Adaptive isogeometric analysis for phase-field modeling of anisotropic brittle fracture

Lin Chen, Bin Li, René de Borst*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The surface energy a phase-field approach to brittle fracture in anisotropic materials is also anisotropic and gives rise to second-order gradients in the phase field entering the energy functional. This necessitates C1 continuity of the basis functions which are used to interpolate the phase field. The basis functions which are employed in isogeometric analysis (IGA), such as nonuniform rational B-splines and T-splines naturally possess a higher order continuity and are therefore ideally suited for phase-field models which are equipped with an anisotropic surface energy. Moreover, the high accuracy of spline discretizations, also relative to their computational demand, significantly reduces the fineness of the required discretization. This holds a fortiori if adaptivity is included. Herein, we present two adaptive refinement schemes in IGA, namely, adaptive local refinement and adaptive hierarchical refinement, for phase-field simulations of anisotropic brittle fracture. The refinement is carried out using a subdivision operator and exploits the Bézier extraction operator. Illustrative examples are included, which show that the method can simulate highly complex crack patterns such as zigzag crack propagation. An excellent agreement is obtained between the solutions from global refinement and adaptive refinement, with a reasonable reduction of the computational effort when using adaptivity.

Original languageEnglish
Pages (from-to)4630-4648
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Issue number20
StatePublished - 30 Oct 2020
Externally publishedYes


  • T-splines
  • adaptivity
  • anisotropic surface energy
  • isogeometric analysis
  • phase-field


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