Exploring Stiffness Gradient Effects in Magnetically Induced Metamorphic Materials via Continuum Simulation and Validation

Magnetic soft continuum robots are capable of bending with remote control in confined space environments, and they have been applied in various bioengineering contexts. As one type of ferromagnetic soft continuums, the Magnetically Induced Metamorphic Materials (MIMMs)-based continuum (MC) exhibits similar bending behaviors. Based on the characteristics of its base material, MC is flexible in modifying unit stiffness and convenient in molding fabrication. However, recent studies on magnetic continuum robots have primarily focused on one or two design parameters, limiting the development of a comprehensive magnetic continuum bending model. In this work, we constructed graded-stiffness MCs (GMCs) and developed a numerical model for GMCs' bending performance, incorporating four key parameters that determine their performance. The simulated bending results were validated with real bending experiments in four different categories: varying magnetic field, cross-section, unit stiffness, and unit length. The graded-stiffness design strategy applied to GMCs prevents sharp bending at the fixed end and results in a more circular curvature. We also trained an expansion model for GMCs' bending performance that is highly efficient and accurate compared to the simulation process. An extensive library of bending prediction for GMCs was built using the trained model.