Lipschitz regularization for softening material models: the Lip-field approach

TL;DR

This paper introduces a Lipschitz regularization method called Lip-field to prevent spurious localization in softening material models, adding a length scale to improve numerical stability and solution accuracy.

Contribution

The paper proposes a novel Lipschitz regularization approach for softening models, providing theoretical bounds and a finite element implementation to mitigate localization issues.

Findings

Reduces mesh dependency in softening models

Enforces a length scale via Lipschitz regularization

Demonstrates effectiveness in 1D finite element simulations

Abstract

Softening material models are known to trigger spurious localizations.This may be shown theoretically by the existence of solutions with zero dissipation when localization occurs and numerically with spurious mesh dependency and localization in a single layer of elements. We introduce in this paper a new way to avoid spurious localization. The idea is to enforce a Lipschitz regularity on the internal variables responsible for the material softening. The regularity constraint introduces the needed length scale in the material formulation. Moreover, we prove bounds on the domain affected by this constraint. A first one-dimensional finite element implementation is proposed for softening elasticity and softening plasticity.