Parameter identification for two-phase nonlinear composites

In many cases, the microstructure of composite materials is not known and cannot directly be accessed such that an inverse analysis is necessary for its investigation. This approach requires the implementation of two tools: an optimization method for the minimization of the error problem and a mechanical approach for the solution of the direct problem, i.e. the simulation of composite materials. Our particular choice deals with the combination of the Levenberg–Marquardt method with the multiscale finite element method. The numerical examples are concerned with the investigation of the elastic parameters for two-phase materials. Emphasis is placed on the discussion of convergence and sensitivity with respect to the initial guess.