  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.
