A method to compute mixed-mode stress intensity factors for nonplanar cracks in three dimensions

Methods to compute the stress intensity factors along a three-dimensional (3D) crack front often display a tenuous rate of convergence under mesh refinement or, worse, do not converge, particularly when applied on unstructured meshes. In this work, we propose an alternative formulation of the interaction integral functional and a method to compute stress intensity factors along the crack front which can be shown to converge. The novelty of our method is the decoupling of the two discretizations: the bulk mesh for the finite element solution and the mesh along the crack front for the numerical stress intensity factors, and hence we term it the multiple mesh interaction integral (MMII) method. Through analysis of the convergence of the functional and method, we find scalings of these two mesh sizes to guarantee convergence of the computed stress intensity factors in a variety of norms, including maximum pointwise error and total variation. We demonstrate the MMII on four examples: a semiinfinite straight crack with the asymptotic displacement fields, the same geometry with a nonuniform stress intensity factor along the crack front, a spherical cap crack in a cylinder under tension, and the elliptical crack under far-field tension and shear.