A Fully Coupled Constitutive Model for Electrostrictive Ceramic Materials

A three-dimensional, electromechanical constitutive law has been formulated for electrostrictive ceramic materials. This fully coupled, phenomenological model relates the key state variables of stress, strain, electric field, polarization and temperature in a set of compact nonlinear equations. The direct and converse electrostrictive effects are modeled by assuming that the electri cally induced strain depends on second-order polarization terms. In addition, a simple empirical relationship for the dielectric behavior is used to model the saturation of the induced polarization with increasing electric field. Unlike previous electrostrictive constitutive laws based on polynomial expansions, this consti tutive law depends on a manageable number of material constants. As an example, material constants for the model were determined from induced strain and dielectic data for a relaxor-ferroelectric based on lead magnesium niobate, Pb(Mg _1/3 Nb _2/3 )O ₃ -PbTiO ₃ -BaTiO ₃ (PMN-PT-BT). Finally, pre dictions of the material's mechanical behavior under constant electric field and its electrical behavior under constant applied stress are made.