A homogenization-based magneto-viscoelastic constitutive model for soft magnetorheological elastomers

Abstract

Soft magnetorheological elastomers (s-MREs) are a kind of smart composites composed of a mechanically soft viscoelastic matrix filled with soft magnetic particles. This work provides a standard two-potential framework for the constitutive model of s-MREs incorporating viscous dissipative mechanism, which rigorously adheres to the physical constrains imposed by even magneto-mechanical coupling, material frame indifference, material symmetry requirement and the second law of thermodynamics. Moreover, a numerical homogenization framework is developed to compute the macroscopic homogenized response of s-MREs. Based on the numerical homogenization results, an explicit free energy function and a dissipative potential that rely on the properties of the underlying microstructure are constructed. Only a small number of model parameters are calibrated by means of the numerically average magnetostriction responses under purely magnetic loading. The validity of the developed model is assessed by comparing the model predictions to the numerical homogenization results, under various matrix material parameters, magnetic loading rates and magneto-mechanical loading paths. The results demonstrate that the proposed model exhibits good agreement with the numerical homogenization results in all cases considered. Finally, the model is employed to solve for the magnetostriction of s-MRE specimens in the air medium. It is found that the simulation results are in excellent agreement with the experimental data reported in the literature. In addition, our research reveals that the proposed model provides a more profound insight into the underlying physical mechanisms behind the magnetostrictive behaviors of the s-MREs.