SIMULATION OF STRAIN LOCALIZATION: A REAPPRAISAL OF THE COSSERAT CONTINUUM

TLDR

Classical continuum models lacking an internal length scale exhibit mesh‑dependent strain‑softening behavior, leading to pathological results in failure analyses. The study regularizes the governing field equations by incorporating rotational degrees of freedom alongside conventional translational ones. An elasto‑plastic Cosserat continuum model is developed, featuring an efficient integration algorithm and consistent tangent operator. The model yields mesh‑independent load‑deflection curves with a finite localization zone width, as shown in an infinitely long shear layer and a biaxial test of a strain‑softening elasto‑plastic von Mises material.

Abstract

Classical continuum models, i.e. continuum models that do not incorporate an internal length scale, suffer from pathological mesh‐dependence when strain‐softening models are employed in failure analyses. In this contribution the governing field equations are regularized by adding rotational degrees‐of‐freedom to the conventional translational degrees‐of‐freedom. This so‐called elasto‐plastic Cosserat continuum model, for which an efficient and accurate integration algorithm and a consistent tangent operator are also derived in this contribution, warrants convergence of the load—deflection curve to a unique solution upon mesh refinement and a finite width of the localization zone. This is demonstrated for an infinitely long shear layer and a biaxial test of a strain‐softening elasto‐plastic von Mises material.