Theory of dielectric elastomers

The combination of polymers with nano- or microsized solid materials displays novel and often enhancedproperties compared to the traditional materials. They can open up possibilities for new technologicalapplications. Materials whose physical properties can be varied by application of magnetic fields belongto a specific class of smart materials. The broad family of magnetic field-controllable soft materialsincludes ferrofluids, magneto-rheological fluids, magnetic gels, and magnetic elastomers. The magneticgels and elastomers (magnetoelasts) represent a new type of composite and consist of small magneticparticles, usually in the nanometer to micron range, dispersed in a highly elastic polymeric matrix.The magnetic particles can be incorporated into the elastic body either randomly or in ordered structure.If a uniform magnetic field is applied to the reactive mixture during the cross-linking process, particlechains form and become locked into the elastomer. The resulting composites exhibit anisotropic properties.

Magnetic Field-Responsive Smart Polymer Composites

A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their coupled magnetoelastic response, MREs are finding an increasing number of engineering applications. In this work, we present a combined experimental and theoretical study of the macroscopic response of a particular MRE consisting of a rubber matrix phase with spherical carbonyl iron particles. The MRE specimens used in this work are cured in the presence of strong magnetic fields leading to the formation of particle chain structures and thus to an overall transversely isotropic composite. The MRE samples are tested experimentally under uniaxial stresses as well as under simple shear in the absence or in the presence of magnetic fields and for different initial orientations of their particle chains with respect to the mechanical and magnetic loading direction. Using the theoretical framework for finitely strained MREs introduced by Kankanala and Triantafyllidis (2004) , we propose a transversely isotropic energy density function that is able to reproduce the experimentally measured magnetization, magnetostriction and simple shear curves under different prestresses, initial particle chain orientations and magnetic fields. Microscopic mechanisms are also proposed to explain (i) the counterintuitive effect of dilation under zero or compressive applied mechanical loads for the magnetostriction experiments and (ii) the importance of a finite strain constitutive formulation even at small magnetostrictive strains. The model gives an excellent agreement with experiments for relatively moderate magnetic fields but has also been satisfactorily extended to include magnetic fields near saturation.

Experiments and modeling of iron-particle-filled magnetorheological elastomers

Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. Due to their strong magnetoelastic coupling response MREs are finding an increasing number of engineering applications, thus necessitating appropriate theoretical descriptions which is the objective of this work. Two different continuum formulations for MREs are presented: an Eulerian (current configuration) based approach using the second law of thermodynamics plus the conservation laws method of mechanics and a new, Lagrangian (reference configuration) based formulation based on the unconstrained minimization of a potential energy functional. It is shown that both approaches yield the same governing equations and boundary conditions. Following a discussion of general properties of the free energy function of MREs, we use a particular such function to illustrate the magnetoelastic coupling phenomena in a cylinder subjected to traction or torsion under the presence of external magnetic fields.

On finitely strained magnetorheological elastomers

In this paper we first summarize the equations governing the deformation of magneto-sensitive (MS) elastic solids with particular reference to elastomers whose mechanical properties may be changed rapidly by the application of a magnetic field. These 'smart materials' typically consist of micron-sized ferrous particles dispersed within an elastomeric matrix. Constitutive relations for isotropic MS-elastic solids are examined. The equations are then applied to a representative geometry appropriate for applications, that in which the material is confined to a circular cylindrical tube in the presence of a radial magnetic field. The material is then subject to an axial shear deformation. Results are illustrated for two specific material models, for each of which the shear stiffness of the material increases with the magnetic field strength, as observed in experiments on MS elastomers.

Magnetoelastic modelling of elastomers

In this paper we first summarize, in a simple form, the equilibrium equations for a solid material capable of large magnetoelastic deformations. Such equations are needed for the analysis of boundary-value problems for elastomers endowed with magnetic properties by the embedding of distributions of ferrous particles. The general constitutive law for an isotropic material in the presence of a magnetic field is described and expressed in a compact form, with either the magnetic field or the magnetic induction as the independent magnetic variable. The equations are applied, in the case of an incompressible material, to the solution of representative problems involving circular cylindrical geometry, specifically the helical shear of a circular cylindrical tube, its specializations to axial and azimuthal shear, and the problem of extension and torsion of a solid circular cylinder. For each problem a general formulation is afforded without specialization of the (isotropic) constitutive law, and then specific results are discussed briefly for special choices of such laws. It is noted, in particular, that certain restrictions may be placed on the class of constitutive laws for a considered combination of deformation and magnetic field to be admitted.

Nonlinear magnetoelastic deformations

Magneto-sensitive (MS) elastomers are “smart materials” whose mechanical properties may be changed rapidly by the application of a magnetic field Such materials typically consist of micron-sized ferrous particles dispersed within an elastomeric matrix The equations governing deformations of these materials were discussed in a recent paper by the present authors and applied in a particular specialization of the constitutive model to the problem of axial shear of a circular cylindrical tube subject to a radial magnetic field In the present paper we develop the governing equations for a more general form of constitutive model and provide alternative forms of the equations, including a Lagrangian formulation To illustrate the theory the problem of azimuthal shear of a circular cylindrical tube is formulated and then solved for a specific constitutive law with a magnetic field that is initially radial The results, which show the stiffening of the azimuthal shear stress/strain response with increasing magnetic field strength, are illustrated graphically

Nonlinear magnetoelastic deformations of elastomers

Nonlinear electroelastostatics: Incremental equations and stability

Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and some differences highlighted.

A. Dorfmann

Papers

Magnetoelastic modelling of elastomers

Nonlinear magnetoelastic deformations

Nonlinear magnetoelastic deformations of elastomers

Nonlinear electroelastostatics: Incremental equations and stability

Nonlinear electroelastostatics: a variational framework