Multiscale modeling of piezoelectric materials

This paper focuses on numerical strategies to predict the behavior of piezoelectric materials and devices characterized by heterogenous microstructural features. Several of these materials are attractive for technological applications including mechanical energy harvesting and pressure/force sensors. After a general introduction on the linear piezoelastic problem, two multiscale strategies are presented and applied to the solution of simple but significant problems frequently encountered in nanotechnology test setups. The first strategy consists in classical homogenization based on the choice of a representative volume element and on the classical micro-macro work equality known as Hill’s lemma. The second strategy is based on the so called FE2 method, where the microscale average response resulting from an homogenization procedure is directly used as a constitutive model at each quadrature point at the macroscale. Both strategies have been implemented within an advanced numeric framework based on the authomatic differentiation technique