Application of the Multipole Expansions Method for Solving 2D- and 3D- Elasticity and Fracture Mechanics Problems for the Medium with Pores

The multipole expansions method is an effective tool for solving the elasticity problems. The idea of the method is to present the unknown solution as a series in terms of the multipoles - singular solutions of elasticity. The coefficients of the series are then obtained by minimizing the error functional describing the difference between the given boundary conditions and those retrieved using the series. In the paper a review of the works of the authors related to application of the multipole expansions method for solving 2D- and 3D-elastisity problems for the media with pores is given. The obtained results are presented and briefly discussed.