# Lipschitz regularization for fracture: the Lip-field approach

arXiv: https://arxiv.org/abs/2111.04771 · HTML: https://mlsanity.com/paper/2111.04771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2021.

## Built on by (most cited first, 1 of 1)

- [Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance](https://mlsanity.com/paper/2303.03918/) (2023)

## Abstract (arXiv)

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.