Remeshing strategies for adaptive ALE analysis of strain localisation

Computational analyses of strain localisation must be carried out in a proper, accurate, and efficient manner. While a continuum material model with an intrinsic length scale parameter can guarantee mesh-objective results, the ratio between accuracy and efficiency can be improved through the application of mesh adaptivity. In this paper, the Arbitrary Lagrangian Eulerian (ALE) technique is applied to strain localisation phenomena. Nodes are detached from the material, so that they can be used optimally in the spatial discretisation. A new remesh indicator is proposed that concentrates nodes in inelastic zones as well as in zones where strain localisation is likely to occur. Thus, the formation of new cracks is anticipated, which is crucial for accurate remeshing. Two algorithms have been tested and compared to equidistribute this remesh indicator. The algorithms give similar results, but the parabolic formulation can be solved explicitly. Multi-dimensional examples are presented. The proposed strategies are able to capture complicated crack patterns with multiple curved cracks. Two and three-dimensional examples illustrate this.