Hard-Magnetic Soft Materials: Theory and Implementation

Magnetorheological elastomers (MREs) are active soft materials that respond to external magnetic fields, enabling applications in soft robotics, flexible electronics, and biomedical devices. Their behavior is governed by coupled magnetoelastic interactions, requiring complex computational models. Zhao et al. [1] proposed a simplified approach by treating the magnetic response as a material parameter, effectively decoupling the magnetoelastic problem into a purely elastic one. However, Dorfmann and Ogden [2] pointed out inconsistencies in this formulation, particularly regarding the constitutive relations, stress symmetry, and frame indifference. In this work, we refine Zhao’s model by integrating Dorfmann’s critiques to achieve a fully consistent decoupling. We identify force-like boundary conditions necessary to maintain physical accuracy and develop a finite element framework to solve the problem in both multiphysics and purely static scenarios. This approach enhances computational efficiency while ensuring a rigorous representation of MRE behavior. Our findings provide a more robust theoretical foundation for MRE modeling, with implications for the design of adaptive structures, biomedical actuators, and next-generation soft robotic systems. By addressing key theoretical and numerical challenges, this work advances the applicability of MREs in engineering and applied sciences.

References

1. R. Zhao, Y. Kim, S. A. Chester, P. Sharma, and X. Zhao, Mechanics of hard-magnetic soft materials, Journal of the Mechanics and Physics of Solids, 124:244–263, 2019.
2. L. Dorfmann and R. W. Ogden, Hard-magnetic soft magnetoelastic materials: energy considerations, International Journal of Solids and Structures, 294:112789, 2024.