Inverse design of magneto-active metasurfaces and robots: Theory, computation, and experimental validation

Chao Wang, Zhi Zhao, Xiaojia Shelly Zhang

Research output: Contribution to journalArticlepeer-review


Magneto-active structures can undergo rapid and reversible deformations under untethered magnetic fields. The capability to design such structures to achieve programmable shape morphing in three dimensions (3D) under magnetic actuation is highly desirable for many applications. In this work, we develop a multi-physics topology optimization framework for the inverse design of magneto-active metasurfaces that can undergo programmable shape morphing in 3D under external magnetic fields. These metasurfaces remain planar in their initial configurations and are deformed into complex 3D target shapes. The proposed framework accounts for large-deformation kinematics and optimizes both the topologies and magnetization distributions of metasurfaces in conjunction with the directions and magnitudes of the external magnetic fields. We demonstrate the framework in the design of kirigami metasurfaces, bio-inspired robots with “swimming”, “steering”, “walking”, and “climbing” motions, and multi-modal magnetic actuators, and the optimized designs show high precision and performance in achieving complex 3D deformations. We also use a hybrid fabrication procedure to manufacture representative designs and conduct experimental tests to validate their programmed 3D deformations, with results showing good agreement with simulation predictions. We envision that the proposed framework could lead to a systematic and versatile approach for the design of magneto-active metasurfaces for robotics applications.

Original languageEnglish (US)
Article number116065
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Aug 1 2023


  • Hard-magnetic soft materials
  • Inverse design
  • Magneto-active metasurfaces and robots
  • Mold casting fabrication
  • Three-dimensional shape programming
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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