Modeling of thin isotropic elastic plates with small piezoelectric inclusions and distributed electric circuits

This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation, with various kinds of electric boundary conditions. We derive the corresponding effective models when the thickness a of the plate and the characteristic dimension ϵ of the inclusions tend together to zero, in the two following situations: first, when a ≃ ϵ, and second, when a ∕ ϵ tends to zero. Copyright © 2013 John Wiley & Sons, Ltd.