Effective properties of viscoelastic piezoelectric materials using homogenisation on representative volume finite elements

This paper introduces a comprehensive methodology for determining the effective piezo-electromechanical properties considering viscoelastic effects in the composite material. The methodology uses finite element (FE) analysis and homogenisation. By formulating the FE solution as a dynamic equilibrium problem, the proposed approach effectively couples linear elastic piezoelectric fibres within a linear viscoelastic matrix. This couples both complex constitutive behaviours into a single representative cell for time-dependent quasi-static load cases. A virtual stress relaxation test is conducted on a Representative Volume Element (RVE) with periodic boundary conditions. The methodology disregards inertial effects to represent quasi-static loading conditions. It assumes a polymeric matrix phase with only mechanical degrees of freedom. The computed effective time-dependent constitutive coefficients are compared with analytical solutions derived from effective field and asymptotic homogenisation methods for a circular piezoelectric fibre in a viscoelastic polymeric matrix. Despite the simplifying assumption for the polymer matrix, the usage of a time-independent Halpin–Tsai model for effective electric permittivity, coupled with the proposed FE approach, accurately predicts time-dependent behaviour of elastic, piezoelectric and dielectric effective coefficients for different fibre volume ratios. Thus, the proposed approach provides a robust and versatile framework for characterising effective piezoviscoelastic properties. This makes a contribution to the field of micromechanical piezoelectric simulation, paving the way for future research into dynamic effects, more complex material constitutive models, and intricate geometric features. • FE methodology for modelling viscoelasticity in piezoelectric materials. • Application of Halpin–Tsai model for dielectric behaviour of polymer matrices. • Prediction of time-dependent constitutive behaviour at different fibre volume ratios. • Prediction of time-dependent piezoelectric behaviour at different fibre volume ratios.