Analytical treatment of composite structures by means of integral equations

In this contribution, the theory of plane elasticity is applied to composite materials in the special case of the analytical treatment of a modified CT-specimen containing a circular elastic inclusion. This specimen is damaged by a crack system consisting of a straight matrix and a curvilinear inclusion/matrix interface crack. The corresponding boundary value problems have been formulated and the related integral equations could be derived. Thereby the kernels of these integral equations contain Cauchy type singularities. If crack kinking occurs then at the kinking point an additional singularity appears. The appropriate characteristic equations described the singular behaviour of the stresses around the crack tips as well as around the kinking point. For the numerical treatment of the resultant equations, direct methods using the solutions of the associated homogeneous characteristic equations as weight functions can be applied.