{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/lipschitz-regularization-for-fracture-the-lip","title":"Lipschitz regularization for fracture: the Lip-field approach","arxiv_id":"2111.04771","date":"2021-11-08","proceeding":null,"authors":["N. Chevaugeon","N. Moes"],"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.","url_abs":"https://arxiv.org/abs/2111.04771v2","url_pdf":"https://arxiv.org/pdf/2111.04771v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"lipschitz-regularization-for-fracture-the-lip","repo_url":"https://gitlab.com/c4506/lipfield","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}