A one-dimensional model for non-linear behaviour of piezoelectric composite materials

In this paper, a one-dimensional analytical model is proposed to investigate the non-linear behaviour for piezoelectric and piezoelectric fibre reinforced composite (PFRC) materials in the fibre direction. The required linear and non-linear constants for purely piezoelectric materials are obtained using the curve-fitting method and the measured S₃–E₃ non-linear loops of the corresponding piezoelectric materials, whereas those for PFRC materials are determined by employing the quadratic non-linear constitutive equations for a purely piezoelectric material, the iso-field assumptions and linear and non-linear constants of the composite constituents. A numerical study is conducted. The numerical results reveal a significant effect of stress T₃ on S₃–E₃ non-linear behaviour for both soft PZT–5H ceramics and PZN–4.5%PT crystals. It is also found that the piezoelectric fibre volume fraction V_f and strain S₃ can significantly affect the T₃–E₃ non-linear behaviour for both PZT–5H/piezo-polymer polyvinylidene fluoride (PVDF) and PZN–4.5%PT/PVDF PFRC materials. A good correlation is noted between the piezoelectric constants d₃₃ and e₃₃ predicted using the present method and those recommended by manufacturer for PZT–5H ceramics and PZN–4.5%PT crystals.