  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.
