ABSTRACT
We consider an electro-and magneto-sensitive deformable body in the three-dimensional Euclidean space. Let X be a position vector of a material point in the reference configuration. The deformation gradient is defined by
F = ,Grad x( ) (1)
where x is the counterpart of X in the current configuration (for the vector and tensor notation we refer to (Itskov 2015)). The relative volume change is then expressed by
J = .det F (2)
In the following, we deal with hyperelastic materials whose behavior can uniquely be defined by a free energy function. It is usually given per unit volume of the reference configuration and expressed as a function of the deformation gradient or the right Cauchy-Green tensor C F FT as
Ψ = Ψ .ˆ ( )C (3)
1 INTRODUCTION
Electro-and magneto-rheological elastomers result from the applying an electro-or, respectively, magnetic field to the rubber mixture during vulcanization (see, e.g. (Chen, Gong, & Li 2007)). Electro-or magneto-sensitive particles (like for example iron particles) added to the elastomer align along the applied field, which leads to mechanical anisotropy. From the technological point of view, the most important feature of electro-and magnetosensitive elastomers is their coupled electro-and magneto-mechanical response. Thus, electric or magnetic fields applied to the elastomer can contactlessly change stress-strain state or vice versa. This coupled response makes electro-and magneto-sensitive elastomers very attractive for such applications as tunable vibration dampers, touchscreen displays or magnetic actuators, just to mention only few examples.
