Conformal topology optimization of multi-material ferromagnetic soft active structures using an extended level set method

Ferromagnetic soft active structures using embedded ferromagnetic particles in the soft polymer matrix can generate flexible locomotion and change configurations remotely, rapidly, and biologically friendly with an applied magnetic field. To achieve the desired motion, these soft active structures can be designed by tailoring the layouts of the ferromagnetic soft polymer. Although many magnetic soft active structures have been designed and fabricated, they are limited by the developer's intuition and experience. Structural topology optimization has become a promising method to achieve innovative structures by optimizing the material layout, opening a new path for architecting ferromagnetic-driven active structures. Given the widespread adoption of thin-shell structures for soft robots, the extended level set method (X-LSM) and conformal geometry theory are employed to perform topology optimization of the ferromagnetic soft active structures on manifolds. The boundary evolution on a free-form 3D surface can be transferred into a 2D rectangular plane by solving a modified Hamilton–Jacobi equation weighted by conformal factors. The reconciled level set (RLS) method is firstly implemented within the X-LSM framework in this paper to enable the design of multi-material ferromagnetic soft active structures on free-from surfaces. The design objective consists of a subobjective function for kinematic requirement and a subobjective function for minimum compliance. The shape sensitivity was analyzed using the material time derivative and the adjoint variable approach. The proposed method was applied to design several single and multi-material ferromagnetic soft active structures. Two topologically optimized designs have been printed using functional 3D printing technology, or the so-called 4D printing, to physically realize soft active structures with built-in functionalities. The results of the numerical verification and experimental validation demonstrate the effectiveness of the proposed design and fabrication framework.