### abstract

- This study presents nonlinear and time-dependent analyses of ferroelectric materials and structures. Phenomenological constitutive models are considered for simulating macroscopic responses of materials undergoing various histories of electromechanical inputs. When the electric field inputs are less than the coercive limit (minor loop simulations), there will be no polarization switching and 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. When the electric field inputs are above the coercive limit (major loop simulations), the electro-mechanical coupling constants are expressed as functions of a polarization state and it is assumed that in absence of the polarization, the material does not exhibit electro-mechanical coupling response. The polarization state consists of time-dependent reversible and irreversible parts, where the irreversible part is incorporated to account for polarization switching responses. This constitutive model is implemented at each material (Gaussian) point within continuum FEs. A quasi-linear viscoelastic (QLV) model is adopted in order to incorporate the time-dependent effect on the nonlinear electro-mechanical response of piezoelectric ceramics. The recursive integration technique is used to solve for the time-dependent constitutive model at each Gaussian point. Finite element method is then used for analyzing behaviors of several piezoelectric structures and structural components under various boundary conditions. Parametric studies are also conducted to examine the effect of loading rates and coupled electro-mechanical boundary conditions on the overall performance of smart structures. The developed FE model is also used for predicting the overall responses Active Fiber Composite (AFC). A unit cell of AFC, where different responses of the constituents (fiber, matrix, electrode finger, kapton layer) are incorporated, is considered and time dependent and nonlinear responses of AFC are determined. The overall responses of AFCs at different frequencies and electric field amplitude determined from the FE are compared with experiments. Reasonably good predictions are observed. Finally, FE analyses are performed to simulate shape changing in smart truss structures. An electro-active truss FE undergoing large deformations is formulated. Each truss member is modeled as an active element with nonlinear time-dependent electromechanical constitutive model. The desired shape is induced in the overall structure by applying electric field to each truss member. The truss FE model can handle both material and also geometric nonlinearities.