Elastic Constants of Layered Media

Abstract

A three-dimensional laminated medium is studied by an approach which replaces the heterogeneous medium by an equivalent homogeneous material. A set of macroscopic elastic constants is developed in terms of the properties of the constituent layers by considering a representative small element of the laminated medium and imposing the condition of continuity of stress and displacement at the layer interfaces. An example boundary value problem is also considered. Based on the solution of the boundary value problem for the homogeneous material, stress and strain fields corresponding to each layer are then calculated. This individual layer solution contains certain dis continuous stresses and strains as does the exact solution for the layered material.