model for Prediction of Bone Stiffness Using a Mechanical Approach of Composite Materials." Journal of Biomechanical Engineering 129, no. 4 (2007): 494–502. http://dx.doi.org/10.1115/1.2746370.

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A model to predict the bone stiffness is presented in this paper. The objective is to obtain a description of bone stiffness of a representative elementary volume (REV) based on a small set of physical parameters. The main idea is to use measurable information related to the orientation and the density of a basic elementary submicrostructure (ESMS). This ESMS is the first arrangement of the basic components. A simple rule-of-mixtures approach is used to provide the elastic properties for the ESMS. The basic properties are dependent on the volume fraction of the mineralized phase. The orientati

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Cunha, Carlos A. "Elastic modeling in discontinuous media." GEOPHYSICS 58, no. 12 (1993): 1840–51. http://dx.doi.org/10.1190/1.1443399.

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Results from elastic‐wave simulations in a simple model show that for models characterized by a set of layers with sharp boundaries (discontinuous stiffness tensor), traditional finite‐difference methods fail to correctly describe the dynamics of the propagation process. The failure comes from the lack of distinction between model and field variables; the same differential operator is applied to discontinuous (model) and continuous (wavefield) components. This problem is solved with a modified high‐order finite‐difference modeling scheme (dual‐operator method) that uses two distinct operators

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Zou, W. N., C. X. Tang, and W. H. Lee. "Identification of symmetry type of linear elastic stiffness tensor in an arbitrarily orientated coordinate system." International Journal of Solids and Structures 50, no. 14-15 (2013): 2457–67. http://dx.doi.org/10.1016/j.ijsolstr.2013.03.037.

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Mastilovic, Sreten. "On elastic response of disordered triangular lattice during dynamic loading." Theoretical and Applied Mechanics 35, no. 1-3 (2008): 255–65. http://dx.doi.org/10.2298/tam0803255m.

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The present investigation focuses on an observation regarding the initial elastic response of a triangular geometrically and structurally disordered lattice during medium-to-high strain rate loading. Namely: a transition from the short-time modulus of elasticity to the long-time one, which is not accompanied by the corresponding change of the stiffness tensor. It is demonstrated that the difference between the two moduli is, in the case of the homogeneous biaxial test simulations performed herein, a consequence of the geometrical and structural disorder "quenched" within the lattice. The inves

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Recchia, Giuseppina, Hongyang Cheng, Vanessa Magnanimo, and Luigi La Ragione. "Failure in granular materials based on acoustic tensor: a numerical analysis." EPJ Web of Conferences 249 (2021): 10005. http://dx.doi.org/10.1051/epjconf/202124910005.

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We investigate localization in granular material with the support of numerical simulations based upon DEM (Distinct Element Method). Localization is associated with a discontinuity in a component of the incremental strain over a plane surface through the condition of the determinant of the acoustic tensor to be zero. DEM simulations are carried out on an aggregate of elastic frictional spheres, initially isotropically compressed and then sheared at constant pressure p0. The components of the stiffness tensor are evaluated numerically in stressed states along the triaxial test and employed to e

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Sokolov, Alexander Pavlovich, and Vitaliy Nikolaevich Schetinin. "Modeling of Phases Adhesion in Composite Materials Based on Spring Finite Element with Zero Length." Key Engineering Materials 780 (September 2018): 3–9. http://dx.doi.org/10.4028/www.scientific.net/kem.780.3.

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A new numerical method for homogenization of elastic properties of dispersedly-reinforced composites was presented. The method takes into account special model of adhesive contact. Homogenization of properties was performed by averaging the solutions of boundary value problems on representative volume cell (RVC) using the finite element method (FEM). A new approach of calculation of components of effective tensor of elastic moduli was proposed. A heterogeneous finite element model with elements of two types was built: three-dimensional tetrahedron elements for every phases and spring element w

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Vogric, Marko, and Erwin Povoden-Karadeniz. "A multiscale mean field model for elastic properties of hypereutectoid pearlitic steels with different microstructures." International Journal of Materials Research 112, no. 5 (2021): 348–58. http://dx.doi.org/10.1515/ijmr-2020-8039.

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Abstract Multiscale modeling of macroscopic elastic properties of pearlitic hypereutectoid steel using the Eshelby matrix–inclusion approach is possible. The model works through successive homogenization steps, based on the elastic properties of cementite and ferrite. Globular pearlite is homogenized using α Mori–Tanaka approach. Lamellar pearlite and pearlite colonies with fragmented proeutectoid cementite are homogenized by α classical self-consistent scheme. In the case of pearlite colonies surrounded by α continuous cementite film, α generalized self-consistent scheme is used. The influenc

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Khnaijar, A., and R. Benamar. "A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations." Advances in Acoustics and Vibration 2017 (March 15, 2017): 1–25. http://dx.doi.org/10.1155/2017/4740851.

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This paper presents a discrete physical model to approach the problem of nonlinear vibrations of beams resting on elastic foundations. The model consists of a beam made of several small bars, evenly spaced. The bending stiffness is modeled by spiral springs, and the Winkler soil stiffness is modeled using linear vertical springs. Concentrated masses, presenting the inertia of the beam, are located at the bar ends. Finally, the nonlinear effect is presented by the axial forces in the bars, assumed to behave as longitudinal springs, due to the change in their length induced by the Pythagorean Th

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Nijenhuis, Nadja, Xuegen Zhao, Alex Carisey, Christoph Ballestrem, and Brian Derby. "Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells." Biophysical Journal 107, no. 7 (2014): 1502–12. http://dx.doi.org/10.1016/j.bpj.2014.07.073.

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