Microstructural effects in elastic composites

In this paper, the static microstructural effects of periodic elastic composites were studied by the homogenization method. This approach is based on the analysis of the momentum balance equations which appear at higher orders. The physical meaning of the corrective terms due to the existence of heterogeneities is discussed in detail. We show that the higher terms introduce the successive gradients of macroscopic strain and tensors characteristic of the microstructure, which result in non-local effects. The boundary conditions for solving problems up to third-order are also given. This analysis is used to define a kinematic criterion for the occurrence of these microstructural effects, and a procedure to assess them. The obtained macroscopic description constitutes a generalization of the second gradient theory, but it is not in agreement with the mechanics of Cosserat media. Moreover, these results can be used to approach the emergence of localization phenomenon. Finally, an application of the method is given using periodically stratified composites as an example.