Invariant Elastic Constants for Crystals

Srinivasan, T.; Nigam, S. D.

doi:10.1512/iumj.1970.19.19038

Cited by 14 publications

(20 citation statements)

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“…The problem has been studied thoroughly by several authors (Srinivasan, 1969;Srinivasan, 1985;Spencer, 1983;Cowin & Mehrabadi, 1987;Hue & Del Piero, 1991;Srinivasan, 1998;Blinowski & Rychlewski, 1998;Tu, 1968). Another interesting material property in anisotropic solids is the direct piezoelectric effect that comprises a group of phenomena in which the mechanical stresses or strains induce in crystals an electric polarization (electric field) proportional to those factors.…”

Section: Form Invariants and Orthonormal Basis Elementsmentioning

confidence: 99%

Estimation of the Degree of Anisotropy and Overall Elastic Stiffness of Advanced Anisotropic Materials

Gaith¹,

Al-Hayek²

2011

Advances in Composite Materials - Ecodesign and Analysis

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Section: Form Invariants and Orthonormal Basis Elementsmentioning

confidence: 99%

Estimation of the Degree of Anisotropy and Overall Elastic Stiffness of Advanced Anisotropic Materials

Gaith¹,

Al-Hayek²

2011

Advances in Composite Materials - Ecodesign and Analysis

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“…The representative references include [Rychlewski 1984;Walpole 1984;Theocaris and Philippidis 1989;Mehrabadi and Cowin 1990;Sutcliffe 1992;Theocaris and Sokolis 2000]. A study of the fourth-order tensors of elastic constants, and their equivalent matrix representations, is also important in the analysis of the invariants of the fourthorder tensors and identification of the invariant combinations of anisotropic elastic constants [Srinivasan and Nigam 1969;Betten 1987;Zheng 1994;Ting 1987;2000;Ting and He 2006]. Furthermore, a study of the representation of the fourth-order tensors with respect to different bases can facilitate tensor operations and the analytical determination of the inverse tensors [Kunin 1981;1983;Walpole 1984;Lubarda and Krajcinovic 1994;Nadeau and Ferrari 1998;Gangi 2000].…”

Section: Introductionmentioning

confidence: 99%

On the elastic moduli and compliances of transversely isotropic and orthotropic materials

Lubarda

Chen

2008

JOMMS

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The relationships between the elastic moduli and compliances of transversely isotropic and orthotropic materials, which correspond to different appealing sets of linearly independent fourth-order base tensors used to cast the elastic moduli and compliances tensors, are derived by performing explicit inversions of the involved fourth-order tensors. The deduced sets of elastic constants are related to each other and to common engineering constants expressed in the Voigt notation with respect to the coordinate axes aligned along the directions orthogonal to the planes of material symmetry. The results are applied to a transversely isotropic monocrystalline zinc and an orthotropic human femural bone.

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“…The representative references include [Rychlewski 1984;Walpole 1984;Theocaris and Philippidis 1989;Sutcliffe 1992;Theocaris and Sokolis 2000]. A study of the fourth-order tensors of elastic constants, and their equivalent matrix representations, is also important in the analysis of the invariants of the fourthorder tensors and identification of the invariant combinations of anisotropic elastic constants [Srinivasan and Nigam 1969;Betten 1987;Zheng 1994;Ting 1987;Ting and He 2006]. Furthermore, a study of the representation of the fourth-order tensors with respect to different bases can facilitate tensor operations and the analytical determination of the inverse tensors [Kunin 1981;Walpole 1984;Lubarda and Krajcinovic 1994;Nadeau and Ferrari 1998;Gangi 2000].…”

Section: Introductionmentioning

confidence: 99%

Untitled

2008

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year. We study an axially symmetric frictionless contact problem between a nonhomogeneous elastic halfspace and a rigid base that has a small axisymmetric surface recess. We reduce the problem to solving Fredholm integral equations, solve these equations numerically, and establish a relationship between the applied pressure and the gap radius. We find and graph the effects of nonhomogeneity on the normal pressure, critical pressure and on the surface displacement.

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Invariant Elastic Constants for Crystals

Cited by 14 publications

References 0 publications

Estimation of the Degree of Anisotropy and Overall Elastic Stiffness of Advanced Anisotropic Materials

Estimation of the Degree of Anisotropy and Overall Elastic Stiffness of Advanced Anisotropic Materials

On the elastic moduli and compliances of transversely isotropic and orthotropic materials

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