article published yes Yingying Ren author 93d68d10-3540-11ef-a265-f748a50dba3d Uday Kusupati author Julian Panetta author Florin Isvoranu author Davide Pellis author Tian Chen author Mark Pauly author We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems. We build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques. Association for Computing Machinery2022 eng 0730-0301 1557-736810.1145/3528223.3530089 4141-15 yes Y. Ren, U. Kusupati, J. Panetta, F. Isvoranu, D. Pellis, T. Chen, M. Pauly, ACM Transactions on Graphics 41 (2022) 1–15. Ren Y, Kusupati U, Panetta J, et al. Umbrella meshes: Elastic mechanisms for freeform shape deployment. <i>ACM Transactions on Graphics</i>. 2022;41(4):1-15. doi:<a href="https://doi.org/10.1145/3528223.3530089">10.1145/3528223.3530089</a> Ren Y, Kusupati U, Panetta J, Isvoranu F, Pellis D, Chen T, Pauly M. 2022. Umbrella meshes: Elastic mechanisms for freeform shape deployment. ACM Transactions on Graphics. 41(4), 1–15. Y. Ren <i>et al.</i>, “Umbrella meshes: Elastic mechanisms for freeform shape deployment,” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4. Association for Computing Machinery, pp. 1–15, 2022. Ren, Yingying, et al. “Umbrella Meshes: Elastic Mechanisms for Freeform Shape Deployment.” <i>ACM Transactions on Graphics</i>, vol. 41, no. 4, Association for Computing Machinery, 2022, pp. 1–15, doi:<a href="https://doi.org/10.1145/3528223.3530089">10.1145/3528223.3530089</a>. Ren, Y., Kusupati, U., Panetta, J., Isvoranu, F., Pellis, D., Chen, T., &#38; Pauly, M. (2022). Umbrella meshes: Elastic mechanisms for freeform shape deployment. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href="https://doi.org/10.1145/3528223.3530089">https://doi.org/10.1145/3528223.3530089</a> Ren, Yingying, Uday Kusupati, Julian Panetta, Florin Isvoranu, Davide Pellis, Tian Chen, and Mark Pauly. “Umbrella Meshes: Elastic Mechanisms for Freeform Shape Deployment.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2022. <a href="https://doi.org/10.1145/3528223.3530089">https://doi.org/10.1145/3528223.3530089</a>. 173832024-08-05T06:30:07Z2024-08-12T09:40:49Z