Two-scale homogenization of piezoelectric perforated structures
Provides a rigorous justification for the asymptotic expansion in periodically perforated piezoelectric materials, but the results are incremental as they confirm existing homogenization techniques.
The paper derives a two-scale homogenized system for piezoelectric perforated structures using two-scale convergence, obtaining homogenized electroelastic coefficients that match those from other methods.
We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of {\it two-scale convergence}. A two-scale homogenized system is obtained as the limit of the periodic problem. While in the static limit the method provides homogenized electroelastic coefficients whicht coincide with those deduced from other homogenization techniques (asymptotic homogenization, $Γ$-convergence).