Multiscale analysis of the coupling between mechanics and electrostatics in polymer chain networks

Electroactive polymers (EAPs) are materials capable of undergoing large deformations when stimulated by an electric field. At the present, there are models describing the polymers uncoupled electrostatic response under the influence of an electric field at both the macroscopic and the microscopic levels. Similarly, there are models describing the polymers reaction to purely mechanical loadings, macroscopically as well as through their molecular microstructure. The connection between the micro- and the macroanalyses shed light on the overall response of polymers and provide tools for optimizing their performances. In recent years, the electro-mechanical coupling in EAPs has been characterized and modeled at the macroscopic-continuum level. To the best of our knowledge, the corresponding analysis at the molecular microscopic level is not available yet. Our studies [1–2] is aimed towards understanding and analyzing the relation between the structure of EAPs and the forces and stresses that develop due to electrostatic excitations. To this end we introduce a multiscale model that assumes known geometries of the chains before and after the deformation. In addition, a variational approach is used leading to the development of an expression for the internally stored electrical enthalpy in the polymer and the corresponding stresses that develop. In a way of an example a polymer with specific chain structure under constant electric excitation and axial deformation is examined. The results are compared with a common phenomenological model as well as with experimental findings. REFERENCES [1] Cohen, N., deBotton, G. The electromechanical response of polymer networks with long-chain molecules. Math. Mech. Solids. 2014 (to appear). [2] Cohen, N., deBotton, G. Multiscale analysis of the electromechanical response of dielectric elastomers. Eur. J. Mech. A-Solids, 2014

Electromechanical Interplay in Deformable Dielectric Elastomer Networks

A systematic, statistical-mechanics-based analysis of the response of dielectric elastomers to coupled electromechanical loading is conducted, starting from the monomer level through the polymer chain and ending with closed-form expressions for the polarization and stress fields. It is found that the apparent response at the macrolevel is dictated by four microscopic parameters—the monomer type and polarizability and the chain length and density. Our analysis further reveals a new electrostrictive effect that either reinforces or opposes the polarization-induced deformation. The validity of the results is attested through comparisons with well-established experimental measurements of both the polarization field and the electrostrictive stress

All-organic dielectric-percolative three-component composite materials with high electromechanical response

By combining the high-dielectric copper phthalocyanine oligomer (PolyCuPc) and conductive polyanline (PANI) within polyurethane (PU) matrix an all-organic three-component dielectric-percolative composite with high dielectric constant is demonstrated. In this three-component composite system, the high-dielectric-constant PolyCuPc particulates enhance the dielectric constant of the PU matrix and this combined two-component dielectric matrix in turn serves as the high-dielectric-constant host for the PANI to realize percolative phenomenon and further enhance the dielectric response. As a result, an electromechanical strain of 9.3% and elastic energy density of 0.4 J/cm(3) under an electric field of 20 V/mum can be induced

Homogenized estimates for soft fiber-composites and tissues with two families of fibers

The macroscopic response of hyperelastic fiber composites is characterized in terms of the behaviors of their constituting phases. To this end, we make use of a unique representation of the deformation gradient in terms of a set of transversely isotropic invariants. Respectively, these invariants correspond to extension along the fibers, transverse dilatation, out-of-plane shear along the fibers, in-plane shear in the transverse plane, and the coupling between the shear modes. With the aid of this representation, it is demonstrated that under a combination of out-of-plane shear and extension along the fibers there is a class of nonlinear materials for which the exact expression for the macroscopic behavior of a composite cylinder assemblage can be determined. The macroscopic response of the composite to shear in the transverse plane is approximated with the aid of an exact result for sequentially laminated composites. Assuming no coupling between the shear modes, these results allow to construct a closed-form homogenized model for the macroscopic response of a fiber composite with neo-Hookean phases. A new variational estimate allows to extend these results to more general classes of materials. The resulting explicit estimates for the macroscopic stresses developing in composites and connective tissues with one and two families of fibers are compared with corresponding finite element simulations of periodic composites and with experimental results. Estimates for the critical stretch ratios at which the composites loose stability at the macroscopic level are compared with the corresponding numerical results too. It is demonstrated that both the primary stress–strain curves and the critical stretch ratios are in fine agreement with the corresponding numerical results

Optimization of Load-driven Soft Dielectric Elastomer Generators

The performance of energy harvesting generators based on dielectric elastomers is investigated in this contribution. The amount of energy extracted by a four-step load-driven cycle is constrained by structural instabilities due to the loss of tension, the electric breakdown and the ultimate stretch ratio. To identify the optimal cycle complying with these limits, we formulate a constraint optimization problem proving the dependency of the generator performance on the ultimate stretch ratio and, moreover, a universal limit on the dielectric strength beyond which the optimal cycle is independent of this parameter. Thus, we reveal that there is an upper bound on the amount of harvested energy that depends only on the ultimate stretch ratio

Electromechanical Interplay in Deformable Dielectric Elastomer Networks

A systematic, statistical-mechanics-based analysis of the response of dielectric elastomers to coupled electromechanical loading is conducted, starting from the monomer level through the polymer chain and ending with closed-form expressions for the polarization and stress fields. It is found that the apparent response at the macrolevel is dictated by four microscopic parameters—the monomer type and polarizability and the chain length and density. Our analysis further reveals a new electrostrictive effect that either reinforces or opposes the polarization-induced deformation. The validity of the results is attested through comparisons with well-established experimental measurements of both the polarization field and the electrostrictive stress

The Rayleigh-Lamb wave propagation in dielectric elastomer layers subjected to large deformations

The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of mechanically traction-free layer, which is an extension of the Rayleigh-Lamb problem in the purely elastic case. Two other loading configurations are accounted for too. Subsequently, numerical examples for the dispersion relations are evaluated for a dielectric solid governed by an augmented neo-Hookean strain energy. It is found that the the phase speeds and frequencies strongly depend on the electric excitation and pre-stretch. These findings lend themselves at the possibility of controlling the propagation velocity as well as filtering particular frequencies with suitable choices of the electric bias field

Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations