Steiner-point free edge cutting of tetrahedral meshes with applications in fracture

Realistic 3D finite strain analysis and crack propagation with tetrahedral meshes require mesh refinement/division. In this work, we use edges to drive the division process. Mesh refinement and mesh cutting are edge-based. This approach circumvents the variable mapping procedure adopted with classical mesh adaptation algorithms. The present algorithm makes use of specific problem data (either level sets, damage variables or edge deformation) to perform the division. It is shown that global node numbers can be used to avoid the Schönhardt prisms. We therefore introduce a nodal numbering that maximizes the trapezoid quality created by each mid-edge node. As a by-product, the requirement of determination of the crack path using a crack path criterion is not required. To assess the robustness and accuracy of this algorithm, we propose 4 benchmarks. In the knee-lever example, crack slanting occurs as part of the solution. The corresponding Fortran 2003 source code is provided.