Stress-driven solution to rate-independent elasto-plasticity with damage at small strains and its computer implementation

TL;DR

This paper develops a stress-driven numerical scheme for rate-independent elasto-plasticity with damage at small strains, ensuring convergence and stability, and demonstrates its effectiveness through finite-element simulations.

Contribution

It introduces a fractional-step discretization method that converges to physically relevant stress-driven solutions in damage and plasticity models, with proven stability and computational implementation.

Findings

Scheme converges to physically relevant solutions

Finite-element implementation demonstrated with 2D simulations

Ensures numerical stability and convergence within weak solutions

Abstract

The quasistatic rate-independent damage combined with linearized plasticity with hardening at small strains is investigated. The fractional-step time discretisation is devised with the purpose to obtain a numerically efficient scheme converging possibly to a physically relevant stress-driven solutions, which however is to be verified a-posteriori by using a suitable integrated variant of the maximum-dissipation principle. Gradient theories both for damage and for plasticity are considered to make the scheme numerically stable with guaranteed convergence within the class of weak solutions. After finite-element approximation, this scheme is computationally implemented and illustrative 2-dimensional simulations are performed.