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On Constitutive Equations of Cauchy Elastic Solids: All Kinds of Crystals and Quasicrystals

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Abstract

Our concern is with the problem of determining general reduced forms of constitutive equations of Cauchy elastic solids under all kinds of material symmetries, including well-known crystal classes and newly discovered quasicrystal classes. By means of Tschebysheff polynomials we present in unified forms simple irreducible representations for elastic constitutive equations under the infinitely many subgroup classes C 2m+1, C 2m+2, D 2m+1 and D 2m+2 for all m = 1, 2,... Moreover, we provide a simple representation for elastic constitutive equations under the most complicated point group, i.e. the icosahedral group. Each presented representation is expressed in terms of not more than nine polynomial tensor generators only.

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Xiao, H. On Constitutive Equations of Cauchy Elastic Solids: All Kinds of Crystals and Quasicrystals. Journal of Elasticity 48, 241–283 (1997). https://doi.org/10.1023/A:1007426414686

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