International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 4, Pages 739-760
A numerical method for the solution of plane crack problems in finite media
Department of Theoretical and Applied Mechanics, The National Technical University of Athens, 5 K. Zografou Street, Zografou, Athens 624, Greece
Received 7 November 1979
Copyright © 1980 P. S. Theocaris and N. Ioakimidis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A general method for the solution of plane isotropic elasticity crack problems inside a finite medium of arbitrary shape or an infinite medium with holes of arbitrary shape is presented. This method is based on the complex potential approach of plane elasticity problems due to Kolosov and Muskhelishvili  and makes no assumption on the way of loading of the cracks and of the other boundaries of the medium.
The whole problem is reduced to a complex singular integral equation along the cracks and the other boundaries and the values of the stress intensity factors at the crack tips may be evaluated directly and accurately from the numerical solution of this equation. An application of the method to a circular medium with a straight crack is also made.