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

TL;DR

This paper presents a theoretical study of how an external magnetic field influences the shear modulus of magnetoactive elastomers through single-particle magnetostriction, with results aligning well with experimental data.

Contribution

It introduces an analytical model for the magnetostriction mechanism affecting the shear modulus in MAEs with soft magnetic inclusions, highlighting non-linear magnetic field dependence.

Findings

Effective shear modulus increases with magnetic field and saturates beyond particle anisotropy field.

The effect is most significant in MAEs with soft elastomer matrices.

Higher filler concentrations amplify the magnetic-field dependence of the shear modulus.

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)]. The planar problem of magnetostriction in an MAE with soft magnetic 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 non-linearly 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. 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 Pad\'e approximants, which correctly 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.