Element-wise fracture algorithm based on rotation of edges

• Published in: Engineering fracture mechanics 2013-09, Vol.110, p.113-137
• Main Authors: Areias, P., Rabczuk, T., Dias-da-Costa, D.
• Format: Article
• Language: English
• Subjects: Algorithms; Criteria; Deflection; Discretization; Ductile materials; Edge rotations; Enrichment; Finite element method; Finite strains; Fracture; Fracture mechanics; Mathematical models; Quasi-brittle materials
• ISSN: 0013-7944; 1873-7315
• DOI: 10.1016/j.engfracmech.2013.06.006

•Finite strain computational fracture.•Edge-based algorithm.•Brittle, cohesive and ductile fracture (with post-localization cracks) with the same underlying method.•Extensive assessment performed.•Shell problems solved with success. We propose an alternative, simpler algorithm for FEM-based computational fracture in brittle, quasi-brittle and ductile materials based on edge rotations. Rotation axes are the crack front edges (respectively nodes in surface discretizations) and each rotated edge affects the position of only one or two nodes. Modified positions of the entities minimize the difference between the predicted crack path (which depends on the specific propagation theory in use) and the edge or face orientation. The construction of all many-to-many relations between geometrical entities in a finite element code motivates operations on existing entities retaining most of the relations, in contrast with remeshing (even tip remeshing) and enrichment which alter the structure of the relations and introduce additional entities to the relation graph (in the case of XFEM, enriched elements which can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding). In this sense, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives and the approach is independent of the underlying element used for discretization. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, two prototype models are used: tip energy dissipation (LEFM) and cohesive-zone approaches. The Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/deflection accuracy.