Programmable inverse design framework for morphing hard-magnetic soft materials

Abstract

As a type of shape-programmable soft materials, hard-magnetic soft materials (HMSMs) exhibit rapid and reversible deformations under applied magnetic fields, showing promise for soft robotics, flexible electronics, and biomedical devices. The realization of various controllable shape transformations is crucial to the rational design of relevant applications. However, due to highly nonlinear relation between large deformations and actuation fields, how to quantitatively design the residual magnetization distribution and driving magnetic field in the initial configuration to morph into a target shape remains a challenge. Here, we propose an inverse design strategy for targeted bending dominated deformations of hard-magnetic beam structures, which combines a 3D hard-magnetic rod model with intelligent optimization algorithms, enabling hard-magnetic beams to achieve multi-step pre-designed shapes by programming the magnetization densities and external magnetic fields in the initial undeformed configuration. Based on the proposed framework, we explore diverse target shapes under various magnetization modes, and compare the numerical accuracy and efficiency of three intelligent optimization algorithms. Moreover, we demonstrate multi-step inverse design examples in which the same sample achieves a flexible transition of various pre-designed deformation modes. The results demonstrate that the presented strategy offers an innovative and versatile approach for programmable inverse design of morphing magnetically-driven flexible devices and soft robotics.