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

P. Areias, Timon Rabczuk

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

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
Volume132
DOIs
Publication statusPublished - 2017 Sep 15
Externally publishedYes

Fingerprint

Steiner Point
Tetrahedral Mesh
Division
Crack
Mesh Refinement
Cracks
Mesh Adaptation
Trapezium or trapezoid
Finite Strain
Path
Prism
Crack Propagation
Vertex of a graph
Prisms
Level Set
Byproducts
Crack propagation
Damage
Maximise
Mesh

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

Cite this

Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. / Areias, P.; Rabczuk, Timon.

In: Finite Elements in Analysis and Design, Vol. 132, 15.09.2017, p. 27-41.

Research output: Contribution to journalArticle

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