research-article

An asymptotic numerical method for inverse elastic shape design

Authors:

Kun ZhouAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 33, Issue 4

Article No.: 95, Pages 1 - 11

https://doi.org/10.1145/2601097.2601189

Published: 27 July 2014 Publication History

Abstract

Inverse shape design for elastic objects greatly eases the design efforts by letting users focus on desired target shapes without thinking about elastic deformations. Solving this problem using classic iterative methods (e.g., Newton-Raphson methods), however, often suffers from slow convergence toward a desired solution. In this paper, we propose an asymptotic numerical method that exploits the underlying mathematical structure of specific nonlinear material models, and thus runs orders of magnitude faster than traditional Newton-type methods. We apply this method to compute rest shapes for elastic fabrication, where the rest shape of an elastic object is computed such that after physical fabrication the real object deforms into a desired shape. We illustrate the performance and robustness of our method through a series of elastic fabrication experiments.

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Cited By

Numerow LLi YCoros SThomaszewski B(2024)Differentiable Voronoi Diagrams for Simulation of Cell-Based Mechanical SystemsACM Transactions on Graphics10.1145/365815243:4(1-11)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658152
Potier-Ferry M(2024)Asymptotic numerical method for hyperelasticity and elastoplasticity: a reviewProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences10.1098/rspa.2023.0714480:2285Online publication date: 6-Mar-2024
https://doi.org/10.1098/rspa.2023.0714
Andrini DMagri MCiarletta P(2024)Optimal surface clothing with elastic netsJournal of the Mechanics and Physics of Solids10.1016/j.jmps.2024.105684188(105684)Online publication date: Jul-2024
https://doi.org/10.1016/j.jmps.2024.105684
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Index Terms

An asymptotic numerical method for inverse elastic shape design
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation
    2. Shape modeling
2. Mathematics of computing
  1. Continuous mathematics
    1. Topology
      1. Geometric topology

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 33, Issue 4

July 2014

1366 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2601097

Issue’s Table of Contents

Copyright © 2014 ACM.

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Publication History

Published: 27 July 2014

Published in TOG Volume 33, Issue 4

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Lenovo's Program for Young Scientists
Columbia Junior Faculty startup fund
National Program for Special Support of Eminent Professionals of China
Intel Corporation
National Natural Science Foundation of China

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Cited By

Numerow LLi YCoros SThomaszewski B(2024)Differentiable Voronoi Diagrams for Simulation of Cell-Based Mechanical SystemsACM Transactions on Graphics10.1145/365815243:4(1-11)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658152
Potier-Ferry M(2024)Asymptotic numerical method for hyperelasticity and elastoplasticity: a reviewProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences10.1098/rspa.2023.0714480:2285Online publication date: 6-Mar-2024
https://doi.org/10.1098/rspa.2023.0714
Andrini DMagri MCiarletta P(2024)Optimal surface clothing with elastic netsJournal of the Mechanics and Physics of Solids10.1016/j.jmps.2024.105684188(105684)Online publication date: Jul-2024
https://doi.org/10.1016/j.jmps.2024.105684
Lu YWang YSong PWong HMok YLiu L(2024)Computational design of custom-fit PAP masksComputers & Graphics10.1016/j.cag.2024.103998122(103998)Online publication date: Aug-2024
https://doi.org/10.1016/j.cag.2024.103998
Li HZhang WZheng JDavis EZeng J(2024)Optimizing heterogeneous elastic material distributions on 3D modelsComputer-Aided Design10.1016/j.cad.2024.103748175:COnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.cad.2024.103748
Zhang ZBrandt CJouve JWang YChen TPauly MPanetta J(2023)Computational Design of Flexible Planar MicrostructuresACM Transactions on Graphics10.1145/361839642:6(1-16)Online publication date: 5-Dec-2023
https://doi.org/10.1145/3618396
Hafner CBickel B(2023)The Design Space of Kirchhoff RodsACM Transactions on Graphics10.1145/360603342:5(1-20)Online publication date: 20-Sep-2023
https://dl.acm.org/doi/10.1145/3606033
Hsu JWang TPan ZGao XYuksel CWu K(2023)Sag-Free Initialization for Strand-Based Hybrid Hair SimulationACM Transactions on Graphics10.1145/359214342:4(1-14)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592143
Hsu JTruong NYuksel CWu K(2022)A general two-stage initialization for sag-free deformable simulationsACM Transactions on Graphics10.1145/3528223.353016541:4(1-13)Online publication date: 22-Jul-2022
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Madan ALevin D(2022)Fast evaluation of smooth distance constraints on co-dimensional geometryACM Transactions on Graphics10.1145/3528223.353009341:4(1-17)Online publication date: 22-Jul-2022
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