A constitutive-based element-by-element crack propagation algorithm with local mesh refinement

In the context of multiple constitutive models, multiple finite element formulations and crack nucleation and propagation hypotheses, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D models which is independent of the constitutive and element specific technology. Observed phenomena such as multiple crack growth and shielding emerge naturally, without specialized algorithms for calculating the crack growth direction. The algorithm consists of a sequence of mesh subdivision, mesh smoothing and element erosion steps. Element subdivision is based on the classical edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity (such as void fraction or principal stress). To assess the robustness and accuracy of this algorithm, we use classical quasi-brittle benchmarks and ductile tests.