  This paper presents a novel derivation of the direct parametrisation method
for invariant manifolds able to build simulation-free reduced-order models for
nonlinear piezoelectric structures, with a particular emphasis on applications
to Micro-Electro-Mechanical-Systems. The constitutive model adopted accounts
for the hysteretic and electrostrictive response of the piezoelectric material
by resorting to the Landau-Devonshire theory of ferroelectrics. Results are
validated with full-order simulations operated with a harmonic balance finite
element method to highlight the reliability of the proposed reduction
procedure. Numerical results show a remarkable gain in terms of computing time
as a result of the dimensionality reduction process over low dimensional
invariant sets. Results are also compared with experimental data to highlight
the remarkable benefits of the proposed model order reduction technique.
