Étude de la stabilité d’une formulation incompressible traitée par X-FEM

Author (s): Legrain, G., Moes, N. and Huerta, A.
Journal: European Journal of Computational Mechanics (Revue Européenne de Mécanique Numérique)

Volume: 15, Issues 1, 2, 3
Pages: 257 – 268
Date: 2006

The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic flows occurs as in forming processes. The use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the inf-sup or LBB condition. Recently, the finite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (X-FEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements. In this paper, some strategies are proposed for the enrichment of low order mixed finite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the finite element convergence rate is preserved and the inf-sup condition is passed.



author = {Legrain, G.; Moës, N. and Huerta, A.},
title = {Etude de la stabilité d’une formulation incompressible traitée par X-FEM},
journal = {European Journal of Computational Mechanics},
volume = {15},
number = {1-3},
pages = {257-268},
year = {2006},
doi = {10.3166/remn.15.257-268},
URL = {http://www.tandfonline.com/doi/abs/10.3166/remn.15.257-268},
eprint = {http://www.tandfonline.com/doi/pdf/10.3166/remn.15.257-268}