Journal
COMPUTATIONAL MECHANICS
Volume 67, Issue 1, Pages 127-137Publisher
SPRINGER
DOI: 10.1007/s00466-020-01923-0
Keywords
Phase-field model; Powell-Sabin B-splines; Anisotropy; Bezier extraction; Adaptive refinement
Funding
- European Research Council [664734 PoroFrac]
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The study utilizes Powell-Sabin B-splines to model brittle fracture in anisotropic materials, allowing for adaptive mesh refinement and discrete crack insertion. Additionally, Bezier extraction ensures accuracy and flexibility in the model.
Phase-field models for brittle fracture in anisotropic materials result in a fourth-order partial differential equation for the damage evolution. This necessitates a C-1 continuity of the basis functions. Here, Powell-Sabin B-splines, which are based on triangles, are used for the approximation of the field variables as well as for the the description of the geometry. The use of triangles makes adaptive mesh refinement and discrete crack insertion straightforward. Bezier extraction is used to cast the B-splines in a standard finite element format. A procedure to impose Dirichlet boundary condition is provided for these elements. The versatility and accuracy of the approach are assessed in two case studies, featuring crack kinking and zig-zag crack propagation. It is also shown that the adaptive refinement well captures the evolution of the phase field.
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