Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials

This paper introduces an extended Voronoi cell finite-element model (X-VCFEM) for modelling cohesive crack propagation in brittle materials with multiple cracks. The cracks are modelled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip. Extension to VCFEM is achieved through enhancements in stress functions in the assumed stress hybrid formulation. In addition to polynomial terms, the stress functions include branch functions in conjunction with level set methods, and multi-resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack-tip stress concentrations. Conditions and methods of stability are enforced in X-VCFEM for improved convergence with propagating cracks. Two classes of problems are solved and compared with existing solutions in the literature for validation of the X-VCFEM algorithms. The first set corresponds to results for static cracks, while in the latter set, the propagation of cohesive cracks are considered. Comparison of X-VCFEM simulation results with results in literature for several fracture mechanics problems validates the effectiveness of X-VCFEM