Numerical simulation of multiple 3D fracture propagation using arbitrary meshes

This paper describes a mesh-independent finite element based method for propagating fractures in three dimensions. The iterative algorithm automatically grows fractures in a 3D brittle medium represented by an isotropic linear elastic matrix. Growth is controlled by an input failure and propagation criterion. The geometry and mesh are stored separately, and mesh refinement is topologically guided. Propagation results in the modification of crack geometry, as opposed to changes in the mesh, as the arbitrary tetrahedral mesh adapts to the evolving geometry. Stress intensity factors are computed using the volumetric J Integral on a virtual piecewise cylinder. Modal stress intensity factors are computed using the decomposition method. Mesh and cylinder size effects are studied, as is computational efficiency. A through-going crack embedded in a thick slab, and a horizontal and inclined penny-shape crack, are used to validate the accuracy of the method. The predicted stress intensity factors are in good agreement with analytical solutions. For six integration points per tip segment, integration local to single tips, and a cylinder radius that adapts to the local geometric conditions, results agree with analytical solutions with less than 5% deviation from experimental results.