Anisotropic material behavior

Abstract

This entry is focused on description of material anisotropy in elastic and plastic ranges. Concise classification of anisotropic materials with respect to symmetry of elastic matrices as referred to the crystal lattice symmetry is given, and extended analogy between symmetries of constitutive material matrices (elastic and yield/failure) is also discussed. In this entry basic features of anisotropic initial yield criteria are discussed. Two ways to account for anisotropy are presented: the explicit vs. implicit formulations. The explicit description of anisotropy is rigorously based on well established theory of common invariants (Sayir, Goldenblat–Kopnov, von Mises, Hill). The implicit approach involves linear transformation tensor of the Cauchy stress that accounts for anisotropy to enhance the known isotropic criteria to be able to capture anisotropy, hydrostatic pressure insensitivity and asymmetry of the yield surface (Barlat, Plunckett, Cazacu, Khan). The advantages and differences of both formulations are critically presented.