Large deformation plasticity and the Poynting effect

The aims of this paper are fourfold: (1) To develop a set of constitutive equations that are applicable to isotropic inelastic materials with large elastic and plastic strains using the multiconfigurational framework (Rajagopal, K.R., Srinivasa, A.R. Int. J. Plasticity 14 (1998) 945; Rajagopal, K.R., Srinivasa, A.R. Int. J. Plasticity 14 (1998), 948), in such a way as to generalize the central ideas (such as isotropy, constant elastic modulii, quadratic yield surfaces and non-hardening behavior) of the Prandtl–Reuss theory to finite deformations, (2) to examine the consequences of using a physically plausible criterion of maximum rate of mechanical dissipation, (3) to examine the relationship of the resulting models to the classical Prandtl–Reuss theory as well as other possible formulations (specifically those that rely on the use of a maximum plastic work postulate), and (4) to consider the effect of finite elastic strains on the response of the material subject to some simple homogenous deformations. By considering the response under simple shear, it is shown that the elastic-plastic counterpart of the well known Poynting effect in finite elasticity has a profound influence on the post-yield behavior of such materials. In particular, it is shown that this gives rise to a strain softening effect even though the overall response is that of a non-hardening material.