Return mapping for nonsmooth and multiscale elastoplasticity

We present a semi-implicit return mapping algorithm for integrating generic nonsmooth elastoplastic models. The semi-implicit nature of the algorithm stems from “freezing” the plastic internal variables at their previous state, followed by implicitly integrating the stresses and plastic multiplier. The plastic internal variables are incrementally updated once convergence is achieved (a posteriori  ). Locally, the algorithm behaves as a classic return mapping for perfect plasticity and, hence, inherits the stability of implicit integrators. However, it differs from purely implicit integrators by keeping the plastic internal variables locally constant. This feature affords the method the ability to integrate nonsmooth (C0)(C0) evolution laws that may not be integrable using implicit methods. As a result, we propose and use the algorithm as the backbone of a semi-concurrent multiscale framework, in which nonsmooth constitutive relationships can be directly extracted from the underlying micromechanical processes and faithfully incorporated into elastoplastic continuum models. Though accuracy of the proposed algorithm is step size-dependent, its simplicity and its remarkable ability to handle nonsmooth relations make the method promising and computationally appealing.