An exact solution for micromechanical analysis of periodically layered composites

This paper presents an exact solution for effective properties and local fields of periodic layered composites, obtained based on variational asymptotic method for unit cell homogenization, a recently developed micromechanics modeling framework. The layered composites could be made of multiple general anisotropic layers. This solution reproduces some published results when specialized to layered composites made of two orthotropic or isotropic layers and is located within the correctly interpreted bounds of the rules of mixtures according to Voigt and Reuss. It is also emphasized in this paper that the rules of mixtures according to Voigt and Reuss are absolute upper and lower bounds for the effective properties of layered composites if the bounds are interpreted in terms of the stiffness matrix or the fourth-order elasticity tensor. The confusion in a few recent papers regarding effective Young's modulus of layered isotropic composites could exceed the Voigt and Reuss estimates is clarified.