Electrostriction: material parameters and stress/strain constitutive relations

Abstract

The objective of this work is to formulate stress/strain constitutive relations in terms of material parameters. A secondary aim is to introduce a sequence of independent tests sufficient to evaluate these parameters. A stress constitutive equation in polarizable materials follows from the Helmholtz free energy related to a unit volume of deformed material. Similarly, a strain constitutive equation is obtained from the Gibbs free energy. These two relations explicitly account for the contribution of elastic deformation, electrostatic interactions of surface charges and the electrostriction effect. Both formulations of the constitutive relations are equivalent, yet yield different sets of electrostriction coefficients. For instance, a complete set of electrostriction parameters can be formulated based on either strain or stress dielectric rules. Strain–dielectric or stress–dielectric measurements necessitate monitoring variations in dielectric constants with the applied strains or stresses. Such measurements demand well-defined distribution of strains, stresses and the electric field across the sample. Meeting these requirements by traditional techniques used for dielectric measurements is quite challenging. This article introduces an experimental technique utilizing a rosette of planar dielectric sensors to overcome many of the experimental difficulties. Using both strain and stress definitions, electrostriction parameters are measured for a polycarbonate specimen. The obtained coefficients are in good agreement with the values provided by a microscopic model. The proposed description is valid for arbitrary anisotropic materials, while isotropic materials are considered as an illustrative example. In addition, all necessary relations for materials having cubic symmetry are provided in an appendix.

Acknowledgments

The author would like to thank Professor R. Rowlands from UW-Madison and Dr R. Perez from TAMU for helpful discussions, and Ho Young Lee for providing experimental data. This work was supported in part by NSF Grant #CMS-0437890.