Second Order Moments in Linear Smart Material Composites

Homogenization is a mean field approach for the determination of the effective properties of heterogeneous materials. It can provide the average fields per phase but also some information about the field distribution such as second order moments. The use of second order moments of fields can notably improve the estimates of the macroscopic behavior in the nonlinear case. This has been studied mainly in the case of uncoupled behavior. We propose to define second order moments in the case of coupled elasto-magneto-electric behavior using homogenization tools. The results are compared to the field fluctuations obtained from a finite element model.