Meshing strategies for the alleviation of mesh-induced effects in cohesive element models

One of the main approaches for modeling fracture and crack propagation in solid materials is adaptive insertion of cohesive elements, in which line-like (2D) or surface-like (3D) elements are inserted into the finite element mesh to model the nucleation and propagation of failure surfaces. In this approach, however, cracks are forced to propagate along element boundaries, following paths that in general require more energy per unit crack extension (greater driving forces) than those followed in the original continuum, which in turn leads to erroneous solutions. In this work we illustrate how the introduction of a discretization produces two undesired effects, which we term mesh-induced anisotropy and mesh-induced toughness. Subsequently, we analyze those effects through polar plots of the path deviation ratio (a measure of the ability of a mesh to represent straight lines) for commonly adopted meshes. Finally, we propose to reduce those effects through K-means meshes and through a new type of mesh, which we term conjugate-directions mesh. The behavior of all meshes under consideration as the mesh size is reduced is analyzed through a numerical study of convergence.