A Comprehensive Mathematical Formulation of an Extended Taylor–Bishop–Hill Model Featuring Relaxed Constraints, the Renouard–Wintenberger Theory and a Strain Rate Sensitivity Model

Abstract

The Taylor theory and the BishopHill theory for the plastic deformation of polycrystals are expressed in a mathematical way which makes extensive use of vectors. These vectors represent either plastic strain rate tensors or deviatoric stress tensors, both in a unified five-dimensional stress-strain space. Such formulation permits a unified formulation of both theories, which can then easily be solved by means of linear programming. The computer implementation of this formalism (in Pascal) conserves this mathematical formalism to a high extent.