The finite cell method (FCM) represents a combination of high-order finite elements with the fictitious domain approach. Due to it's simple mesh generation the FCM reduces the pre-processing effort. For heterogeneous problems of solid mechanics however, discontinuities occur at the material interfaces, which cannot be captured by the smooth shape functions of the FCM anymore, whereby the convergence deteriorates. Thus, to recover the optimal convergence rate, we extend the FCM ansatz by specially designed shape functions, which are able to capture discontinuities at the material interfaces. To get more insight into the problem, we study the performance of the proposed method by means of a two-dimensional example.