The Dynamics of Fabric Drape

The aim of this paper is to model the unique dynamic deformation properties of textile materials. Fabric deformation is modeled as a nonlinear dynamic system so that a fabric can be completely specified under general boundary conditions. Fabric deformation or fabric drape is dynamically analogous to waves traveling 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 from the analysis of fabric deformation belong to the Klein-Gordon family of equations, and become the sine-Gordon equation in three dimensions. The sine-Gordon equation has its origins in the study of Bäcklund Transformations is used to transform a trivial solution into a series of solitary waves within the fabric. These analytical expressions describing the curvature parameters of a surface represent actual solutions of fabric dynamic systems.