Invariance Considerations in Large Strain Elasto-Plasticity

Abstract

This paper addresses a number of issues in the ongoing debate over the relevance and/or appropriateness of the rotational invariance requirement which is generally associated with the intermediate unstressed configuration. In particular, it is argued that the principle of material frame invariance has been “misapplied” by the proponents of full rotational invariance. Insistence on a strictly “kinematic” interpretation of the deformation gradient (F = FeFp) constituents Fe and Fp justifies elimination of the plastic rotational component Rp(Fp = RpUp) based on the principle of determinism for stress — not invariance of frame. However, simple physical considerations, including a physical example involving a “structurally anisotropic” crystal, suggest that a more intricate definition of the gradient constituents is required in order to adequately account for microstructural characteristics. These considerations suggest alternative definitions for the gradient constituents Fe and Fp with associated constitutive invariance requirements.