Effect of single-particle magnetostriction on the shear modulus of compliant magnetoactive elastomers

Abstract

The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al., Phys. Rev. E 93, 062503 (2016)10.1103/PhysRevE.93.062503]. The planar problem of magnetostriction in an MAE with magnetically soft inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain, and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is nonlinearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. The obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Padé approximants, which predicts that both the absolute and relative changes of the magnetic-field-dependent effective shear modulus will significantly increase with the growing concentration of filler particles.

Magnetorheological effect in elastomers containing uniaxial ferromagnetic particles

“…It is taken into account in equation (2.2) that the sample as a whole uniformly rotates by ψ/2 angle with shear, as shown in figure 1 [21]. The relative volume concentration of particles is equal to p = nV 0 .…”

“…The MRE caused by the rotation of magnetically uniaxial ferromagnetic particles in MAE was examined in reference [21]. However, in this paper the particles were considered of discus form for calculation simplification, although the spherical form of particles is most common in usual experimental investigations of MAE (see references [1][2][3][4]).…”

Renormalization of the critical exponent for the shear modulus of magnetoactive elastomers

“…In 19 , the equation connecting the shear angle ψ and the shear stress τ has been obtained. The effective shear modulus G e , relating the shear angle and the shear stress, has the following form where and p is the concentration of filler particles, is the shear modulus of the composite material in the absence of external magnetic field and m is the particle’s magnetization.…”

“…Therefore, there is no second term in Eq. ( 3 ) 19 . Figure 1b illustrates the shear test geometry and the characteristic angles.…”

“…Renormalization of the critical index by magnetic field (10) was performed on the basis of expression (4) for . This expression has been obtained in 19 in the approximation of a single inclusion with infinite large elastic moduli in an elastic medium with the shear modulus μ . Several approaches are known allowing one to improve calculation of effective coefficients based on the approximation of single inclusions using the self-consistency method.…”