An Efficient Numerical Method for the Solution of the Problem of Elasticity and Poroelasticity for 3D-homogeneous Elastic Medium with Cracks and Inclusions

摘要

An efficient numerical method for solution of elasticity and poroelasticity problems for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Cracks and inclusions occupy a finite region of the medium that is subjected to arbitrary external forces. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. The method is mesh free. Stress fields inside inclusions and crack opening vectors are approximated by Gaussian functions centered at a system of nodes. The elements of this matrix are calculated in closed analytical forms (for inclusions) or expressed in terms of five standard ID-integrals (for cracks) that can be tabulated. For regular node grids, the matrix of discretized system has Toeplitz's structure, and a Fast Fourier Transform technique can be used for calculation of matrix-vector products with such matrices. In the present work, the problem for media with both heterogeneous inclusions and cracks are solved in the framework of a general numerical scheme.