A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation

Abstract

A strain-space formulation of elastoplasticity at finite strains is developed based on a multiplicative decomposition of the deformation gradient. The notion of covariance—which embodies material frame indifference as a particular case—is systematically exploited to uniquely determine reduced forms of the free energy and yield condition that do not preclude anisotropic response. It is shown that the structure of the associative flow rule is uniquely defined as the Kuhn-Tucker optimality condition emanating from the principle of maximum plastic dissipation. Specialization is made to deviatoric plasticity. The isochoric constraint is treated through the exact multiplicative decomposition of the deformation gradient into volume-preserving and spherical parts. As an application, a hyperelastic extension of J 2- flow theory is presented with poly-convex hyperelastic uncoupled stored energy function. Computational aspects and large-scale simulations are examined in Part II of this work.