2002•The Quarterly Journal of Mechanics and Applied MathematicsRequires access

Invariants and Structural Invariants of the Anisotropic Elasticity Tensor

Faiz Ahmad

Abstract

We study invariants of the anisotropic elasticity tensor. The invariants are obtained by defining certain tensors of order two associated with the elasticity tensor. We find four second‐order invariants with respect to arbitrary orthogonal transformations. This increases by two the number of already known such invariants. When the transformation is confined to rotations about the x3‐axis, the number of second‐order invariants becomes seventeen, again an increase by two in the already known number. We describe a method for ascertaining linear independence of these invariants. We also recover structural invariants of Ting and find a few new structural invariants.

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Key concepts: Invariants of tensors, Elasticity (physics), Mathematics, Tensor (intrinsic definition), Anisotropy, Pure mathematics, Symmetric tensor, Transformation (genetics)