Stress Rate Formulation for Elastoplastic Models with Internal Variables Based on Augmented Lagrangian Regularisation

The constitutive laws of elasto-plasticity with internal variables are described through the de®nition of suitable dual potentials, which include various hardening models. A family of variational principles for inelastic problems is obtained using convex analysis tools. The structural problem is analysed using the complementary energy (Prager± Hodge) functional. The functional is regularised introducing an Augmented Lagrangian Regularisation for the indicator function of the elastic domain so that a smooth optimisation problem is obtained. In the numerical solution the discretised problem is reformulated in a ®nite step form using a fully implicit integration scheme and the functional is rede®ned in the space of the self-equilibrated nodal stresses, after enforcing satisfaction of the equilibrium equations in a weak form. Numerical tests have shown good performance on the part of the algorithm, which approaches the converged solution for a considerably smaller number of elements as compared with other algorithms. The method is equally available for perfect or hardening plasticity.