Multiscale homogenization for linear mechanics

In this work, some results related to multiscale heterogeneous media under the asymptotic homogenization framework are collected. A multiscale asymptotic expansion is proposed and local problems and analytical effective coefficients are derived for fibrous and wavy laminated composites. The solution of the local problem is based on the application of Muskhelishvili’s complex potentials in the form of Taylor and Laurent series. Numerical implementation is done to compute the effective coefficients for elastic and viscoelastic composites. Comparisons with other theoretical approaches are shown