A FORMULATION OF FINITE ELASTOPLASTICITY BASED ON DUAL CO-VARIANT ANDCONTRA-VARIANT EIGENVECTOR TRIADS NORMALIZED WITH RESPECT TO A PLASTIC METRIC

The article presents a new formulation of isotropic elastoplasticity a t large strains in both the Lagrangian and the Eulerian geometric sett ing and addresses aspects of its numerical implementation. The key ing redients on the theoretical side are the introduction of a plastic met ric for the description of the local history-dependent inelastic mater ial response, the definition of a convex elastic domain in the space o f the local stress-like variable conjugate to the plastic metric, deno ted as the plastic force, and a fully equivalent Lagrangian and Euleri an representation of all constitutive functions in spectral form for g eneral non-Cartesian coordinate charts in terms of dual co- and contra -variant eigenvector triads which are normalized with respect to the p lastic metric. On the numerical side, we propose a stress update algor ithm for general non-associative isotropic elasto(visco)plastic respon se with an arbitrary number of scalar internal variables. The algorith m is based on an exponential map integrator and is recast into a gener al return mapping scheme, methodically organized with tensorial pre- a nd postprocessing and a constitutive box in the eigenvalue space. Furt hermore, we propose a new perturbation stabilization technique which d ramatically enhances the convergence of the general return algorithm. The theoretical and numerical developments are applied to a constituti ve model problem with large elastic and large plastic strains: the von Mises-/Tresca-type associative plastic flow in Ogden-type large-strai n elastic materials. (C) 1998 Elsevier Science S.A.