Constitutive Equations for Anisotropic and Isotropic Materials

Abstract

Part 1 Basic concepts: transformation properties of tensors description of material symmetry restrictions due to material symmetry constitutive equations. Part 2 Group representation theory: elements of group theory group representations Schur's Lemma and orthogonality properties group characters continuous groups. Part 3 Elements of invariant theory: some fundamental theorems. Part 4 Invariant tensors: decomposition of property tensors frames, standard tableaux and young symmetry operators the inner product of property tensors and physical tensors symmetry class of products of physical tensors symmetry types of complete sets of property tensors examples. Part 5 Group averaging methods: averaging procedure for scalar-valued functions decomposition of physical tensors averaging procedures for tensor-valued functions examples generation of property tensors. Part 6 Anisotropic constitutive equations and Schur's Lemma: application of Schur's Lemma - finite groups the crystal class D[3] product tables. Part 7 Generation of integrity bases - the crystallographic groups: reduction to standard form integrity bases for the triclinic, monoclinic, rhombic, tetragonal and hexagonal crystal classes generation of product tables. Part 8 Generation of integrity bases - continuous groups: identities relating 3 x 3 matrices generation of the multilinear elements of an integrity basis transversely isotropic functions. Part 9 Generation of integrity bases - the cubic crystallographic groups: introduction - tetartoidal class, T, 23 gyrodial class, 0, 432. Part 10 Irreducible polynomial constitutive expressions: generating functions irreducible expressions - the crystallographic groups. (Part Contents).