Method of singular integral equations in linear and elastoplastic problems of fracture mechanics

A brief survey of investigations carried out at the Karpenko Physicomechanical Institute of the Ukrainian National Academy of Sciences and devoted to the application of the method of singular integral equations to the solution of two-dimensional problems of fracture mechanics is presented. Special attention is given to the integral equations defined on piecewise smooth closed or open contours appearing in the boundary-value problems of the theory of elasticity for angular domains. We propose a new method aimed at the solution of dynamic problems by using finite differences with respect to time and singular integral equations on the boundary contours. Integral equations also appear in the elastoplastic problems of fracture mechanics solved by using the model of plastic strips and in the general case of continual plastic zones. © 2004 Springer Science+Business Media, Inc.