Dissipative Finite-Element Formulation Applied to Piezoelectric Materials With the Debye Memory

This work presents a finite-element study of the Debye memory in piezoelectric devices. The memory dependence is due to the spontaneous polarization of the electric dipoles, and it can be understood as a transient viscosity-like effect. The formulation assumes a small strain and rotation hypothesis, and the main contribution is the inclusion of the time-dependent constitutive behavior. For this purpose, a unique numerical formulation that uses convolution integrals is developed to solve the time-dependent electric constitutive equation. A consistent and monolithic finite-element formulation is then obtained and implemented. Finally, a commercial piezoelectric device is simulated for two operational modes, an actuator and a sensor. Several important conclusions on the coupled mechanical and electric fields are reported, and the stability of the time integration scheme is tested by representing the time evolution of the electromechanic energy.