Elastic Dielectric Properties Research Articles

Saturation effects on the joint elastic–dielectric properties of carbonates

We used a common microstructural model to investigate the cross-property relations between elastic wave velocities and dielectric permittivity in carbonate rocks. A unified model based on validated self-consistent effective medium theory was used to quantify the effects of porosity and water saturation on both elastic properties (compressional and shear wave velocities) and electromagnetic properties (dielectric permittivity). The results of the forward models are presented as a series of cross-plots covering a wide range of porosities and water saturations and for microstructures that correspond to different predominant aspect ratios. It was found that dielectric permittivity correlated approximately linearly with elastic wave velocity at each saturation stage, with slopes varying gradually from positive at low saturation conditions to negative at higher saturations. The differing sensitivities of the elastic and dielectric rock properties to changes in porosity, pore morphology and water saturation can be used to reduce uncertainty in subsurface fluid saturation estimation when co-located sonic and dielectric surveys are available. The joint approach is useful for cross-validation of rock physics models for analysing pore structure and saturation effects on elastic and dielectric responses.

The Overall Elastic Dielectric Properties of Fiber-Strengthened/Weakened Elastomers

By employing recent results (Lopez-Pamies, O., 2014, “Elastic Dielectric Composites: Theory and Application to Particle-Filled Ideal Dielectrics,” J. Mech. Phys. Solids, 64, p. 6182 and Spinelli, S. A., Lefèvre, V., and Lopez-Pamies, O., “Dielectric Elastomer Composites: A General Closed-Form Solution in the Small-Deformation Limit,” J. Mech. Phys. Solids, 83, pp. 263–284.) on the homogenization problem of dielectric elastomer composites, an approximate solution is generated for the overall elastic dielectric response of elastomers filled with a transversely isotropic distribution of aligned spheroidal particles in the classical limit of small deformations and moderate electric fields. The solution for such a type of dielectric elastomer composites is characterized by 13 (five elastic, two dielectric, and six electrostrictive) effective constants. Explicit formulae are worked out for these constants directly in terms of the elastic dielectric properties of the underlying elastomer and the filler particles, as well as the volume fraction, orientation, and aspect ratio of the particles. As a first application of the solution, with the objective of gaining insight into the effect that the addition of anisotropic fillers can have on the electromechanical properties of elastomers, sample results are presented for the case of elastomers filled with aligned cylindrical fibers. These results are confronted to a separate exact analytical solution for an assemblage of differential coated cylinders (DCC), wherein the fibers are polydisperse in size, and to full-field simulations of dielectric elastomer composites with cylindrical fibers of monodisperse size. These results serve to shed light on the recent experimental findings concerning the dielectric elastomers filled with mechanically stiff fibers. Moreover, they serve to reveal that high-permittivity liquid-like or vacuous fibers—two classes of filler materials yet to be explored experimentally—have the potential to significantly enhance the electrostriction capabilities of dielectric elastomers.

Dielectric elastomer composites: A general closed-form solution in the small-deformation limit

A solution for the overall electromechanical response of two-phase dielectric elastomer composites with (random or periodic) particulate microstructures is derived in the classical limit of small deformations and moderate electric fields. In this limit, the overall electromechanical response is characterized by three effective tensors: a fourth-order tensor describing the elasticity of the material, a second-order tensor describing its permittivity, and a fourth-order tensor describing its electrostrictive response. Closed-form formulas are derived for these effective tensors directly in terms of the corresponding tensors describing the electromechanical response of the underlying matrix and the particles, and the one- and two-point correlation functions describing the microstructure. This is accomplished by specializing a new iterative homogenization theory in finite electroelastostatics (Lopez-Pamies, 2014) to the case of elastic dielectrics with even coupling between the mechanical and electric fields and, subsequently, carrying out the pertinent asymptotic analysis.Additionally, with the aim of gaining physical insight into the proposed solution and shedding light on recently reported experiments, specific results are examined and compared with an available analytical solution and with new full-field simulations for the special case of dielectric elastomers filled with isotropic distributions of spherical particles with various elastic dielectric properties, including stiff high-permittivity particles, liquid-like high-permittivity particles, and vacuous pores.

The overall elastic dielectric properties of a suspension of spherical particles in rubber: An exact explicit solution in the small-deformation limit

A solution is constructed for the homogenization problem of the elastic dielectric response of rubber filled with a random isotropic distribution of polydisperse spherical particles in the classical limit of small deformations and moderate electric fields. In this limit, the overall elastic dielectric response is characterized by five (two elastic, one dielectric, and two electrostrictive) effective constants. Explicit formulas are derived for these constants directly in terms of the corresponding constants describing the elastic dielectric response of the underlying rubber and the filler particles, as well as the concentration of particles. By means of comparisons with finite-element simulations, these formulas are shown to also be applicable to isotropic suspensions of monodisperse spherical particles, provided that the particle concentration is sufficiently away from percolation. With the aim of gaining physical insight into the extreme enhancement in electrostrictive properties displayed by emerging dielectric elastomer composites, specific results are examined for the case of suspensions wherein the rubber is incompressible and the particles are mechanically rigid and of infinite permittivity.

Some simple explicit results for the elastic dielectric properties and stability of layered composites

A string of partial results—aimed at shedding light on the behavior of dielectric elastomer composites—have been recently reported in the literature for the macroscopic electroelastic response and stability of layered composites with ideal elastic dielectric phases. Such results have been restricted to two phases and plane-strain loading conditions. It is the purpose of this paper to place on record simple explicit expressions for the macroscopic electroelastic response and stability of layered composites with any number of ideal elastic dielectric phases under general electromechanical loading conditions. Inter alia, these expressions provide insight into a variety of practical and theoretical issues in relation to the modeling of elastic dielectric composites with anisotropic microstructures, ranging from the choice of invariants to describe their free energy function to the effects of interphasial phenomena.This paper also places on record the conditions of ordinary and strong ellipticity for elastic dielectrics in full generality.