The effective non-linear properties of a composite coating and a composite sandwich layer

Hashin–Shtrikman based bounds and estimates are obtained for the linear and non-linear effective properties of composites in the form of a thin coating or sandwich layer. It is assumed that the thickness of the layer is of the same order of magnitude as the correlation length between phases, and size effects thereby result. Boundary layers exist within the coating adjacent to the substrate and to the free surface (in the case of a coating). Attention is focused on two-dimensional problems by considering anti-plane shear of an isotropic 2-phase composite on a single-phase substrate, with microstructure prismatic along the direction of anti-plane shear.