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The influence of an external magnetic field on the static shear strain andthe effective shear modulus of a magnetoactive elastomer (MAE) is studiedtheoretically in the framework of a recently introduced approach to thesingle-particle magnetostriction mechanism [V. M. Kalita et al, Phys. Rev. E93, 062503 (2016)]. The planar problem of magnetostriction in an MAE with softmagnetic inclusions in the form of a thin disk (platelet) having the magneticanisotropy in the plane of this disk is solved analytically. An externalmagnetic field acts with torques on magnetic filler particles, createsmechanical stresses in the vicinity of inclusions, induces shear strain andincreases the effective shear modulus of these composite materials. It is shownthat the largest effect of the magnetic field on the effective shear modulusshould be expected in MAEs with soft elastomer matrices, where the shearmodulus of the matrix is less than the magnetic anisotropy constant ofinclusions. It is derived that the effective shear modulus is non-linearlydependent on the external magnetic field and approaches the saturation value inmagnetic fields exceeding the field of particle anisotropy. It is shown thatmodel calculations of the effective shear modulus correspond to aphenomenological definition of effective elastic moduli and magnetoelasticcoupling constants. Obtained theoretical results compare well with knownexperimental data. Determination of effective elastic coefficients in MAEs andtheir dependence on magnetic field is discussed. The concentration dependenceof the effective shear modulus at higher filler concentrations has beenestimated using the method of Pad\'e approximants, which correctly predictsthat both the absolute and relative changes of the magnetic-field dependenteffective shear modulus will significantly increase with the growingconcentration of filler particles.

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