observed that crack paths obtained from pinwheel meshes are more stable as the meshes are refined compared to other types of meshes. The work of Radin and Sadun shows that the pinwheel tiling of the plane has the isoperimetric property. A mesh that satisfies these requirements is said to be isoperimetric. It is desirable, then, for the path deviation ratio to be independent on the segment direction (to avoid mesh-induced anisotropy) and to tend to one as the mesh size tends to zero (to avoid, in the limit, mesh-induced toughness). In 2-dimensional problems, the ability of a mesh to represent a straight segment is characterized by the path deviation ratio, defined as the ratio between the shortest path on the mesh edges connecting two nodes, and the Euclidian distance between them (see Fig. If we think of an arbitrary crack as a rectifiable path (2D) or surface (3D), the ability of a mesh to represent a straight line (2D) or plane (3D) as the mesh is refined is a necessary condition for the convergence of the cohesive element approach. When a mesh is introduced to represent the continuum fracture problem within the cohesive element formulation, a constraint is introduced into the problem due to the inability of the mesh to represent the shape of an arbitrary crack. However, the problem of mesh dependency, more precisely mesh-induced anisotropy and mesh-induced toughness, is an active area of research. However, the robustness of the method makes it one of the most common approaches for pervasive fracture and fragmentation analysis.Īrtificial compliance and lift-off effects can be avoided by using an initially rigid cohesive law or, more elegantly, a discontinuous Galerkin formulation with an activation criterion for cohesive elements. Even though this approach is well suited for problems involving pre-defined crack directions, a number of known issues affect its accuracy when dealing with simulations including arbitrary crack paths, e.g., problems with the propagation of elastic stress waves (artificial compliance), spurious crack tip speed effects (lift-off), and mesh dependent effects (c.f. On the other hand, the cohesive element approach consists on the insertion of cohesive finite elements along the edges or faces of the 2D or 3D mesh correspondingly. While the X-FEM approach can deal with arbitrary crack paths, it becomes increasingly complicated for problems involving pervasive fracture and fragmentation. Subsequently, the method was extended to account for cohesive cracks. first utilized the X-FEM for modeling 3D crack growth by adding a discontinuous function and the asymptotic crack tip field to the finite elements. Some of the mainstream technologies proposed to introduce the cohesive theory of fracture into finite element analysis are the eXtended Finite Element Method (X-FEM) and cohesive elements.
Cohesive zone models are widely adopted by scientists and engineers perhaps due to their straightforward implementation within the traditional finite element framework. In their work, fracture is regarded as a progressive phenomenon in which separation takes place across a cohesive zone ahead of the crack tip and is resisted by cohesive tractions.
The classical cohesive zone theory of fracture finds its origins in the pioneering works by Dugdale, Barenblatt and Rice.