arXiv subjects

Nicolas Moes

Publications and source records attributed to Nicolas Moes.

2 recordsLinked to original sources

arXiv2021

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↗