Solving primal plasticity increment problems in the time of a single predictor-corrector iteration

TL;DR

The paper demonstrates that the TNNMG method efficiently solves primal elastoplasticity problems, outperforming classical predictor-corrector methods, and can handle nonsmooth yield functions without relying on differentiability.

Contribution

It introduces applying the TNNMG method to primal elastoplasticity problems, proving convergence and showing superior computational efficiency over traditional methods.

Findings

TNNMG is faster than classical predictor-corrector methods.

The method handles nonsmooth yield functions like Tresca.

Solving an entire increment is faster than a single predictor-corrector iteration.

Abstract

The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a well-established method for the solution of strictly convex block-separably nondifferentiable minimization problems. It achieves multigrid-like performance even for non-smooth nonlinear problems, while at the same time being globally convergent and without employing penalty parameters. We show that the algorithm can be applied to the primal problem of classical linear elastoplasticity with hardening. Numerical experiments show that the method is considerably faster than classical predictor-corrector methods. Indeed, solving an entire increment problem with TNNMG takes less time than a single predictor-corrector iteration for the same problem. Since the algorithm does not rely on differentiability of the objective functional, nonsmooth yield functions like the Tresca yield function can be easily incorporated. The method is closely related to a predictor-corrector scheme with a consistent tangent predictor and line search. We explain the algorithm, prove global convergence, and show its efficiency using a standard benchmark from the literature.