This paper is concerned with the mechanics of woven fabrics under tensile loading. The yarns are treated as elastica. The yarns bent into shape for both warp and weft are assumed to be elastic, homogenous, and weightless. During deformation the yarns are subjected to bending, extension and transverse compression. The initial geometry of the yarns in the fabric, under no external loading, is first obtained using a force-equilibrium method based on Love’s ordinary approximate theory, a generalisation of the Bernoulli-Euler theory of elastic rods. A non-linear boundary-value problem with a system of five differential equations has been formulated and solved. Application of load will further change the shape of the bent yarns due to bending and stretching. For a yarn with given initial geometry, as obtained by the force-equilibrium method, the solution of the deformed configuration is obtained from the solution of two nonlinear differential equations using appropriate boundary conditions. The formulation of the latter problem is based on the energy method. The sum of the energy terms due to bending, stretching together with the potential energy due to the applied load provides an expression for the total energy of the system. The variation of the total energy in terms of the variations of two parameters is then obtained, using the techniques from calculus of variations. One parameter described the deviation of the bent yarn from a straight line while the other is the length as measured along the yarn axis. This leads to a set of differential equations that fully describe the deformed yarns. The models, initially developed for plain weave, are being currently extended to non-plain weaves and 3D woven fabrics.
