A Theory of Self-Crimping Bicomponent Filaments

Abstract

An elementary theory of the bending of two, coupled, thin elastic elements is presented as a model for computing the curvature of bicomponent filaments. The curvature is expressed in terms of a differential extension between the two elements at the moment of "activation." The model requires expressions for the deformational energy of the interacting elements, and an explicit "material" relation expressing the details of the interactions between the "driving" and "driven" elements of the filament structure. It is closed by minimizing this energy with respect to a parameter measuring the inefficiency ΔL/L2 of the activation strain ε. Curvatures computed for near-unity ratios of rectangular cross sections and elastic moduli yield results comparable to previously published work for both ratio values near unity (the Timo shenko limit). At larger and smaller values of these ratios the curvatures obtained by the new model are lower than those obtained previously and in limited cases appear to approximate experimental experience. A discussion of the general problem of computing and understanding practical crimp situations is given.