---
_id: '17383'
abstract:
- lang: eng
  text: "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.\r\nWe 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."
article_processing_charge: No
article_type: original
author:
- first_name: Yingying
  full_name: Ren, Yingying
  id: 93d68d10-3540-11ef-a265-f748a50dba3d
  last_name: Ren
- first_name: Uday
  full_name: Kusupati, Uday
  last_name: Kusupati
- first_name: Julian
  full_name: Panetta, Julian
  last_name: Panetta
- first_name: Florin
  full_name: Isvoranu, Florin
  last_name: Isvoranu
- first_name: Davide
  full_name: Pellis, Davide
  last_name: Pellis
- first_name: Tian
  full_name: Chen, Tian
  last_name: Chen
- first_name: Mark
  full_name: Pauly, Mark
  last_name: Pauly
citation:
  ama: '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>'
  apa: '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>'
  chicago: '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>.'
  ieee: '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.'
  ista: '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.'
  mla: '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>.'
  short: Y. Ren, U. Kusupati, J. Panetta, F. Isvoranu, D. Pellis, T. Chen, M. Pauly,
    ACM Transactions on Graphics 41 (2022) 1–15.
date_created: 2024-08-05T06:30:07Z
date_published: 2022-07-22T00:00:00Z
date_updated: 2024-08-12T09:40:49Z
day: '22'
doi: 10.1145/3528223.3530089
extern: '1'
intvolume: '        41'
issue: '4'
language:
- iso: eng
month: '07'
oa_version: None
page: 1-15
publication: ACM Transactions on Graphics
publication_identifier:
  eissn:
  - 1557-7368
  issn:
  - 0730-0301
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Umbrella meshes: Elastic mechanisms for freeform shape deployment'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 41
year: '2022'
...