Two-scale homogenization of piezoelectric perforated structures

TL;DR

This paper develops a two-scale homogenization method for piezoelectric materials with perforations, deriving effective electroelastic properties and validating the approach against existing techniques.

Contribution

It introduces a two-scale convergence approach to homogenize perforated piezoelectric structures, providing a rigorous derivation of effective properties.

Findings

Derived homogenized electroelastic coefficients consistent with existing methods

Validated the two-scale convergence approach for perforated piezoelectric materials

Provided asymptotic expansion justifications for the homogenization process

Abstract

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, $\Gamma$-convergence).