Dynamic modeling and analysis of viscoelastic hard-magnetic soft actuators with thermal effects

Hard-magnetic soft materials (HMSMs) are a class of magnetoactive smart polymers capable of sustaining a high residual magnetic flux density and can undergo large actuation strains under an external magnetic excitation. Due to these exceptional characteristics, soft actuators based on HMSMs hold enormous potential for remote-controlled applications. The temperature and viscoelasticity considerably influence the performance of these materials during the operation. This work aims to develop an analytical framework for modeling the dynamic behavior of a planar hard-magnetic soft actuators (HMSA) considering temperature and viscoelastic effects. The constitutive behavior of the viscoelastic HMSA is described by employing an incompressible neo-Hookean model in conjunction with a Zener rheological model and the Rayleigh dissipation function. The dynamic governing differential equations of motion are derived by utilizing the non-conservative form of the Euler–Lagrange equation. This study delves into the collective influence of temperature and viscoelastic properties on the stability, periodicity, and resonance characteristics of nonlinear vibrations exhibited by HMSM-based planar actuator subjected to dynamic magnetic loading, presenting the findings through time-history responses, Poincaré maps, and phase-plane plots. The presented results can help in the efficient and robust design of HMSM-based actuators and can also serve as an initial step toward the development of advanced actuators exposed to dynamic loading under variable temperatures for diverse applications in the fields of engineering and medicine.