On the Application of the Method of Difference Potentials to Linear Elastic Fracture Mechanics

The Difference Potential Method (DPM) [1] proved to be a very efficient tool for solving boundary value problems (BVPs) in complex regions. It allows BVPs to be reduced to a boundary equation without the knowledge of Green’s functions. The method has been successfully used for solving very different problems related to the solution of partial differential equations [1]. However, it has mostly been considered in regular (Lipschitz) domains. In the current paper, for the first time the method has been applied to a problem of linear elastic fracture mechanics. This problem requires solving BVPs in domains with a cut. In DPM the reduction of the BVP to a boundary equation is based on generalized surface projections [1, 2]. The projection is fully determined by the clear trace (notion introduced by Ryaben’kii). In the current paper, for the first time the minimal clear trace found in [3] for the problem with cuts has been numerically realized.