Variational formulations, convergence and stability properties in nonlocal elastoplasticity

Abstract

A thermodynamically consistent formulation of nonlocal plasticity in the framework of the internal variable theories of inelastic behaviors of associative type is presented. A family of mixed variational formulations, with different combinations of state variables, is provided starting from the finite-step nonlocal elastoplastic structural problem. It is shown that a suitable minimum principles provides a rational basis to exploit the iterative elastic predictor-plastic corrector algorithm in terms of the dissipation functional. A sufficient condition is proved for the convergence of the iterative elastic predictor-plastic corrector algorithm based on a suitable choice of the elastic operator in the prediction phase and a necessary and sufficient condition for the existence of a unique solution (if any) of the nonlocal problem at hand is then provided. The nonlinear stability analysis of the nonlocal problem is carried out following the concept of nonexpansivity proposed in local plasticity.