Commun. Comput. Phys., 14 (2013), pp. 1228-1251.


Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

Yan Li 1*, I-Liang Chern 2, Joung-Dong Kim 1, Xiaolin Li 1

1 Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA.
2 Department of Applied Mathematics, Center of Mathematical Modeling and Scientific Computing, National Chiao Tung University, Hsin Chu, 300, Taiwan; Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan; National Center for Theoretical Sciences, Taipei Office, Taipei, 106, Taiwan.

Received 12 June 2012; Accepted (in revised version) 8 March 2013
Available online 13 June 2013
doi:10.4208/cicp.120612.080313a

Abstract

We use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the "Impulse method" which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency. This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

AMS subject classifications: 74B20, 65D17, 65Z05

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Key words: Front tracking, spring model, eigen frequency.

*Corresponding author.
Email: yli@ams.sunysb.edu (Y. Li), chern@math.ntu.edu.tw (I-L. Chern), selom114@ams.sunysb.edu (J.-D. Kim), linli@ams.sunysb.edu (X. Li)
 

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