Remeshing techniques for r-adaptive and combined h/r-adaptive analysis with application to 2D/3D crack propagation

Remeshing strategies are formulated for r-adaptive and h/r-adaptive analysis of crack propagation. The relocation of the nodes, which typifies r-adaptivity, is a very cheap method to optimize a given discretisation since the element connectivity remains unaltered. However, the applicability is limited. To further improve the finite element mesh, a combined h/r-adaptive method is proposed in which h-adaptivity is applied whenever r-adaptivity is not capable of further improving the discretisation. Two and threedimensional examples are presented. It is shown that the r-adaptive approach can optimize a discretisation at minimal computational costs. Further, the combined h/r-adaptive approach improves the performance of a fully r-adaptive technique while the computational costs are lower than that of a fully h-adaptive approach. Thus, the combined h/r-adaptive method combines the advantages of r-adaptivity and h-adaptivity.