A discrete model for the coupling between the yarns in a woven fabric

The coupling between yarns in a piece of fabric has been analysed at the mesoscopic scale, in terms of its impact on the macroscopic unidirectional behaviour. Starting from a discrete model of a woven structure associated to a variational formulation of the equilibrium of the structure, the coupling between both yams is introduced, the potential energy of which is calculated. The initial shape of the yam, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The coefficients of the series are expressed vs. the contact force exerted at the top of the undulations, and vs. the mechanical properties of the solicited yam. The contact force is then expressed vs. the mechanical properties of the transverse yam and vs. the vertical displacement of the contact point. The potential energy of the coupling is then built, assuming the continuity of the displacement at the contact points. The equilibrium shape of the yarn submitted to unidirectional traction is obtained numerically as the minimum of the total potential energy. The simulated traction curve reproduces in a satisfactorily manner the observed behaviour. The respective contributions of the flexional and extensional effects of the yam are analysed. The consideration of the coupling enhances the rigidity of the response of the yam; one demonstrates the effect of the geometrical and mechanical parameters of the transverse yam. (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.