Inverse programming of ferromagnetic domains for 3D curved surfaces of soft materials

Reconfigurable 3D surfaces found in nature are inspiring for advancing technologies in smart materials, soft robotics and precision medicine. Although ferromagnetic soft materials enable the dynamic and reversible regulation of 3D shape transformation, challenges lie in the programming of ferromagnetic domains to design 3D curved surfaces, because previous methods based on optimization models or machine learning incur a computational burden. Here we report the template-free, inverse programming of hard-magnetic domains embedded in a soft material. This method can trigger shape morphing into 3D curved surfaces under the actuation of a magnetic field. A ferromagnetic hydrogel resin and photodosage-based printing method are developed to prepare a ferromagnetic soft material with controllable distribution of crosslinking densities, resulting in heterogeneous swelling upon solvent stimulation to transform the soft material into a designed 3D morphological shape. By applying a strong pulsed magnetic field followed by recovery to the initial 2D configuration, the ferromagnetic soft material is programmed with a 3D magnetization profile. An inverse design algorithm is used to flatten the 3D surface into a 2D pattern with programmed crosslinking densities, serving as the exposure guidance for photodosage-based printing of the ferromagnetic soft material.