On the variational modeling of non-associative plasticity

Abstract In this work, the energetic formulation for rate-independent dissipative materials is extended to consider non-associative plasticity models. In associative models, the fulfilment of the principle of maximum dissipation naturally leads to a variational formulation of the evolution problem. This is no longer true for non-associative models, which are generally presented in the literature in a non-variational form. However, recent studies have unveiled the possibility to recover a variational structure in non-associative plasticity by relying on a suitable state-dependent dissipation potential. Here, this idea is further elaborated in the framework of the energetic formulation, providing a systematic variational approach to non-associative plasticity. A clear link between the classical governing equations of non-associative plasticity and the energetic formulation is established, for which a state-dependent dissipation potential is derived from a generalization of the principle of maximum dissipation. The proposed methodology is then applied to recast specific non-associative plasticity models in variational form, highlighting the flexibility of the formulation. The examples include a Drucker-Prager model with combined isotropic-kinematic hardening and a ratcheting plasticity model. Several thermomechanical insights are provided for both examples. Moreover, exploiting the flexibility of the energetic formulation, extensions to gradient plasticity are devised, leading to representative finite element simulations.