An Alternative Framework for Developing Material Models for Finite-Strain Elastoplasticity

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.