Volume 14, Issue 5
Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

Yan Li, I-Liang Chern, Joung-Dong Kim & Xiaolin Li

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

Published online: 2013-11

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  • 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.


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@Article{CiCP-14-1228, author = {Yan Li, I-Liang Chern, Joung-Dong Kim and Xiaolin Li}, title = {Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {5}, pages = {1228--1251}, 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120612.080313a}, url = {http://global-sci.org/intro/article_detail/cicp/7200.html} }
TY - JOUR T1 - Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model AU - Yan Li, I-Liang Chern, Joung-Dong Kim & Xiaolin Li JO - Communications in Computational Physics VL - 5 SP - 1228 EP - 1251 PY - 2013 DA - 2013/11 SN - 14 DO - http://dor.org/10.4208/cicp.120612.080313a UR - https://global-sci.org/intro/cicp/7200.html KW - AB -

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.


Yan Li, I-Liang Chern, Joung-Dong Kim & Xiaolin Li. (1970). Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model. Communications in Computational Physics. 14 (5). 1228-1251. doi:10.4208/cicp.120612.080313a
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