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. This, in turn, leads to erroneous solutions. We illustrate how the introduction of a discretization produces mesh-induced anisotropy and mesh-induced toughness for problems involving brittle fracture. Subsequently, we quantify those effects through polar plots of the path deviation ratio for commonly adopted meshes. Finally, we propose to reduce those effects through a new type of mesh, which we term conjugate-directions mesh.