Mesh-independent equivalent domain integral method for J-integral evaluation

The equivalent domain integral method is a reliable tool for J-integral computation in two- and three-dimensional elastic and elastic-plastic fracture mechanics problems. A variant of this method that is independent of finite element mesh is presented. Finite element solution of a boundary value problem is performed on a mesh composed of arbitrary elements. Nodal results are approximated by the moving least squares method that does not require knowledge of mesh topology. Domain integrals are evaluated on a background mesh of hexahedral elements. The mesh has the polar structure with the refinement towards the crack front. Elements of the background mesh are generated in the coordinate system associated with the crack front and then transformed to the global system. Domain integration for each background element is performed once during computations. Evaluation of J-integral for multiple domains is achieved by multiplication of an element domain integral with multiple domain weight functions. Performance of the proposed algorithm is demonstrated by the examples of three-dimensional cracks using meshes of both hexahedral and tetrahedral elements.