Stress fields in 3D-elastic material containing multiple interacting cracks of arbitrary shapes: Efficient calculation

An efficient numerical method for the 3D-problem of elasticity for a solid with multiple interacting cracks is developed. The problem is reduced to a system of 2D-integral equations for the crack opening vectors. Discretization of these equations is performed by Gaussian approximation functions centered at a set of nodes uniformly distributed on the crack surfaces; the procedure results in five standard 1D-integrals that can be tabulated. For planar cracks of arbitrary shapes, these integrals are calculated in closed analytical forms. The method is mesh free. Examples of various interacting, as well as intersecting, cracks are considered and compared with the solutions available in literature.