Nonlinear and time dependent behaviors of piezoelectric materials and structures

•We analyze nonlinear electro-mechanical response of piezoelectric materials.•We study nonlinear time-dependent hysteretic response under electrical stimuli.•We implement the electro-mechanical constitutive model in finite element.•We simulate nonlinear responses of actuators under electric field inputs.

This study presents an analysis of nonlinear and time-dependent responses of polarized piezoelectric materials and structures. A nonlinear time-dependent electro-mechanical constitutive model based on a single integral form is considered for the piezoelectric materials undergoing small deformation gradients and large electric field. The nonlinearity is accounted for by incorporating higher order terms of the electric field and the effect of loading history is incorporated through the time integrand. An incremental formulation based on a recursive-iterative method is used to obtain solutions for the nonlinear and time-dependent integral constitutive model. This constitutive model is implemented at each material (Gaussian) point within continuum finite elements. Experimental data on polarized piezoelectric ceramics, e.g. Lead Zirconate Titanate (PZT), available in the literature are used to validate the nonlinear and time-dependent electro-mechanical constitutive model. In addition, the nonlinear electro-mechanical response of telescopic actuators made of PZT is simulated using the presented time-dependent electro-mechanical model. The calculated results are consistent with experimental data.