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1. Multi-material Topology Optimization of Ferromagnetic Soft Robots Using Reconciled Level Set Method

   Tian, Jiawei; Gu, Xianfeng David; Chen, Shikui (August 2021, Proceedings of the International Design Engineering Technical Conferences & Computers and Information in Engineering Conference)

   null (Ed.)

   Ferromagnetic soft materials can generate flexible mobility and changeable configurations under an external magnetic field. They are used in a wide variety of applications, such as soft robots, compliant actuators, flexible electronics, and bionic medical devices. The magnetic field enables fast and biologically safe remote control of the ferromagnetic soft material. The shape changes of ferromagnetic soft elastomers are driven by the ferromagnetic particles embedded in the matrix of a soft elastomer. The external magnetic field induces a magnetic torque on the magnetized soft material, causing it to deform. To achieve the desired motion, the soft active structure can be designed by tailoring the layouts of the ferromagnetic soft elastomers. This paper aims to optimize multi-material ferromagnetic actuators. Multi-material ferromagnetic flexible actuators are optimized for the desired kinematic performance using the reconciled level set method. This type of magnetically driven actuator can carry out more complex shape transformations by introducing ferromagnetic soft materials with more than one magnetization direction. Whereas many soft active actuators exist in the form of thin shells, the newly proposed extended level set method (X-LSM) is employed to perform conformal topology optimization of ferromagnetic soft actuators on the manifolds. The objective function comprises two sub-objective functions, one for the kinematic requirement and the other for minimal compliance. Shape sensitivity analysis is derived using the material time derivative and the adjoint variable method. Three examples are provided to demonstrate the effectiveness of the proposed framework. 

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2. Encoding reprogrammable properties into magneto-mechanical materials via topology optimization

   https://doi.org/10.1038/s41524-023-00980-2  

   Zhao, Zhi; Zhang, Xiaojia Shelly (December 2023, npj Computational Materials)

   Abstract The properties of materials and structures typically remain fixed after being designed and manufactured. There is a growing interest in systems with the capability of altering their behaviors without changing geometries or material constitutions, because such reprogrammable behaviors could unlock multiple functionalities within a single design. We introduce an optimization-driven approach, based on multi-objective magneto-mechanical topology optimization, to design magneto-active metamaterials and structures whose properties can be seamlessly reprogrammed by switching on and off the external stimuli fields. This optimized material system exhibits one response under pure mechanical loading, and switches to a distinct response under joint mechanical and magnetic stimuli. We discover and experimentally demonstrate magneto-mechanical metamaterials and metastructures that realize a wide range of reprogrammable responses, including multi-functional actuation responses, adaptable snap-buckling behaviors, switchable deformation modes, and tunable bistability. The proposed approach paves the way for promising applications such as magnetic actuators, soft robots, and energy harvesters. 

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3. Cable-Driven Jamming of a Boundary Constrained Soft Robot

   https://doi.org/10.1109/RoboSoft48309.2020.9116042  

   Tanaka, Koki; Karimi, Mohammad Amin; Busque, Bruno-Pier; Mulroy, Declan; Zhou, Qiyuan; Batra, Richa; Srivastava, Ankit; Jaeger, Heinrich M.; Spenko, Matthew (May 2020, 2020 3rd IEEE International Conference on Soft Robotics (RoboSoft))

   Soft robots employ flexible and compliant materials to perform adaptive tasks and navigate uncertain environments. However, soft robots are often unable to achieve forces and precision on the order of rigid-bodied robots. In this paper, we propose a new class of mobile soft robots that can reversibly transition between compliant and stiff states without reconfiguration. The robot can passively conform or actively control its shape, stiffen in its current configuration to function as a rigid-bodied robot, then return to its flexible form. The robotic structure consists of passive granular material surrounded by an active membrane. The membrane is composed of interconnected robotic sub-units that can control the packing density of the granular material and exploit jamming behaviors by varying the length of the interconnecting cables. Each robotic sub-unit uses a differential drive system to achieve locomotion and self-reconfigurability. We present the robot design and perform a set of locomotion and object manipulation experiments to characterize the robot's performance in soft and rigid states. We also introduce a simulation framework in which we model the jamming soft robot design and study the scalability of this class of robots. The proposed concept demonstrates the properties of both soft and rigid robots, and has the potential to bridge the gap between the two 

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4. Designing Programmable Ferromagnetic Soft Metastructures for Minimally Invasive Endovascular Therapy

   https://doi.org/10.1115/DETC2023-116342  

   Zhuang, Ran; Tian, Jiawei; Tassiopoulos, Apostolos; Sadasivan, Chandramouli; Gu, Xianfeng; Chen, Shikui (August 2023, American Society of Mechanical Engineers)

   Abstract Minimally invasive endovascular therapy (MIET) is an innovative technique that utilizes percutaneous access and transcatheter implantation of medical devices to treat vascular diseases. However, conventional devices often face limitations such as incomplete or suboptimal treatment, leading to issues like recanalization in brain aneurysms, endoleaks in aortic aneurysms, and paravalvular leaks in cardiac valves. In this study, we introduce a new metastructure design for MIET employing re-entrant honeycomb structures with negative Poisson’s ratio (NPR), which are initially designed through topology optimization and subsequently mapped onto a cylindrical surface. Using ferromagnetic soft materials, we developed structures with adjustable mechanical properties called magnetically activated structures (MAS). These magnetically activated structures can change shape under noninvasive magnetic fields, letting them fit against blood vessel walls to fix leaks or movement issues. The soft ferromagnetic materials allow the stent design to be remotely controlled, changed, and rearranged using external magnetic fields. This offers accurate control over stent placement and positioning inside blood vessels. We performed magneto-mechanical simulations to evaluate the proposed design’s performance. Experimental tests were conducted on prototype beams to assess their bending and torsional responses to external magnetic fields. The simulation results were compared with experimental data to determine the accuracy of the magneto-mechanical simulation model for ferromagnetic soft materials. After validating the model, it was used to analyze the deformation behavior of the plane matrix and cylindrical structure designs of the Negative Poisson’s Ratio (NPR) metamaterial. The results indicate that the plane matrix NPR metamaterial design exhibits concurrent vertical and horizontal expansion when subjected to an external magnetic field. In contrast, the cylindrical structure demonstrates simultaneous axial and radial expansion under the same conditions. The preliminary findings demonstrate the considerable potential and practicality of the proposed methodology in the development of magnetically activated MIET devices, which offer biocompatibility, a diminished risk of adverse reactions, and enhanced therapeutic outcomes. Integrating ferromagnetic soft materials into mechanical metastructures unlocks promising opportunities for designing stents with adjustable mechanical properties, propelling the field towards more sophisticated minimally invasive vascular interventions. 

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5. Level-Set Nonlinear Topology Optimization for Large-Deformation Compliant Mechanisms with Hyperelastic Materials

   Zhuang, Ran; Sadasivan, Chander; Gu, Xianfeng David; Chen, Shikui (August 2025, American Society of Mechanical Engineers (ASME))

   The level set method has been widely applied in topology optimization of mechanical structures, primarily for linear materials, but its application to nonlinear hyperelastic materials, particularly for compliant mechanisms, remains largely unexplored. This paper addresses this gap by developing a comprehensive level set-based topology optimization framework specifically for designing compliant mechanisms using neo-Hookean hyperelastic materials. A key advantage of hyperelastic materials is their ability to undergo large, reversible deformations, making them well-suited for soft robotics and biomedical applications. However, existing nonlinear topology optimization studies using the level set method mainly focus on stiffness optimization and often rely on linear results as preliminary approximations. Our framework rigorously derives the shape sensitivity analysis using the adjoint method, including crucial higher-order displacement gradient terms often neglected in simplified approaches. By retaining these terms, we achieve more accurate boundary evolution during optimization, leading to improved convergence behavior and more effective structural designs. The proposed approach is first validated with a mean compliance problem as a benchmark, demonstrating its ability to generate optimized structural configurations while addressing the nonlinear behavior of hyperelastic materials. Subsequently, we extend the method to design a displacement inverter compliant mechanism that fully exploits the advantages of hyperelastic materials in achieving controlled large deformations. The resulting designs feature smooth boundaries and clear structural features that effectively leverage the material's nonlinear properties. This work provides a robust foundation for designing advanced compliant mechanisms with large deformation capabilities, extending the reach of topology optimization into new application domains where traditional linear approaches are insufficient. The developed methodology is expected to provide a timely solution to computational design for soft robotics, flexible mechanisms, and other emerging technologies that benefit from hyperelastic material properties. 

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