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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2022

Lipschitz regularization for fracture: The Lip-field approach

Résumé

The Lip-field approach is a new regularization method for softening material models. It was presented first in [Moës, Chevaugeon 2021], providing onedimensional 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 nonregularized 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 [Moës, Chevaugeon 2021] and used in the present paper. The implementation of the Lipschitz regularity constraint on a finite element mesh and details of the overall solution scheme are presented. Four numerical examples demonstrate the capability of the new approach.
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Dates et versions

hal-03927211 , version 1 (06-01-2023)

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Nicolas Chevaugeon, Nicolas Moes. Lipschitz regularization for fracture: The Lip-field approach. Computer Methods in Applied Mechanics and Engineering, 2022, 402, pp.115644. ⟨10.1016/j.cma.2022.115644⟩. ⟨hal-03927211⟩
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