Gene

Computational science

Algorithm

Engineering

Classification of discontinuities

Materials science

Robustness (evolution)

Fatigue testing

Adaptive mesh refinement

Biochemistry

Computer science

Finite element method

Mathematics

Mathematical analysis

Structural engineering

Chemistry

Fracture mechanics

Finite Elements in Analysis and Design

A new approach combining the eXtended Finite Element Method (X-FEM) and automatic Adaptive Mesh Refinement (AMR) is presented taking advantage of both methods. The X-FEM, developed over the past two decades by a large community, have proven its efficiency to handle evolving discontinuities in a variety of fracture analysis. Since this method enables to describe the crack and its propagation independently of the mesh of the structure, a simple hierarchical mesh refinement procedure can be applied. Automatic adaptive remeshing is a valuable method in 3D elastic-plastic crack propagation analysis since it permits a locally fine mesh and then an accurate description of physical quantities in a limited area around the crack front. This is particularly important when local fracture criteria are concerned. Moreover local refinement saves computational effort, which is relevant for engineer-sized problems, particularly when the propagation path is not a priori known. In the present work, it is shown that both methods combine with minimal effort: the kinematic continuity relations and the field transfer process, needed for history-dependent material, must include in a proper way the enrichment of the model. If this requirement is not fulfilled, numerical error may be introduced. Implementation of this combined X-FEM/AMR approach is presented in detail. In particular, an innovative field transfer strategy is proposed. Numerical applications in 2 and 3 dimensions of crack propagation in elastic-plastic media demonstrate accuracy, robustness and efficiency of the technique.

A 3D automatic mesh refinement X-FEM approach for fatigue crack propagation