Piezoelectric Beam, Plate and Truss

Piezoelectric Material

The constitutive equations of a general piezoelectric material are

$T_{ij}=c_{ijkl}^ES_{kl} - e_{kij}E_k$ (4.1)

$D_i = e_{ikl}S_{kl} + {\varepsilon}_{ik}^S E_k$ (4.2)

where T _ij and S _kl are the components of the stress and strain tensors, respectively, $c_{ijkl}^E$ are the elastic constants under constant electric field (Hooke’s tensor), e _ikl the piezoelectric constants (in Coulomb/m²) and ${{\varepsilon}_{ij}^S}$ the dielectric constant under constant strain. These formulae use classical tensor notations, where all indices i,j,k,l = 1,2,3, and there is a summation on all repeated indices.