Model development for piezoceramic nanopositioners

In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic field-displacement relations inherent to piezoceramic elements employed in present nanopositioner designs. We focus specifically on piezoceramic rods utilizing d₃₃ motion and piezoceramic shells driven in d₃₁regimes, but the modeling framework is sufficiently general to accommodate a variety of drive geometries. In the first step of the model development, lattice-level energy relations are combined with stochastic homogenization techniques to construct nonlinear constitutive relations which accommodate the hysteresis inherent to piezoceramic compounds. Secondly, these constitutive relations are employed in classical rod and shell relations to construct system models appropriate for presently employed nanopositioner designs.