Relevant bibliographies by topics / Elastic Stiffness Tensor

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Elastic Stiffness Tensor'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Elastic Stiffness Tensor"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Elastic Stiffness Tensor"

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Ahmadi, Pouya. "Elastic Anisotropy of Deformation Zones in both Seismic and Ultrasonic Frequencies: An Example from the Bergslagen Region, Eastern Sweden." Thesis, Uppsala universitet, Geofysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-201696.

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Estimation of elastic anisotropy, which is usually caused by rock fabrics and mineral orientation, has an important role in exploration seismology and better understanding of crustal seismic reflections. If not properly taken care of during processing steps, it may lead to wrong interpretation or distorted seismic image. In this thesis, a state-of-the-art under the development Laser Doppler Interferometer (LDI) device is used to measure phase velocities on the surface of rock samples from a major deformation zone (Österbybruk Deformation Zone) in the Bergslagen region of eastern Sweden. Then,
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Chang, Wei-Shan, and 張瑋珊. "Changes in Stiffness of Tibialis Posterior Tendon After Elastic Anti-pronation Taping." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/38p6t3.

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碩士<br>國立臺灣大學<br>物理治療學研究所<br>105<br>Excessive pronation motion during the stance phase of a gait cycle is frequently noted in adults with pronated foot, which has been believed to result in tibialis posterior tendon dysfunction due to repetitive microtrauma. The facts that poor shock absorption of the medial longitudinal arch during walking is found in patients with tibialis posterior tendon dysfunction and poor blood supply of the insulted tendon retards its healing process affect patients’ quality of life. Previous motion analysis or foot pressure studies showed that anti-pronation taping may
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Moravcová, Kamila. "Viskózní a elastické vlastnosti svalové a vazivové tkáně "in situ"." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-324912.

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Title: Viscousand elastic properties of soft tissue"in situ" Goals and methods: The aim of this thesis is to measure the viscoelastic properties of human soleus muscle and Achilles tendonin vivo and post mortem in situ. It is a pilot study that uses myotonometry as the method of measurement. Based on the response of connective tissues on deformation made by tip of myotonometer, resp. its viscoelastic properties, curves in graphsare created. Three main described parameters of thecurveare steepness, deflection and its surface area. Main goal of the experiment is to compare properties of differen
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Book chapters on the topic "Elastic Stiffness Tensor"

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Newnham, Robert E. "Elasticity." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0015.

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All solids change shape under mechanical force. Under small stresses, the strain x is related to stress X by Hooke’s Law (x) = (s)(X), or the converse relationship (X) = (c)(x). The elastic compliance coefficients (s) are generally reported in units of m2/N, and the stiffness coefficients (c) in N/m2. For a fairly stiff material like a metal or a ceramic, c is about 1011 N/m2 = 1012 dynes/cm2 = 100 GPa = 0.145 × 108 PSI. Hooke’s Law is a linear relation between stress and strain, and does not describe the elastic behavior at high stress levels that requires higher order elastic constants (Chapter 14). Irreversible phenomena such as plasticity and fracture occur at still higher stress levels. Two directions are needed to specify stress (the direction of the force and the normal to the face on which the force acts), and two directions are needed to specify strain (the direction of the displacement and the orientation of the measurement axis). Thus there are four directions involved in measuring elastic stiffness, which is therefore a fourth rank tensor: . . . Xij = cijklxkl . . . .
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Ogi, H., G. Shimoike, M. Hirao, K. Takashima, and H. Ledbetter. "Elastic-stiffness tensor of metal-matrix composites measured by electromagnetic acoustic resonance." In Nondestructive Characterization of Materials X. Elsevier, 2001. http://dx.doi.org/10.1016/b978-008043799-6/50009-4.

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Ting, T. T. C. "Linear Anisotropic Elastic Materials." In Anisotropic Elasticity. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195074475.003.0005.

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The relations between stresses and strains in an anisotropic elastic material are presented in this chapter. A linear anisotropic elastic material can have as many as 21 elastic constants. This number is reduced when the material possesses a certain material symmetry. The number of elastic constants is also reduced, in most cases, when a two-dimensional deformation is considered. An important condition on elastic constants is that the strain energy must be positive. This condition implies that the 6×6 matrices of elastic constants presented herein must be positive definite. Referring to a fixed rectangular coordinate system x1, x2, x3, let σij and εks be the stress and strain, respectively, in an anisotropic elastic material. The stress-strain law can be written as . . . σij = Cijksεks . . . . . .(2.1-1). . . in which Cijks are the elastic stiffnesses which are components of a fourth rank tensor. They satisfy the full symmetry conditions . . . Cijks = Cjiks, Cijks = Cijsk, Cijks = Cksij. . . . . . .(2.1-2). . .
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Chimenti, Dale, Stanislav Rokhlin, and Peter Nagy. "Waves in Periodically Layered Composites." In Physical Ultrasonics of Composites. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780195079609.003.0011.

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Composite materials, unless they are quite thin, often include periodic layering, where laminated plates composed of alternating uniaxial plies in two or more directions result in more evenly distributed in-plane stiffness. The oriented plies can generally be reduced to a unit cell geometry which repeats throughout the laminate and is composed of sublayers each having highly directional in-plane stiffness, but identical out-of-plane properties. As the transverse isotropy of a uniaxial fibrous ply derives from the geometry of the two-phase material, composite laminates of these plies will have microscopic elastic stiffness tensors which change only in the plane of the laminate, as we saw in Chapter 1. The elastic properties normal to the laminate surface remain unchanged from ply to ply. In this chapter we take up the subject of waves in periodically layered plates. Unusual guided wave dispersion effects have been observed experimentally in periodically layered plates. Shull et al. found, for guided waves polarized in the vertical plane in plates of alternating aluminum and aramid–epoxy composites, that dispersion never scales with the frequency–thickness product, as it would in homogeneous isotropic, or layered transversely isotropic, plates. Instead, grouping of the mode curves has been observed. In an attempt to understand this behavior in terms of periodic layering, Auld et al. have analyzed the simpler case of SH wave propagation in periodically layered plates and have demonstrated that these observed phenomena can be attributed to the pass band and stop band structure caused by the periodic layering. In this section, we will show that Floquet modes play a critical role in the behavior of guided waves in plates that are periodically layered. To analyze the problem, we apply an extension of the stiffness matrix method of the previous chapter. Floquet modes, which are the characteristic modes for the infinite periodically layered medium, can be thought of as the analogy—in a periodically layered medium—to the quasilongitudinal and quasishear modes for the infinite homogeneous medium. On the topic of infinite periodic media, many calculations, both approximate and exact, have been performed to model elastic wave propagation in this important class of structures.
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Newnham, Robert E. "Thermodynamic relationships." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0008.

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In the next few chapters we shall discuss tensors of rank zero to four which relate the intensive variables in the outer triangle of the Heckmann Diagram to the extensive variables in the inner triangle. Effects such as pyroelectricity, permittivity, pyroelectricity, and elasticity are the standard topics in crystal physics that allow us to discuss tensors of rank one through four. First, however, it is useful to introduce the thermodynamic relationships between physical properties and consider the importance of measurement conditions. Before discussing all the cross-coupled relationships, we first define the coupling within the three individual systems. In a thermal system, the basic relationship is between change in entropy δS [J/m3] and change in temperature δT [K]: . . . δS = CδT, . . . where C is the specific heat per unit volume [J/m3 K] and T is the absolute temperature. S, T, and C are all scalar quantities. In a dielectric system the electric displacement Di [C/m2] changes under the influence of the electric field Ei [V/m]. Both are vectors and therefore the electric permittivity, εij , requires two-directional subscripts. Occasionally the dielectric stiffness, βij , is required as well. . . . Di = εijEj Ei = βijDj. . . . Some authors use polarization P rather than electric displacement D. The three variables are interrelated through the constitutive relation . . . Di = Pi + ε0Ei = εijEj. . . . The third linear system in the Heckmann Diagram is mechanical, relating strain xij to stress Xkl [N/m2] through the fourth rank elastic compliance coefficients sijkl [m2/N]. . . . xij = sijklXkl. . . . Alternatively, Hooke’s Law can be expressed in terms of the elastic stiffness coefficients cijkl [N/m2]. . . Xij = cijklxkl. . . . When cross coupling occurs between thermal, electrical, and mechanical variables, the Gibbs free energy G(T, X, E) is used to derive relationships between the property coefficients. Temperature T, stress X, and electric field E are the independent variables in most experiments.
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Conference papers on the topic "Elastic Stiffness Tensor"

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Gaith, Mohamed, and Imad Alhayek. "The Calculation of Stiffness for Semiconductor Components." In ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2009. http://dx.doi.org/10.1115/smasis2009-1210.

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In this study, the correlation between macroscopic and microscopic properties of the II-IV semiconductor compounds CdX (X = S, Se, Te) is investigated. Based on constructing orthonormal tensor basis elements using the form-invariant expressions, the elastic stiffness for cubic system materials is decomposed into two parts; isotropic (two terms) and anisotropic parts. A new scale for measuring the overall elastic stiffness of these compounds is introduced and its correlation with the calculated bulk modulus and lattice constants is analyzed. The overall elastic stiffness is calculated and found
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Gaith, Mohamed, and Cevdet Akgoz. "On the Properties of Anisotropic Piezoelectric and Fiber Reinforced Composite Materials." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14075.

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A new procedure based on constructing orthonormal tensor basis using the form-invariant expressions which can easily be extended to any tensor of rank n. A new decomposition, which is not in literature, of the stress tensor is presented. An innovational general form and more explicit physical property of the symmetric fourth rank elastic tensors is presented. The new method allows to measure the stiffness and piezoelectricity in the elastic fiber reinforced composite and piezoelectric ceramic materials, respecively, using a proposed norm concept on the crystal scale. This method will allow to
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Gaith, Mohamed S., and I. Alhayek. "The Measurement of Overall Elastic Stiffness and Bulk Modulus in Anisotropic Materials: Semiconductors." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10097.

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In this study, the correlation between macroscopic and microscopic properties of the II-IV semiconductor compounds ZnX (X = S, Se, Te) is investigated. Based on constructing orthonormal tensor basis elements using the form-invariant expressions, the elastic stiffness for cubic system materials is decomposed into two parts; isotropic (two terms) and anisotropic parts. A scale for measuring the overall elastic stiffness of these compounds is introduced and its correlation with the calculated bulk modulus and lattice constants is analyzed. The overall elastic stiffness is calculated and found to
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Pisano, Aurora, Alba Sofi, and Paolo Fuschi. "A Finite Element Approach for Nonhomogeneous Nonlocal Elastic Problems." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68240.

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The paper deals with the implementation of a method, known in the relevant literature as Nonlocal Finite Element Method, for solving 2D boundary value problems in the context of nonhomogeneous nonlocal elasticity. The method, founded on a consistent thermodynamic formulation, is here improved making use of a phenomenological strain-difference-based nonhomogeneous nonlocal elasticity model. The latter assumes a two components local/nonlocal constitutive relation in which the stress is conceived as the sum of two contributions governed by the standard elastic moduli tensor and by a nonlocal stif
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Abdelhamid, Mohamed, and Aleksander Czekanski. "On the Effective Properties of 3D Metamaterials." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-67407.

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A continuum-based model is developed for the octet-truss unit cell in order to describe the effective mechanical properties (elastic modulus) of the lattice structure. This model is to include different geometric parameters that impact the structural effects; these parameters are: lattice angle, loading direction, thickness to diameter ratio, diameter to length ratio, and ellipticity. All these geometric parameters are included in the stiffness matrix, and the impact of each parameter on the stiffness tensor is investigated. Specifically, the effect of the lattice angle on the elastic moduli i
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Gaith, Mohamed S., and Imad Alhayek. "On the Measurement of the Overall Elastic Stiffness and Bulk Modulus in Anisotropic Materials: Semiconductors." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86559.

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In this study, the correlation between macroscopic and microscopic properties of the II-IV semiconductor compounds CdX (X = S, Se, Te) is investigated. Based on constructing orthonormal tensor basis elements using the form-invariant expressions, the elastic stiffness for cubic system materials is decomposed into two parts; isotropic (two terms) and anisotropic parts. A new scale for measuring the overall elastic stiffness of these compounds is introduced and its correlation with the calculated bulk modulus and lattice constants is analyzed. The overall elastic stiffness is calculated and found
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Leigh, S. H., G. C. Lee, and C. C. Berndt. "Modelling of Elastic Constants of Plasma Spray Deposits with Spheroid-Shaped Voids." In ITSC 1998, edited by Christian Coddet. ASM International, 1998. http://dx.doi.org/10.31399/asm.cp.itsc1998p0587.

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Abstract The five independent elastic constants of plasma spray deposits were calculated from constitutive equations and the microstructural information (void aspect ratios and porosity) were gained from stereological analysis. The voids within the deposit were assumed to be a spheroidal shape. The structure of the deposit was considered to be transversely isotropic with respect to the spray direction, which requires five independent elastic constants of a stiffness tensor. Solid mechanics models containing spheroid-shape voids were applied to obtain the five independent elastic constants of t
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Liu, H. T., L. Z. Sun, and J. W. Ju. "An Interfacial Debonding Model for Particle-Reinforced Composites." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33106.

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To simulate the evolution process of interfacial debonding between particle and matrix, and to further estimate its effect on the overall elastic behavior of particle-reinforced composites, a two-level microstructural-effective damaged model is developed. The microstructural damage mechanism is governed by the interfacial debonding of reinforcement and matrix. The progressive damage process is represented by the debonding angles that are dependent on the external loads. For those debonded particles, the elastic equivalency is constructed in terms of the stiffness tensor. Namely, the isotropic
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Hage, Ilige S., Charbel Y. Seif, Ré-Mi Hage, and Ramsey F. Hamade. "A Verified Non-Linear Regression Model for Elastic Stiffness Estimates of Finite Composite Domains Considering Combined Effects of Volume Fractions, Shapes, Orientations, Locations, and Number of Multiple Inclusions." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86231.

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A non-linear regression model using SAS/STAT (JMP® software; Proc regression module) is developed for estimating the elastic stiffness of finite composite domains considering the combined effects of volume fractions, shapes, orientations, inclusion locations, and number of multiple inclusions. These estimates are compared to numerical solutions that utilized another developed homogenization methodology by the authors (dubbed the generalized stiffness formulation, GSF) to numerically determine the elastic stiffness tensor of a composite domain having multiple inclusions with various combination
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Keskinen, Erno, Michel Cotsaftis, and Matti Martikainen. "Half-Critical Response of Cylindrical Rotor to Distributed Elasticity Excitation." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85365.

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Due to the limitations of manufacturing accuracy, long cylindrical rotors used in heavy power transmission lines and paper machinery are dynamically excited by internal elastic forces. The origin of these forces is the out-of-roundness profile of the inner and outer radii of the rotor, which contributes to the bending stiffness distribution along the rotor span. Distributed anisotropy of the rotor under gravitational load is reason of the existence of half-critical speeds, on which the rotor experiences non-classical resonance state. This problem has been formulated in terms of nominal and dev
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