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

P. Areias, T. Rabczuk

Research output: Contribution to journalArticlepeer-review

136 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)27-41
Number of pages15
JournalFinite Elements in Analysis and Design
Publication statusPublished - 2017 Sept 15

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.


  • 3D edge-based division
  • 3D fracture
  • Local mesh refinement
  • Tetrahedral cutting

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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