Extended irreversible thermodynamics modeling for self-heating and dissipation in piezoelectric ceramics

Self-heating or dissipation of piezoelectric ceramic elements is observed to be severe under dynamic operations even in the linear range. In this paper, a nonequilibrium thermodynamic model is developed to delineate the coupled irreversible mechanical, electric, and thermal processes, which jointly contribute to dissipation. Specifically, additional nonequilibrium state variables, also known as thermodynamic fluxes, are brought in to describe each of these processes. The characteristic relaxation of these processes is modeled. The nonnegative rate of entropy production is found to be in quadratic form of thermodynamics fluxes. The energy balance equation, which governs the transformation between different energy forms, is obtained in the framework of extended irreversible thermodynamics. Using this model, the dissipation of a piezoceramic stack actuator under harmonic electric or mechanical loadings in linear operation range is studied. The harmonic-balance methods are utilized as solution techniques. In contrast to the existing piezoelectric dissipation models, the dissipation by the developed model is verified to nonlinearly depend on operating frequency, with a peak dissipation occurring at some operating frequency that is related to characteristic relaxation of irreversible processes. The measurements of newly introduced parameters are also discussed.