A micropolar isotropic plasticity formulation for non associated flow rule and softening featuring multiple classical yield criteria. Part II -- FE integration and applications

TL;DR

This paper presents an efficient finite element integration scheme for a micropolar plasticity model with multiple yield criteria, demonstrating improved numerical stability and applicability to complex geotechnical problems.

Contribution

It introduces a simplified implicit FE integration method for Cosserat continuum plasticity that handles singularities and coincident principal stresses effectively.

Findings

Efficient single-equation solution for stress integration.

Enhanced handling of yield surface singularities.

Improved modeling of softening and non-associated flow behaviors.

Abstract

A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral decomposition of the former, considerable benefits are achieved. The integration requires the solution of a single equation in a single unknown, which is a considerable improvement as compared to the system of seven or four equations required by other approaches available in the literature for the Cauchy medium. The scheme also allows for a very efficient treatment of the singularity which affects the apex of most of the existing yield and plastic potential surfaces. Moreover, no complications arise when some of the principal stresses coincide. The algorithm has been implemented in a proprietary Finite Element program, and used for the constitutive model proposed in part I of this paper. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr-Coulomb, Matsuoka-Nakai and Lade-Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non-associated flow and softening behaviour.