Basic concepts

In this chapter we describe the basic concepts associated with crystal symmetry, crystal elasticity, crystal plasticity, and continuum mechanics (kinematics) used throughout the book. Basic constitutive laws such as linear elasticity, linear viscosity, and viscoplasticity are introduced, with an emphasis on anisotropy, which gives the tensorial character to such laws. Basic concepts concerning the treatment of tensors, texture representation, and plastic yield surface of single crystals are presented. We describe the fundamental concepts associated with stress and strain, accounting for heterogeneity and anisotropy, and the corresponding equations that determine the mechanical behavior of deformable solids, in particular polycrystalline materials: constitutive equations that provide a relation between local or overall stress and strain, and governing equations that provide the conditions that stress and strain fields obey in a deformed solid.