Gal deBotton

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.

Variational estimates for the creep behaviour of polycrystals

A variational procedure is developed for estimating the effective constitutive behaviour of polycrystalline materials undergoing high-temperature creep. The procedure is based on a new variational principle allowing the determination of the effective potential function of a given nonlinear polycrystal in terms of the corresponding potential for a linear comparison polycrystal with an identical geometric arrangements of its constituent single-crystal grains. As such, it constitutes an extension, to locally anisotropic behaviour, of the variational procedure developed by Ponte Castañeda (1991) for nonlinear heterogeneous media with locally isotropic behaviour. By way of an example, the procedure is applied to the determination of bounds of the Hashin-Shtrikman type for the effective potentials of statistically isotropic nonlinear polycrystals. The bounds are computed for the special class of untextured FCC polycrystals with isotropic pure power-law viscous behaviour, first considered by Hutchinson (1976), in the context of a calculation of the self-consistent type. The new bounds are found to be more restrictive than the corresponding classical Taylor-Bishop-Hill bounds, and also more restrictive, if only slightly so, than related bounds of the Hashin-Shtrikman type by Dendievel et al. (1991). The new procedure has the advantage over the self-consistent procedure of Hutchinson (1976) that it may be applied, without any essential complications, to aggregates of crystals with slip systems exhibiting different creep rules - with, for example, different power exponents - and to general loading conditions. However, the distinctive feature of the new variational procedure is that it may be used in conjunction with other types of known bounds and estimates for linear polycrystals to generate corresponding bounds and estimates for nonlinear polycrystals.

Electroactive Heterogeneous Polymers: Analysis and Applications to Laminated Composites

A general framework for characterizing the behavior of electroactive heterogeneous media is developed. The governing equations of the coupled electromechanical problem are obtained together with the appropriate boundary and interface continuity conditions. Preliminary calculations for the class of sequentially laminated composites are carried out. These calculations demonstrate that the electromechanical coupling can be improved by considering non-homogeneous electromechanical actuators. In particular, we show that the overall response of a composite actuator can be better than the responses of its constituents. These findings are in agreement with recent experimental work showing that the limitations of these actuators can be overcome by making composites of flexible and high dielectric modulus materials.

Analysis of microstructural induced enhancement of electromechanical coupling in soft dielectrics

Electroactive polymers (EAP) are capable of large deformations in response to electric stimulus. A sketch of a planar actuator is shown in Fig. 1. The top and bottom faces of the soft dielectric are covered with compliant electrodes [1] inducing an electric field through the material. The resulting Maxwell stress leads to the deformation of the material. The variety of possible applications of these “artificial muscles” motivated an intensive search for appropriate polymers. Indeed, recent experimental studies achieved remarkable milestones in terms of the magnitudes of the actuation strains [1–7]. In parallel, the concept of enhancing the responsiveness of EAP devices by means of snap-through unstable mechanisms was examined too [8–10]. However, these studies did not tackle the main limitation of EAPs, namely the huge electric fields needed for meaningful actuations. We address this challenge and investigate a mechanism by which the exciting electric field can be reduced by an order of magnitude. In this regard we recall that recent experimental works [7, 11] involving soft elastomers with high dielectric particles demonstrate an improved response of the heterogeneous systems. In agreement, theoretical studies [12, 13] of idealized heterogeneous dielectrics predicted an enhancement of the electromechanical coupling. In this work the non-linear theory of electroelasticity at finite strains [14–17] is adopted and an exact analytical solution for an idealized heterogeneousElectroactive soft elastomers require huge electric field for a meaningful actuation. We demonstrate, by means of numerical simulation, that this can be dramatically reduced and large deformations can be achieved with suitably designed heterogeneous actuators. The mechanism by which the enhancement is attained is illustrated with the aid of both idealized and periodic models.

On the homogenized yield strength of two-phase composites

This paper is concerned with the determination of the effective yield strength of two-phase, rigid-perfectly plastic composite materials. The individual phases are assumed to satisfy, for simplicity, incompressible, isotropic yield criteria of the Mises type. The volume fractions of the constituent phases are prescribed, but their distribution within the composite is otherwise arbitrary. Using the homogenization framework of Suquet (1983) to define the homogenized, or effective, yield strength domain of rigid-perfectly plastic composites, a variational statement is introduced allowing the estimation of the associated effective dissipation functions of plastic composites in terms of the effective dissipation functions of corresponding classes of linearly viscous comparison composites. Thus the variational statement suggests a procedure for generating bounds and estimates for the effective yield strength of rigid-perfectly plastic composites from well-known bounds and estimates for the effective properties of the corresponding linear comparison composites. Sample results are given in the form of upper bounds and lower estimates of the Hashin-Shtrikman type for the effective yield strength of two-phase composites with overall isotropy. Additionally, estimates and bounds are also given for the effective strength domains of two-phase laminated and fibre-reinforced composites, with overall transverse isotropy.

Elastoplastic constitutive relations for fiber-reinforced solids

Abstract In this paper, we make use of a procedure for estimating the effective properties of nonlinear composite materials, proposed recently by Ponte Castaneda (1991, J. Mech. Phys. Solids 39 , 45–71), to study the effective constitutive behavior of ductile, fiber-reinforced composites. Both estimates and rigorous bounds are obtained for the effective energy functions of multiple-phase, fiber composites with general ductile behaviors (in the context of deformation theory of plasticity) for the isotropic constituent phases. The resulting expressions for the energy functions may be differentiated in a straightforward manner to obtain corresponding estimates for the anisotropic effective stress-strain relations. Explicit calculations are carried out for the case of an aluminum-matrix composite reinforced with boron fibers. The results reveal some interesting features distinguishing the constitutive behavior of ductile-matrix, fiber-reinforced composites from that of linear-elastic, fiber-reinforced composites. One such feature is the strong coupling between the dilatational and distortional modes for the ductile fiber composites. Finally, comparisons are made with available experimental data.

On the ductility of laminated materials

Abstract A laminated material is one of the few composite systems for which the effective constitutive behavior can be determined exactly. This is well known for laminated composites with linearly elastic phases in prescribed volume fractions. For these composites, explicit expressions for the effective moduli have been available for at least 30 years. However, it appears that corresponding expressions for the effective energy functions of laminated composites with phases exhibiting nonlinear constitutive behavior are currently unavailable. In this paper, we make straightforward use of a new variational procedure, recently developed by one of the authors, to obtain simple expressions for the effective energy functions of laminated composites with Isotropie ductile phases in prescribed volume fractions. The same expressions are given an alternative derivation, starting directly from the classical variutional principles. Explicit results are then computed for ductile/brittle systems, such as aluminum/alumina laminates, and also for laminated composites made up of two perfectly plastic phases with different yield stresses. The results—which are representative of other anisotropic geometries, such as fiber-reinforced solids—exhibit a strong coupling between different loading modes that is enhanced by material nonlincarity.

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

Abstract The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular to the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity. Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.

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 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.

High-rank nonlinear sequentially laminated composites and their possible tendency towards isotropic behavior

Abstract This work is concerned with the determination of the effective behavior of sequentially laminated composites with nonlinear behavior of the constituting phases. An exact expression for the effective stress energy potential of two-dimensional and incompressible composites is introduced. This allows to determine the stress energy potential of a rank- N sequentially laminated composite with arbitrary volume fractions and lamination directions of the core laminates in terms of an N -dimensional optimization problem. Stress energy potentials for sequentially laminated composites with pure power-law behavior of the phases are determined. It is demonstrated that as the rank of the lamination becomes large the behaviors of certain families of sequentially laminated composite tend to be isotropic. Particulate composites with both, stiffer and softer inclusions are considered. The behaviors of these almost isotropic composites are, respectively, softer and stiffer than the corresponding second-order estimates recently introduced by Ponte Castaneda (1996).