Micromechanics of smart electrostrictive materials

Two micromechanics models have been developed to estimate the local fields, the effective properties, and the electro-mechanical coupling in smart electrostrictive materials.

The first model is based on the laminated plate theory. The nonlinear relations between the polarization and the electric field are considered in the model and an iterative formulation has been developed. Closed-form solutions are also obtained by ignoring the nonlinear terms in the constitutive relations between the polarization and the electric field. The effects of material properties, and the thickness and the number of plies on the mechanical and electrical response of the electrostrictive composite are studied. The model focuses on laminated composites and considers not only applied mechanical loads but also prescribed electric fields. However, it is not able to predict the deformation in the thickness direction of the composites.

The second model considers electrostrictive materials containing periodically distributed inhomogeneities. The local fields and the effective properties of three dimensional electrostrictive composites are predicted using the equivalent inclusion method (Esheby, 1957) and the Fourier series (Nemat-Nasser et al, 1993). Linear constitutive relations between the polarization and the electric field are employed in the model, which involves very few assumptions and can be applied to a broad class of electrostrictive composites. Furthermore, the effective properties of electrostrictive materials containing periodically distributed, aligned two dimensional (2-D) line cracks are studied. A 2-D line crack can be considered as a limiting case of a flat elliptical cylindrical void with its thickness approaching zero. Thus, a limiting process is employed to estimate the effective properties of an electrostrictive solid with periodically distributed, aligned 2-D line cracks.