Material constants identification in anisotropic materials using boundary element techniques

This article addresses the resolution of the inverse problem for parameter identification in anisotropic materials. It is based on Boundary Element techniques and it is approached as an optimization problem of a residual cost functional. For this purpose, a standard non-linear minimization method, the Levenberg–Marquardt algorithm, is used. This algorithm makes use of the functional derivatives with respect to the material constants, which in this article have been calculated using direct differentiation procedures. The formulation is developed for plane problems that are in general anisotropic, for homogeneous or piece-wise homogeneous domains. Several examples have been carried out in order to prove the validity of the proposed procedure. The numerical results presented demonstrate the effectiveness of the method employed.