Thermal derivatives of compliances, piezoelectric coefficients and permittivities in Lagrangian description

The aim of this paper is to present constitutive relations expressing the strain and electric displacement as functions of Piola-Kirchoff stress tensors of the first or second kind and of material electric field. These relations are necessary to allow the use of Lagrangian (or material) description of vibrating piezoelectric devices submitted to a change of temperature. Connections between these new coefficients and the classical ones are given and numerical values for them are proposed.