The Mechanical Properties of Textiles

Abstract

This paper is concerned with the deformation of a number of essentially independent molecules or molecular segments distributed statistically with respect to the distance between the ends of the molecules. They are supposed to be free to assume many configurations (as a result of thermal agitation) except at certain points which are stabilized by chemical forces to form the more or less tightly held (and thus well-defined) ends of the molecules. The problem solved here is as follows: Given an equilibrium distribution as a function of certain parameters, and given the expression for bulk properties in terms of molecular coordinates, what is the form of the tension as a function of the elongation and the various parameters?