Numerical Method of Discontinuous Displacements in Spatial Problems of Fracture Mechanics

— The article proposes a numerical method for solving spatial problems of fracture mechanics (method of discontinuous displacements). The advantage of the method is the representation of the solution in the form of a finite series of expansion in terms of the found analytically presented functions. The expansion coefficients are determined from the conditions for fulfilling the boundary conditions in the geometric centers of gravity of the boundary elements. The reliability of the numerical results is shown on test problems for spatial cracks with an analytical solution. The undoubted advantage of the method is the possibility of a mobile solution of the problem for a system of a finite number of cracks with an arbitrary mutual orientation and location in space. The advantage of the method is also a high speed of calculations with satisfactory accuracy, including when calculating stress intensity factors. As a test of the method for a system of cracks, this paper shows the comparison results for the problem of interaction of two cracks, depending on the distance between the planes of the cracks. A comparison is made with a system of two elliptical cracks lying in the same plane. The influence factor (the ratio of the stress intensity factor in the case of a system of cracks to the corresponding value for a single crack) was used as the main characteristic. The comparison with the results of other authors showed good qualitative and quantitative agreement.