A maxwell-consistent variational framework for piezoelectric laminates: from single plates to multilayer structures

Abstract This paper develops a variational modeling framework for voltage-actuated piezoelectric plates and multilayer laminates under full electromagnetic coupling. By applying Hamilton’s principle to a continuum setting, the formulation retains full electromagnetic coupling through Maxwell’s equations, capturing both electric and magnetic field effects. This enables consistent reductions to quasi-static and electrostatic regimes without sacrificing physical fidelity. Unlike traditional models based on electrostatic assumptions, the present framework accounts for field-induced inertia and magnetic back-reaction forces that can significantly influence system behavior at high frequencies or small scales. From a structural mechanics perspective, the model rigorously couples bending, stretching, and shear deformations with distributed electromagnetic fields. Reduced two-dimensional constitutive laws are derived under Kirchhoff–Love assumptions, yielding a system of partial differential equations that govern laminate dynamics. The framework naturally incorporates both global (surface electrode) and local (patch) actuation scenarios, including correct interface and transmission conditions. Well-posedness in natural energy spaces is established using semigroup theory, supporting future work in control and simulation. Classical plate models are recovered as limiting cases, validating the generality of the approach. The resulting hierarchy of Maxwell-consistent models provides a foundation for accurate modeling and control of smart composite structures with multifunctional capabilities.