Model order-reduction for hard-magnetic soft beams with large viscoelastic deformations

Hard-magnetic soft beams (HMSBs) exhibit large viscoelastic deformations under magnetic fields, enabling promising applications in soft robotics. However, the inherent material viscoelasticity, geometric nonlinearity from large deformation, and high dimensions of the accurate models hinder real-time dynamic simulations. To overcome these challenges, an accurate dynamic model that accounts for large viscoelastic deformations is first developed for HMSBs and an efficient model order-reduction approach is then proposed to obtain an accurate nonlinear reduced-order model (NLROM). Key innovations lie in three aspects: integrating a generalized Maxwell model into the absolute nodal coordinate formulation for HMSBs; constructing the NLROM by projecting generalized coordinates onto a modal subspace enriched with modal derivatives; and deriving pre-integrated viscoelastic and external forces to greatly increase efficiency. Numerical results show that the NLROM accurately captures large viscoelastic deformations while reducing computational cost and the number of degrees of freedom by over 90%. This work offers an accurate and efficient dynamics model for real-time simulations of magnetically actuated soft robots.