Two-scale homogenization of piezoelectric perforated structures

Details Two-scale homogenization of piezoelectric perforated structures Two-scale homogenization of piezoelectric perforated structures

2007-09-07

arxiv.org/abs/0709.1079v1

Mathematics

Numerical Analysis

21 pages

Scientific paper

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).

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