The Eshelby theorem and application to the optimization of an elastic patch (Q2903527)

In the paper the authors consider the elastic patch problem: an ellipsoidal, anisotropic, homogeneous elastic body is inserted inside a region of a given solid subject to exterior traction loading at the surface and other conditions. The aim is to find the optimal rotation of the anisotropic material inclusion with respect to integral (optimizing elastic energy) and local (minimizing stress) functionals. The problem with local cost functional needs to apply asymptotic theory for elliptic boundary problems in domains with perturbed boundaries. The authors use the Eshelby theorem and the representation of stresses based on the link matrix. An analytical model reduction technique allows for efficient numerical computations that are demonstrated on two examples.