A time-integration method for stable simulation of extremely deformable hyperelastic objects

Ryo Kikuuwe

Research output: Contribution to journalArticle

Abstract

This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application.

Original languageEnglish
Pages (from-to)1335-1346
Number of pages12
JournalVisual Computer
Volume33
Issue number10
DOIs
Publication statusPublished - Oct 1 2017

Fingerprint

Linear equations
Stiffness matrix
Equations of motion

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

Cite this

A time-integration method for stable simulation of extremely deformable hyperelastic objects. / Kikuuwe, Ryo.

In: Visual Computer, Vol. 33, No. 10, 01.10.2017, p. 1335-1346.

Research output: Contribution to journalArticle

@article{71de11146ed34067948a674954f7c5bb,
title = "A time-integration method for stable simulation of extremely deformable hyperelastic objects",
abstract = "This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application.",
author = "Ryo Kikuuwe",
year = "2017",
month = "10",
day = "1",
doi = "10.1007/s00371-016-1225-0",
language = "English",
volume = "33",
pages = "1335--1346",
journal = "Visual Computer",
issn = "0178-2789",
publisher = "Springer Verlag",
number = "10",

}

TY - JOUR

T1 - A time-integration method for stable simulation of extremely deformable hyperelastic objects

AU - Kikuuwe, Ryo

PY - 2017/10/1

Y1 - 2017/10/1

N2 - This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application.

AB - This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application.

UR - http://www.scopus.com/inward/record.url?scp=84964058370&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964058370&partnerID=8YFLogxK

U2 - 10.1007/s00371-016-1225-0

DO - 10.1007/s00371-016-1225-0

M3 - Article

VL - 33

SP - 1335

EP - 1346

JO - Visual Computer

JF - Visual Computer

SN - 0178-2789

IS - 10

ER -