Generalized rheology of active materials

High-strain active materials often exhibit relaxation in their response to an electric or magnetic field. This phenomenon has been previously describe d by a loss factor (tangent of the phase shift). However, the loss factor c annot express frequency-dependent, nonperiodic time-dependent, or nonlinear responses, therefore more fundamental material constants are needed. We pr esent a phenomenological model that describes the time and frequency-depend ent behavior of electromechanically (piezoelectric and electrostrictive) an d magnetomechanically (magnetic shape memory and magnetostrictive) active m aterials. Expanding rheology, we introduce electrorheological and magnetorh eological models incorporating time constants corresponding not only to the viscoelastic response, i.e., strain versus stress, but also: (1) polarizat ion or magnetization versus field, (2) strain versus polarization or magnet ization, (3) ferro- and antiferroelectric, ferro- and antiferromagnetic, or ferroelastic domain switching under applied field and/or stress. A single set of constitutive equations is obtained that can describe pure and mixed cases of ferroic, antiferroic, and nonferroic response. The simulated behav ior agrees well with experimental data for both polycrystalline piezoelectr ics and high electromechanical strain single crystals. (C) 2000 American In stitute of Physics. [S0021-8979(00)07624-6].