Viscoelectroelastic closed form models for frequency and time dependent effective properties of reinforced viscoelectroelastic composites

In this paper, closed form models of time and frequency dependent effective properties of reinforced viscoelectroelastic composites are elaborated. Based on the correspondence principle of linear viscoelectroelasticity and the Mori-Tanaka micromechanical mean field approach, the effective properties are derived in the Laplace-Carson domain and then inverted numerically to the time domain. New analytical models for decoupled and coupled effective properties of transversely isotropic viscoelectroelastic materials are elaborated using compact matrix formulations. Explicit relationships are presented for different effective viscoelectroelastic moduli of piezoelectric materials with various inclusions shapes. Various viscoelastic time dependent models for the phases can be used. Only few Eshelby tensor coefficients are required to be analytically or numerically computed. Results based on the elaborated effective viscoelectroelastic models are presented for various types of piezoelectric inclusions and compared to the available predictions. These models are suitable for designers to predict composite viscoelectroelastic moduli of heterogeneous materials with optimized active and passive characteristics.