Lipschitz regularization for fracture: the Lip-field approach

TL;DR

This paper introduces a two-dimensional Lipschitz regularization method for elasto-damage models in fracture mechanics, improving damage field regularity without gradient dependence, demonstrated through numerical examples.

Contribution

It extends the Lip-field regularization approach to 2D elasto-damage models, providing a new finite element implementation and solution scheme.

Findings

Effective regularization of damage fields in 2D fracture models

Convex iterative scheme for displacement and damage fields

Numerical examples demonstrate improved damage modeling

Abstract

The Lip-field approach is a new regularization method for softening material material models. It was presented first in a previous paper providing one-dimensional simulations for damage and plasticity. The present paper focuses on a two-dimensional implementation for elasto-damage models (quasi-brittle fracture). The incremental potential used in the Lip-field approach is the non-regularized one. The regularization comes from the addition of a Lipschitz constraint on the damage field. In other words, the free energy does not depend on the damage gradient. The search of the displacement and damage fields from one time-step to the next is based on an iterative staggered scheme. The displacement field is sought for a given damage field. Then, a Lipschitz continuous damage field is sought for a given displacement field. Both problems are convex. The solution to the latter benefits from bounds proven in a previous paper and used here. The paper details the implementation of the Lipschitz regularity on a finite element mesh and details the overall solution scheme. Four numerical examples demonstrate the capability of the new approach.