A Thermopiezoelectric Mixed Variational Theorem for smart multilayered composites

This work extends for thermopiezoelectric media the Piezoelectric Mixed Variational Theorem (PMVT), proposed recently by the authors, by adding the transverse thermal field-temperature increment relation as a constraint via a Lagrange multiplier. The latter is shown to be the transverse (normal) heat flux, which continuity can now be fulfilled in a natural way as is the case for the transverse stresses and transverse electric field in the PMVT. Hence the resulting Thermopiezoelectric Mixed Variational Theorem (TMVT) will be well suited for implementing new accurate and fully coupled analytical or closed-form and numerical, such as finite element, solutions for thermopiezoelectric multilayered smart composites. Mixed thermopiezoelectric constitutive equations to be used in conjunction with the new TMVT are developed and guidelines for their numerical implementation are also given.