Discrete shear transformation zone plasticity

A method for solving small strain plasticity problems with plastic deformation arising from the evolution of a collection of discrete shear transformation zones (STZs) is presented. The STZs are represented as transforming Eshelby inclusions. At each instant, superposition is used to represent the solution in terms of the Eshelby inclusions, which are given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions on the finite solid of interest. The image problem corresponds to a standard linear elastic boundary value problem. Constitutive relations are specified for the kinetics of the transformation. The general three dimensional formulation is given. Solutions for compression of a plane strain block are presented that illustrate the potential of the framework.