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

Abstract

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 meshinduced 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.

The Thick Level-Set model for dynamic fragmentation

“…While the cohesive approach has been used to successfully represent crack initiation, extension, branching, and coalescence in a variety of problems, it suffers from mesh sensitivity because the crack path is limited to element boundaries. This may result in a lack of spatial convergence between an ideal crack path and its discrete representation, increasing the energy required to open the crack and limiting the model's accuracy [37,40]. Consequently, the crack path may be influenced by the existence of energetically-favorable extension directions [40].…”

“…This may result in a lack of spatial convergence between an ideal crack path and its discrete representation, increasing the energy required to open the crack and limiting the model's accuracy [37,40]. Consequently, the crack path may be influenced by the existence of energetically-favorable extension directions [40].…”

Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

“…Note that a 4k structured mesh consists of sets of four isosceles right triangles within a rectangular domain. Rimoli and Rojas addressed bias in 4k structured meshes and proposed a strategy to alleviate mesh dependence using barycentric subdivision with k ‐means meshes, named as a conjugate‐directions mesh. Alternatively, polygonal elements were utilized to solve dynamic fracture problems .…”

Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements

“…Recently, nodal perturbation and edge‐swap operators have been proposed to unstructure the geometry and topology of the 4k mesh, respectively, and to reduce the error in crack path convergence . These operators significantly reduce the error in the crack path; however, the mesh still introduces unwarranted anisotropies into the problem domain .…”

“…The unstructured, conjugate‐directions mesh is presented by Rimoli and coworkers . They use a barycentric subdivision of the k‐means mesh to construct a new mesh that has the same isotropic property of the k‐means mesh, but has more potential crack directions.…”