By A. J. M. Spencer (auth.), Jean-Paul Boehler (eds.)
Read or Download Mechanical Behavior of Anisotropic Solids / Comportment Méchanique des Solides Anisotropes: Proceedings of the Euromech Colloquium 115 Villard-de-Lans, June 19–22, 1979 / Colloque Euromech 115 Villard-de-Lans, 19–22 juin 1979 PDF
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Additional resources for Mechanical Behavior of Anisotropic Solids / Comportment Méchanique des Solides Anisotropes: Proceedings of the Euromech Colloquium 115 Villard-de-Lans, June 19–22, 1979 / Colloque Euromech 115 Villard-de-Lans, 19–22 juin 1979
Mr is a permutation of ii' jl> i 2 , j2' ... ip ' jp and 2p = 2q + r (and hence r is even). 4), with a chosen to coincide in direction with the x 3 -axis, were given by Smith and Rivlin . 2), it follows that ep(C) is a linear combination of polynomials in ai and Cij , with coefficients which are products of Kronecker deltas; thus ep (C) is an isotropic invariant of a and C. An isotropic integrity basis for a and C is a transversely isotropic integrity basis for C. It must be noted, however, that an irreducible isotropic integrity basis for a and C is not necessarily irreducible when it is regarded as a transversely isotropic basis for C.
Deformations of Fibre-Reinforced Materials"Oxford University Press, 1972. LM. S. RIVLlN_ - "The theory of matrix polynomials and its application to the mechanics of isotropic continua", Arch. Rat. Mech. , 2 (1959) : 309-336. M. S. RIVLIN. - "Finite integrity bases for five or fewer symmetric 3 x 3 matrices". Arch. Rat. Mech. , 2 (1959): 435-446. M. S. RIVLIN. - "Further results in the theory of matrix polynomials". Arch. Rat. Mech. , 4 (1960): 214-230. M. S. RIVLIN. - "Isotropic Integrity Bases for Vectors and Second-Order Tensors, Part I".
It is apparent that this approach can be extended to the determination of integrity bases for systems of vectors and tensors, and can be applied to other symmetry groups besides those considered in Sections 3 and 4. A similar method has been applied to a variety of problems by Boehler . S. linear Elasticity For a linear elastic solid the strain-energy function is a quadratic function of the components E;j of the infinitesimal strain tensor E. 3 are elastic constants. M Spencer 16 This is in agreement with the well-known expression for the stress in a transversely isotropic linearly elastic material.