Stability of Hard-Magnetic Soft Materials Under Bi-Axial Compression

Abstract

Hard-magnetic soft materials (HMSMs) are susceptible to wrinkling instability, especially under compressive loading, which can significantly affect their functional performance. In this study, we report a theoretical framework based on continuum mechanics principles and nonlinear field theory of HMSMs to analyze both equal and unequal bi-axial deformation in planar hard-magnetic soft plates. The constitutive behavior of the HMSMs is modeled using a hyperelastic incompressible neo-Hookean model in conjunction with the ideal HMSM model. The presented theoretical framework incorporates classical tension field theory for predicting the onset and evolution of stable states in HMSM plates. A parametric study is conducted to highlight the effect of applied magnetic flux density, remanent magnetization, and bi-axiality ratio on the deformation behavior and stability of the HMSM plate. The insights gained from this study contribute toward the design and development of remotely controlled next-generation magneto-active polymer (MAP)-based soft robotic systems. © 2025 Elsevier B.V., All rights reserved.