3D constitutive modeling of electro-magneto-visco-hyperelastic elastomers: a semi-analytical solution for cylinders under large torsion-extension deformation

The rise of a new class of smart materials known as electro-magnetorheological elastomers (EMREs) requires comprehensive understanding of their electro-magneto-visco-hyperelastic behaviors. The aim of this paper is to develop a generalized three-dimensional (3D) continuum-based framework of the electro-magneto-visco-hyperelastic behaviors of EMREs. The finite strain model is established based on the linear viscoelasticity theory and non-linear electro-magneto-elastic framework. As EMRE devices can be used in a cylindrical shape undergoing shear and normal stresses in many engineering applications like artificial muscles, a boundary-value problem simulating torsion-extension deformations of EMRE cylinders is developed in the finite strain regime and solved semi-analytically. The behaviors of EMRE cylinders under different loading conditions such as purely mechanical loading, purely electric loading as well as full coupling between mechanical, electric and magnetic loading are studied in detail. Influence of different parameters such as electric field, magnetic field, applied strain (-rate) and their coupling on the induced moment and axial force of the EMRE cylinder as well as its relaxation and creep under torsion-extension loading is also examined. It is shown that EMREs have adaptive capability and great potential in applications where the stiffness needs to be controllable. Due to simplicity and accuracy, the model is expected to be used in the future studies dealing with the analysis of EMREs in particular cylinders under torsion-extension developments like 4D printing of artificial EMRE-based cylindrical muscles.