A multiscale extended finite element method for crack propagation

By Pierre-Alain Guidault, Olivier Allix, L. Champaney, C. Cornuault. 2008

145 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/815a63bd6b39cf013de58122154a62ca51d70fc9

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In Mechanics of Materials

Citations in the corpus

A simple method for crack growth in mixed mode with X-FEM (2012, methodology): “Same results are found by Guidault et al. (2008) with increments of 0.1.”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, methodology): “[84] based on the LATIN method and domain decomposition concepts, the method of Pierres et al.”
A PGD-based homogenization technique for the resolution of nonlinear multiscale problems (2013, methodology): “3 for a macrobasis which extracts the linear part; other choices can be found in [51].”
Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “It has also been reported in the literature that substructuring may lead to ill-conditione d systems when the difference in element sizes in the global and local meshes is large [ 36 ].”
Bridging multiple structural scales with a generalized finite element method (2015, methodology): “[27], and the multigrid method proposed in [28]; the method of Fish et al.”
A two-scale approach for the analysis of propagating three-dimensional fractures (2012, methodology): “[26] based on the LATIN method and domain decomposition concepts; the method of Pierres et al.”
Local enrichment of the finite cell method for problems with material interfaces (2013, background): “simulation of evolving discontinuities such as crack propagation [6–8], two-phase fluids [9,10], or fluid-structure interactions [11,12].”
A two‐scale approximation of the Schur complement and its use for non‐intrusive coupling (2011, methodology): “For that reason, we also investigated long-scale approximations, most of which are inspired from multiscale homogenization techniques; that is, to prescribe a small number of interface loads on the whole subdomain, representing their ‘large-scale’ behaviour [12, 13, 17, 19, 20].”