Two-Scale Homogenization of Piezoelectric Perforated Structures

We are interested in the homogenization of the elastic-electric coupling equation with rapidly oscillating coefficients, in a periodically perforated piezoelectric body. The holes, whose size are supposed to tend to zero, are periodically distributed. We give a new approach, based on the two-scale convergence, and we justify the two first terms in the usual asymptotic development of the solution. A two-scale homogenized system is obtained as the limit of the periodic problem, and explicit formulae of elastic, piezoelectric and dielectric homogenized coefficients are reported. In the static limit, the method provides homogenized electroelastic coefficients coinciding with those deducted from alternative approaches.