arXiv subjects

Nicolas Chevaugeon

Publications and source records attributed to Nicolas Chevaugeon.

5 recordsLinked to original sources

arXiv2026

Dynamic brittle fracture using Lip-field approach in an explicit dynamics context

This paper aims to investigate the dynamic response of a material body undergoing fracture subjected to high strain rate loading conditions such as impact or explosion. In particular, our focus is limited to softening elastic damage models using Lip-field regularization. The Lip-field approach is a new technique to introduce length scale into the softening damage models. It was first presented for the quasi-static case and then extended to a one-dimensional dynamic case. This paper extends the application of the Lip-field approach to dynamic fracture in two-dimensional cases. Lip-field approach is a variational approach, in which the potential to be minimized is a non-regularized one. A potential without regularization can result in spurious strain localization, but the Lip-field approach resolves this issue by imposing Lipschitz constraints on the damage field. Our focus is limited to utilizing an explicit staggered scheme to determine the displacement and damage fields. Numerical studies are conducted for two-dimensional cases to assess the dynamic behavior of the proposed model.

cs.CE↗

arXiv2025

Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study

We consider a one-dimensional fracture problem modelled using either the phase-field or lip-field approach. In both cases, we optimise the incremental potential with respect to the displacement and damage fields and the nodal coordinates of the mesh. This is thus a variational mesh study. We observe that, as the damage reaches its maximum value, the optimisation drives the most damaged element to zero size as the damage reaches its maximum value. This peculiar element provides a precise displacement jump representation as the bar breaks. The overall solution is also shown to be much more accurate than the fixed mesh solution. This work forms part of an exploration into the capabilities of extreme meshes in computational mechanics (X-Mesh).

cs.CE↗

arXiv2023

Variational Approach to Viscoelastic Fracture : Comparison of a phase-field and of a lip-field approach

Fracture of viscoelastic materials is considered to be a complex phenomenon due to their highly rate sensitive behavior. In this context, we are interested in the quasi-static response of a viscoelastic solid subjected to damage. This paper outlines a new incremental variational based approach and its computational implementation to model damage in viscoelastic solids. The variational formalism allows us to embed the local constitutive equations into a global incremental potential, the minimization of which provides the solution to the mechanical problem. Softening damage models in their local form are known to result in spurious mesh-sensitive results, and hence non-locality (or regularization) has to be introduced to preserve the mathematical relevance of the problem. In the present paper, we consider two different regularization techniques for the viscoelastic damage model : a particular phase-field and a lip-field approach. The model parameters are calibrated to obtain some equivalence between both these approaches. Numerical results are then presented for the bidimensional case and both these approaches compare well. Numerical results also demonstrate the ability of the model to qualitatively represent the typical rate-dependent behaviour of the viscoelastic materials. Besides, the novelty of the present work lies in the use of lip-field approach for the first time in a viscoelastic context.

cs.CE↗

arXiv2023

The eXtreme Mesh deformation approach (X-MESH) for the Stefan phase-change model

The eXtreme Mesh deformation approach (X-MESH) is a new paradigm to follow sharp interfaces without remeshing and without changing the mesh topology. Even though the mesh does not change its topology, it can follow interfaces that do change their topology (nucleation, coalescence, splitting). To make this possible, the key X-MESH idea is to allow elements to reach zero measure. This permits interface relaying between nodes as well as interface annihilation and seeding in a time continuous manner. The paper targets the Stefan phase change model in which the interface (front) is at a given temperature. Several examples demonstrate the capability of the approach.

cs.CE↗

arXiv2021

Lipschitz regularization for softening material models: the Lip-field approach

Softening material models are known to trigger spurious localizations.This may be shown theoretically by the existence of solutions with zero dissipation when localization occurs and numerically with spurious mesh dependency and localization in a single layer of elements. We introduce in this paper a new way to avoid spurious localization. The idea is to enforce a Lipschitz regularity on the internal variables responsible for the material softening. The regularity constraint introduces the needed length scale in the material formulation. Moreover, we prove bounds on the domain affected by this constraint. A first one-dimensional finite element implementation is proposed for softening elasticity and softening plasticity.

cs.CE↗