Generalized Inelasticity

Abstract

The two-term multiplicative decomposition of the deformation gradient used in Chapter 6 does not explicitly account for residual deformation of the lattice, or in other words, does not account for irreversible deformations that are not lattice-preserving. Recall from Section 3.2 that the lattice- preserving part of the deformation gradient is attributed to plasticity from crystal dislocations, specifically dislocation glide and relative shearing of crystallographic planes in increments of the Burgers vector for slip. Residual deformations that are not explicitly addressed in the definition of plastic deformation used in this text may emerge from the following physical mechanisms: residual elastic deformation and residual volume changes associated with self-equilibrated stress fields of defects (Section 3.2.9 and Chapter 7), lattice rotations and reflections associated with twinning (Chapter 8), volumetric deformation associated with voids and point defects (Sections 3.2.8 and 7.4), and anisotropic damage mechanisms such as ductile or brittle fracture and material rupture. When treated distinctly from mechanically reversible elastic deformation as in the non-standard model of thermoelasticity of Section 5.5, deformation associated with thermal strains can also be categorized as a residual deformation mode distinct from plastic deformation.