This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. In the rst step, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theory with domain interactions incorporated through mean eld relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. In the second step, hysteresis is incorporated through the consideration of domain wall dynamics and the quanti cation of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. In the rst step, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theory with domain interactions incorporated through mean eld relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. In the second step, hysteresis is incorporated through the consideration of domain wall dynamics and the quanti cation of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

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 electrically 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 constitutive 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, predictions of the material's mechanical behavior under constant electric field and its electrical behavior under constant applied stress are made.

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Three-dimensional finite element computations have been done to study the growth of initially spherical voids in periodic cubic arrays. The numerical method is based on finite strain theory and the computations account for the interaction between neighboring voids. The void arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear, and high triaxial stress. The macroscopic stress-strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction, and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field.