Unified formulae of variational bounds for multiphase anisotropic elastic composites

Using the spherical and deviator decomposition of the polarization and strain tensors, we present a general algorithm for the calculation of variational bounds of dimension d for any type of anisotropic linear elastic composite as a function of the properties of the comparison body. This procedure is applied in order to obtain analytical expressions of bounds for multiphase, linear elastic composites with cubic symmetry where the geometric shapes of the inclusions are arbitrary. For the validation, it can be proved that for the isotropic particular case, the bounds coincide with those recently reported by Gibiansky and Sigmund. On the other hand, based on this general procedure some, classical bounds reported by Hashin for transversely isotropic composites, are reproduced. Numerical calculations and some comparisons with other models and experimental data are shown.