A piezoelectric mixed variational theorem for smart multilayered composites

This work derives, for piezoelectric media, the analog of Reissner's mixed variational theorem (RMVT), initially developed for elastic media, by adding the transverse electric field-potential relation as a constraint via a Lagrange multiplier. The latter is shown to be the transverse (normal) electric displacement, for which continuity can now be fulfilled in a natural way as is the case for transverse stresses in the RMVT. Hence, the newly proposed piezoelectric mixed variational theorem (PMVT) will be well suited for layered piezocomposites. Mixed piezoelectric constitutive equations to be used in conjunction with the PMVT are developed and guidelines for their numerical implementation are also given.