Modeling the Evolution of Deformed Fabric Surfaces as a Nonlinear Dynamical System

Abstract

Fabric drape is modeled as a nonlinear dynamical system. A localized two-dimensional deformation ( e.g., folding or buckling), considered as the initial state, evolves, yarn by yarn, through the fabric, which bifurcates into complex wave configurations to form a three-dimensional fabric surface. Differential equations that arise in modeling fabric deformation such as buckling, folding, and drape can be generalized to the sine-Gordon equation. Tchebyshev nets are used to propose a generalized mathematical model for fabric deformation. The sine-Gordon equation is the compatibility condition that yields the net coordinates over the deformed fabric surface. Complex solutions of the sine-Gordon equation are constructed and plotted in three dimensions.