Constitutive Equations for Anisotropic and Isotropic Materials

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).