Numerical study on the instabilities of hard-magnetic soft materials with viscoelastic effects

As a type of soft composite material, the hard-magnetic soft materials (HMSM) can retain high residual magnetization due to the high-coercivity of hard-magnetic particles. Meanwhile, the inherent viscoelasticity of the soft polymer matrix usually causes the rate dependent behavior and affects the stability of HMSM. The effects of viscoelasticity on the finite deformation and instability of HMSM are studied in this paper. A numerical model is developed for magneto-mechanical coupled problems of the viscoelastic HMSM. With this model, the instabilities of two typical HMSM structures (i.e. beam and spherical shell) with viscoelastic effects are investigated, including the buckling and snap-through instability. The results show that the viscoelastic effects delay the onset of instability and suppress the snap-back phenomenon during the unloading process. In addition, three different buckling behaviors (i.e. fully relaxed immediate buckling, elastic immediate buckling and the delayed buckling) at different loading rate ranges are observed in both beam and spherical shell. This work provides an effective numerical model to analyze the finite deformation and instabilities of viscoelastic HMSM and may guide the design of HMSM devices.