Developing a simple heuristic viscoelastic theory of piezoelectricity

In its simplest form, the linear theory of piezoelectricity takes no account of losses or dissipation phenomena in electroactive materials. This deficiency is often addressed by allowing the dielectric, mechanical, and piezoelectric coefficients to be represented as complex numbers. This paper discusses a related exercise in which the electroactive material is considered to be a three-parameter viscoelastic solid. The piezoelectric equations are redeveloped via the incorporation of a generalized version of Hooke’s law representing a single relaxation process. Through examination of the responses of the system in creep, stress relaxation, and dynamic loading scenarios, the time and frequency dependences of the associated relaxation and dynamic compliances are inferred. The formalism is applied to a simple longitudinal vibrator geometry, and it is demonstrated that primitive viscoelastic behavior can be advantageously described using standard equivalent circuit analogies. The method can readily be generalized to accommodate more complete viscoelastic models.