Frequency and time viscoelectroelastic effective properties modeling of heterogeneous and multi-coated piezoelectric composite materials

In this paper, the time and frequency dependent effective behaviors of multi-phase and multi-coated viscoelectroelastic composites are investigated. The correspondence principle, extended to linear viscoelectroelasticity, and the Mori–Tanaka micromechanical mean field approach are used. Based on integral equations and on the obtained viscoelectroelastic interfacial operators closed form expressions of the concentration tensors for viscoelectroelastic composites are derived. The effective properties are obtained in the Carson domain and then inverted numerically to the time domain. They are presented in frequency and time domains for various types, shapes and volume fractions of inclusions as well as for various thicknesses of the coating and showed relaxation effects on all resultant electroelastic coefficients. The frequency dependent storage and loss factors of the obtained effective electroelastic coefficients as well as their cycle limits are elucidated. By this methodological approach, new hybrid composite materials can be obtained and their active–passive properties can be optimized with respect to phase, coating layer and inclusion characteristics.