Theory of Elasticity for Plain-Weave Fabrics

Abstract

A new concept of pseudo-continuum model is proposed to analyze the complicated nonlinear behavior of plain-weave fabrics in in-plane problem. The deformation of plain-weave fabric is categorized into three types in view of thread deformations, that is, skewing, straightening and extension. In this categorization, it is assumed that the bending and shear of threads caused by heterogeneity and friction can be neglected. The skewing and straightening give rise to in-plane transverse compressive strain, and the extension means axial tensile strain. The warp and weft are individually subject to these two strains with in-plane and anti-plane finite rotation. The geometrical nonlinearity, therefore, arises from the finite rotation of threads, while these strains are defined in the sense of infinitesimal strain. The framework of this pseudo-continuum model, which consists of the equilibrium equation, the strain-displacement relationship and the constitutive law, is newly constructed. The nonlinear behavior under biaxial extension, that is a characteristic mechanical behavior of the plain-weave fabric, is analyzed for the proof of validity of the proposed model.