Contemporary plasticity theories and their related material models for finite deformations are either based on additive decomposition of a strain-rate tensor or on multiplicative decomposition of a deformation gradient tensor into an elastic part and a plastic part. From the standpoint of the nonlinear continuum mechanics, the former theories, which are used to model hypoelastic-plastic materials, are rather incomplete theories, while the latter theories, which are used to model hyperelastic-plastic materials, are not even continuum-based theories, while none of their related material models are thermodynamically consistent. Recently, a nonlinear continuum theory for finite deformations of elastoplastic media was proposed, which allows for the development of objective and thermodynamically consistent material models. Therefore, the analysis results of the models are independent of the description and the particularities of their mathematical formulation. Here by the description we mean total or updated Lagrangian description and by the particularities of formulation, the ability to describe the model in various stress spaces using internal mechanical power conjugate stress measures and strain rates. In this chapter, an alternative framework for developing objective and thermodynamically consistent hypoelastic-plastic-and hyperelastic-plastic-based material models is presented using the first nonlinear continuum theory of finite deformations of elastoplastic media. Keywords: nonlinear continuum theory for finite deformations of elastoplastic media, objective and thermodynamically consistent formulation, J 2 generalised plasticity with isotropic hardening, hypoelastic-plastic-and hyperelasticplastic-based material models with internal damping

Contemporary multiplicative plasticity models are now generally accepted as “proper material models” for modelling plastic behaviour of deformable bodies within the framework of finite-strain elastoplasticity. The models are based on the assumptions that the intermediate configuration of the body is stress-free or locally unstressed, for which no plastic deformation exists that meets the conditions of compatibility. The assumption; however, has never really been questioned nor justified, but was rather taken as an axiom and therefore considered to be generally true. In this study, we take a critical look at the assumption from both, physical and mathematical points of view, in order to investigate whether contemporary multiplicative plasticity models are indeed continuum based and if there are alternatives to them.

At present multiplicative plasticity theories are used to model material degradation of hyperelastic materials within the framework of finite-strain elastoplasticity. The theories assume that the intermediate configuration of the body is unstressed and that such multiaxially stretched bodies do not have compatible unstressed configurations. As a result, there does not exist a motion whose material gradient could define the plastic deformation gradient. The assumption is however not consistent with the theory of nonlinear continuum mechanics and the related theories are not continuum based. In this paper material degradation of a silicone cross-shaped specimen in biaxial tension is studied using a thermodynamically consistent Mooney-Rivlin material model. The material model is based on the first nonlinear continuum theory of finite deformations of elastoplastic media which allows for the development of objective and thermodynamically consistent material models within the framework of finite-strain elastoplasticity. Such material models are independent of the model description and the particularities of the model formulation and moreover they can relate the internal power density of the model to the internal power density of the specimen coming from the tensile test of the modelled material. In this paper a few analysis results are presented and briefly discussed.