Minimum energy multiple crack propagation. Part III: XFEM computer implementation and applications

Abstract

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith’s theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-III of the three-part paper are as follows: (1) implementation of XFEM in Matlab with emphasis on the design of the code to enable fast and efficient computational times of fracture problems involving multiple cracks and arbitrary crack intersections, (2) verification of the minimum energy criterion and comparison with the maximum tension criterion via multiple benchmark studies, and (3) we propose a numerical improvement to the crack growth direction criterion that gives significant gains in accuracy and convergence rates of the fracture paths, especially on coarse meshes. Finally, the open-source Matlab code, documentation, benchmarks and other example cases are included as supplementary material.