Dynamic modeling and control of hard-magneto-viscoelastic plates

Hard-magnetic soft materials can rapidly respond to remote magnetic fields, offering great potential for soft robotics and biomedical applications. Herein, this study proposes a systematic computational framework for dynamic modeling and control of hard-magneto-viscoelastic (HMVE) plates actuated by magnetic fields. The dynamic model of the hard-magneto-viscoelastic plate is developed using the absolute nodal coordinate formulation (ANCF) to accurately capture its dynamic responses with geometric nonlinearity. The constitutive model of ideal hard-magnetic soft materials, incorporating the Kelvin-Voigt dissipation, is embedded into a four-point fully parametrized ANCF plate element. The element internal forces and their Jacobians are derived. Then the dynamic equations of the HMVE plate system are constructed and numerically solved by the implicit generalized-α time integration. Furthermore, a novel strategy of dynamic feedforward control for the plate system is proposed. The inverse dynamic solver is constructed to establish the relation between the configuration with target coordinates and the applied magnetic field. This solver fully accounts for the inertial effects within the implicit time integration, maintaining the same level of accuracy as the forward solver of dynamic modeling. Finally, numerical simulations and corresponding experimental validations are conducted to demonstrate the effectiveness of the proposed dynamic modeling and control methods for HMVE plates. Moreover, a novel particle transport application is explored through the HMVE plate control in the case studies. This work may inspire further advances in precise prediction, dynamic control, and applications of soft robots composed of actively deformed plates.