Lipschitz regularization for fracture: the Lip-field approach

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.