A Generalized Micromechanics of Continuous-Filament Yarns. Part I: Underlying Formalism

Abstract

A constitutive theory is proposed to predict the stress-strain behavior of a twisted filament yarn under extensive elongation from the structural parameters and constituent moduli. This theory can predict the radial distributions of local stress and strain as well as the load-elongation relation, if the initial distributions of the local apparent density and fiber direction together with several elastic moduli of the parallel fiber bundle at any strain are known as the elemental information. The underlying mathematics is developed so as to be closed before a special assumption to specify the orientational structure of the yarn, such as the cylindrical-helix model, the conical-helix model, etc., is put in force, and furthermore to be free from the critical problem that most of the earlier theories have, i.e., the defect that an approximation valid only for an infinitesimal deformation is assumed for a finite elongation.

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