Mathematics

Computer science

Quantum mechanics

Engineering

Adaptive mesh refinement

Isogeometric analysis

Computational science

Isotropy

Structural engineering

Applied mathematics

Materials science

Physics

Finite element method

International Journal for Numerical Methods in Engineering

Summary Phase‐field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric‐meshfree approach is developed for the phase‐field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric‐meshfree approach uses moving least‐squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase‐field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowle...

Phase‐field modeling of brittle fracture in a <scp>3D</scp> polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach