The Integrable Variant of the Theory of Slip

Abstract

The model of elastoplastic medium is based on the concept of slip proposed by Batdorf and Budiansky. The conditions of slip on a slip plane take into account "the local loading criterion". Under some assumptions we succeeded in integrating the plastic shears over all possible slip planes in case of arbitrary three-dimensional stress state and obtained an expression for the plastic strain tensor increments and the closed variant of the elastoplastic model, which turns out to be a variant of the plastic flow theory. The integration method proposed can be applied for establishing the links between local conditions and macroscopic equations, and for some other slip conditions too.