Multi-material topology optimization for shape-morphing ultra‐soft magneto‐active structures

  • Perez-Garcia, Carlos (Universidad Carlos III de Madrid)
  • Martínez-Frutos, Jesús (Technical University of Cartagena)
  • Ortigosa, Rogelio (Technical University of Cartagena)
  • Garcia-Gonzalez, Daniel (Universidad Carlos III de Madrid)

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Ultra‐soft magnetoactive materials (stiffness <10 kPa) have transformed bioengineering and soft robotics, enabling remote actuation within soft biologically relevant environments. Despite major advances in the last decade, the complexity of their magneto‐mechanical coupled behavior still hinders efficient topology and material optimization strategies for these smart structures. In this work, we present an integrated computational framework for the design of ultra-soft magnetoactive structures that combines material characterization, constitutive modeling, magnetic field resolution—including vacuum effects—and inverse design within a unified pipeline. The framework is motivated by the identification of a previously overlooked deformation mechanism: residual mechanical anisotropy arising from remanent magnetization in hard-magnetic magnetorheological elastomers, even in the absence of external magnetic fields. To capture this behavior, we employ a physics-augmented neural network for constitutive modeling coupled with a multimaterial topology optimization scheme, enabling the design of programmable structures with complex actuation responses. Experimental validation demonstrates that neglecting remanence-induced anisotropy leads not only to quantitative inaccuracies but also to qualitative errors, such as deformation mode switching. We further show that the proposed framework enables precise and programmable deformations in regimes where conventional design approaches fail. These results establish a foundation for the next generation of magnetically actuated soft systems and highlight the critical role of material anisotropy in their mechanical performance. The authors acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program (grant agreement no. 947723, project: 4DBIOMAP, and grant agreement no. 101247449, project: MAGMATED), and Sponsorship agreement UC3M-NAVANTIA-MONODON. R. Ortigosa and J. Martinez-Frutos acknowledge the support of grant PID2022-141957OA-C22 funded by MICIU/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”.