Mathematical derivation of sensor and actuator plates models in linear piezoelectricity

Abstract
Here, we rigorously derive a theory of linearly piezoelectric plates by studying the limit behavior of a three-dimensional flat body as its thickness tends to zero. In the static case, two limit models appear depending essentially on the nature and the magnitude of the electromechanical loading. The two limit constitutive laws are explicitly derived for each piezoelectric crystal class.