A formulation of finite elastoplasticity based on dual co- and contra-variant eigenvector triads normalized with respect to a plastic metric Original Research Article

The article presents a new formulation of isotropic elastoplasticity at large strains in both the Lagrangian and the Eulerian geometric setting and addresses aspects of its numerical implementation. The key ingredients on the theoretical side are the introduction of a plastic metric for the description of the local history-dependent inelastic material response, the definition of a convex elastic domain in the space of the local stress-like variable conjugate to the plastic metric, denoted as the plastic force, and a fully equivalent Lagrangian and Eulerian representation of all constitutive functions in spectral form for general non-Cartesian coordinate charts in terms of dual co- and contra-variant eigenvector triads which are normalized with respect to the plastic metric. On the numerical side, we propose a stress update algorithm for general non-associative isotropic elasto(visco)plastic response with an arbitrary number of scalar internal variables. The algorithm is based on an exponential map integrator and is recast into a general return mapping scheme, methodically organized with tensorial pre- and postprocessing and a constitutive box in the eigenvalue space. Furthermore, we propose a new perturbation stabilization technique which dramatically enhances the convergence of the general return algorithm. The theoretical and numerical developments are applied to a constitutive model problem with large elastic and large plastic strains: the von Mises-/Tresca-type associative plastic flow in Ogden-type large-strain elastic materials.