A new method to characterize the nonlinear magneto-viscoelasticity behavior of magneto-active elastomers under large amplitude oscillatory axial (LAOA) loading

Abstract The nonlinear viscoelasticity of magneto-active elastomers (MAEs) under large amplitude oscillatory shear (LAOS) loading has been extensively characterized. A reliable and effective methodology, however, is lacking for such characterizations under large amplitude oscillatory axial (LAOA) loading. This is partly due to complexities associated with experimental compression mode characterizations of MAEs and in-part due to their asymmetric stress–strain behavior leading to different elastic moduli during extension and compression. This study proposes a set of new nonlinear measures to characterize nonlinear and asymmetric behavior of MAEs subject to LAOA loading. These include differential large/zero strain moduli and large/zero strain-rate viscosity, which could also facilitate physical interpretations of the inter- and intra-cycle nonlinearities observed in asymmetric and hysteretic stress–strain responses. The compression mode stress–strain behavior of MAEs was experimentally characterized under different magnitudes of axial strain (0.025 to 0.20), strain rate (frequency up to 30 Hz) and magnetic flux density (0 to 750mT). The measured stress–strain responses were decomposed into elastic, viscous and viscoelastic stress components using Chebyshev polynomials and Fourier series. The stress decomposition based on Chebyshev polynomials permitted determination of equivalent nonlinear elastic and viscous stress components, upon which the proposed measures were obtained. An equivalent set of Fourier coefficients was also obtained for estimating equivalent elastic/viscous stress, thereby facilitating faster calculation of the proposed material measures. The proposed methodology is considered to serve as an effective tool for deriving constitutive models for describing nonlinear and asymmetric characteristics of MAEs.