The effective stiffness and stress concentrations of a multi-layer laminate

Using the jump conditions for the geometrically linearized strains and the Cauchy stresses and assuming homogeneous strain and stress fields inside the layers, we determine the effective stiffness tetrad of a laminate consisting of linearly elastic layers. From a two-layer reference solution, an explicit solution for the multi-layer case is derived. Unlike classical methods, the present approach applies to any loading case and an arbitrary number of layers with arbitrary stiffness tetrads, and can be considered as the explicit analytical solution of the multi-layer homogenization in linear elasticity.