Large deformation plasticity and the Poynting effect

The aims of this paper are fourfold: (1) To develop a set of constitutive e quations that are applicable to isotropic inelastic materials with large el astic and plastic strains using the muiticonfigurational framework (Rajagop al, K.R., Srinivasa, A.R. Int. J. Plasticity 14 (1998) 945; Rajagopal, K.R. , Srinivasa, A.R. fm. J. Plasticity 14 (1998), 948), in such a way as to ge neralize the central ideas (such as isotropy, constant elastic modulii, qua dratic yield surfaces and non-hardening behavior) of the Prandtl-Reuss theo ry to finite deformations, (2) to examine the consequences of using a physi cally 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 tha t rely on the use of a maximum plastic work postulate), and (4) to consider the effect or finite elastic strains on the response of the material subje ct to some simple homogenous deformations. By considering the response unde r simple shear, it is shown that the elastic-plastic counterpart of the wel l known Poynting effect in finite elasticity has a profound influence on th e post-yield behavior of such materials, In particular, it is shown that th is gives rise to a strain softening effect even though the overall response is that of a non-hardening material. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.