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Modelling fabric deformation as a nonlinear dynamical system using Bäcklund Transformations

Jacqueline R. Postle (Department of Textile Technology, University of New South Wales, Sydney, Australia)
Ron Postle (Department of Textile Technology, University of New South Wales, Sydney, Australia)

International Journal of Clothing Science and Technology

ISSN: 0955-6222

Article publication date: 1 August 1996

278

Abstract

Aims to analyse unique deformation properties of textile materials in terms of basic mechanical properties. Models fabric deformation as a nonlinear dynamical system so that a fabric can be completely specified in terms of its mechanical behaviour under general boundary conditions. Fabric deformation is dynamically analogous to waves travelling in a fluid. A localized two‐dimensional deformation evolves through the fabric to form a three‐dimensional drape or fold configuration. The nonlinear differential equations arising in the analysis of fabric deformation belong to the Klein‐Gordon family of equations which becomes the sine‐Gordon equation in three dimensions. The sine‐Gordon equation has its origins in the study of Bäcklund Transformations in differential geometry. Describes fabric deformation as a series of transformations of surfaces, defined in terms of curvature parameters using Gaussian representation of surfaces. By considering a deformed fabric as a two‐dimensional surface, algebraically constructs analytical solutions of fabric deformation by solving the sine‐Gordon Equation. The theory of Bäcklund Transformations is used to transform a trivial solution into a series of solitary wave solutions. These analytical expressions describing the curvature parameters of a surface represent actual solutions of fabric dynamical systems.

Keywords

Citation

Postle, J.R. and Postle, R. (1996), "Modelling fabric deformation as a nonlinear dynamical system using Bäcklund Transformations", International Journal of Clothing Science and Technology, Vol. 8 No. 3, pp. 22-42. https://doi.org/10.1108/09556229610120381

Publisher

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MCB UP Ltd

Copyright © 1996, MCB UP Limited

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