The use of Powell-Sabin B-Splines in a higher-order phase-field model for crack kinking

TY - JOUR

T1 - The use of Powell-Sabin B-Splines in a higher-order phase-field model for crack kinking

AU - Chen, Lin

AU - Li, Bin

AU - de Borst, René

N1 - Publisher Copyright: © 2020, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2021/1

Y1 - 2021/1

N2 - Phase-field models for brittle fracture in anisotropic materials result in a fourth-order partial differential equation for the damage evolution. This necessitates a C1 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. Bézier 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.

AB - Phase-field models for brittle fracture in anisotropic materials result in a fourth-order partial differential equation for the damage evolution. This necessitates a C1 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. Bézier 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.

KW - Adaptive refinement

KW - Anisotropy

KW - Bézier extraction

KW - Phase-field model

KW - Powell-Sabin B-splines

UR - http://www.scopus.com/inward/record.url?scp=85091042672&partnerID=8YFLogxK

U2 - 10.1007/s00466-020-01923-0

DO - 10.1007/s00466-020-01923-0

M3 - 文章

AN - SCOPUS:85091042672

SN - 0178-7675

VL - 67

SP - 127

EP - 137

JO - Computational Mechanics

JF - Computational Mechanics

IS - 1

ER -