Magnetostriction and Field Stiffening of Magneto-Active Elastomers

Abstract

Filled with certain amount of magnetic particles, an elastomer can be made magneto active for numerous applications. When a magneto-active elastomer (MAE) is subject to a homogeneous magnetic field, both magnetostriction and field-stiffening effect can be observed. Inspired by experimental observations and microstructure simulations in the literature, this paper presents a simplified phenomenological model for MAEs by considering a uniaxial deformation state. The model hypothesizes the field-stiffening effect to be a direct consequence of the inverse magnetostriction, i.e., the strain-dependent magnetization, in the context of finite deformation. By taking the elastic energy to be independent of magnetic field and the magnetization energy to be strain dependent, the model can capture both magnetostriction and field stiffening of an MAE. The functional form of the strain-dependent magnetization energy is determined by the underlying microstructure. MAEs with different microstructures exhibit different magnetostriction and field-stiffening behaviors. To predict the behavior of a specific MAE, one only needs to measure the effective permeability of an MAE as a function of the axial strain. The mathematical simplicity of the model could enable simulation and optimization of MAE-based devices under complex loading conditions.