The Mechanics of Elastomers Filled with Electro-Active Solid and Fluid Inclusions
Advisor: Professor Oscar Lopez-Pamies
The overarching objective of this dissertation work is to develop analytical and computational tools
to understand and describe from bottom up the homogenized or macroscopic response of elastomers filled with inclusions exhibiting interface phenomena at the elastomer-inclusions interfaces. The focus is on the electromechanical response of two classes of material systems: i) elastomers filled with solid inclusions surrounded by space charges and ii) elastomers filled with fluid inclusions.
In preparation to deal with the various homogenization problems that are considered, a general twopotential constitutive framework is first put forth to describe the electromechanical behavior of elastomers in the setting of electro-quasistatics. The framework is used to construct a specific model for isotropic incompressible elastomers that accounts for the non-Gaussian elasticity, the nonlinear viscosity, and the deformation-dependent electrostriction typical of emerging classes of dielectric elastomers.
Having established an appropriate constitutive framework for the electromechanical behavior of elastomers, several limiting homogenization problems are then considered. The first one corresponds to the homogenization of the time-dependent dielectric response of elastomers filled with solid inclusions surrounded by space charges in the absence of deformation. It is shown that the presence of suitably distributed space charges can lead to extreme dielectric behaviors, some of which have been recently observed in spectroscopy experiments on various polymer nanoparticulate composites.
The second homogenization problems considered are those of the nonlinear viscoelastic response of Gaussian elastomers with constant viscosity filled with isotropic distributions of either rigid inclusions or vacuous bubbles under arbitrary quasi-static finite deformations. Strikingly, in spite of the fact that the underlying elastomers have constant viscosity, the solutions reveal that the viscoelastic response of the filled/porous elastomers exhibits an effective viscosity that is nonlinear. What is more, the solutions indicate that the viscoelastic response of the filled/porous elastomers features the same type of short-range-memory behavior— as opposed to the generally expected long-range-memory behavior — as that of the underlying elastomers.
Finally, the last homogenization problem that is considered is that of the nonlinear elastic response of
elastomers filled with liquid inclusions under finite quasistatic deformations, wherein the elastomer-inclusions interfaces exhibit their own elastic behavior. The focus is on the non-dissipative case when the elastomer is a hyperelastic solid, the liquid making up the inclusions is a hyperelastic fluid, the interfaces separating the solid elastomer from the liquid inclusions feature their own hyperelastic behavior (which includes surface tension as a special case), and the inclusions are initially n-spherical (n = 2, 3) in shape. The macroscopic behavior of such filled elastomers turns out to be that of a hyperelastic solid, albeit one that depends directly on the size of the inclusions and the constitutive behavior of the interfaces.