A micromechanical model of woven structures accounting for yarn-yarn contact based on Hertz theory and energy minimization

The equilibrium shape of plain weave fabric, accounting for yarn to yarn contact and incorporating the transverse compressibility, is presently investigated, relying on an energetic analysis of the textile. Each yarn is modeled as an undulated beam at a mesoscopic level, with a shape modeled by a Fourier series. In order to get an accurate description of the contact between yarns, we have considered the contact occurring on a surface (distributed contact) of finite extent according to Hertz contact theory. This method allows evaluating the reaction forces between weft and warp from the pressure distribution in the contact zone between yarns, and the evolution of the contact area versus the applied tension. The overall response of fabric under uniaxial and biaxial tension is computed as the minimum of the total potential energy of the set of interwoven yarns, including the work of reaction forces on the contact zones. The calculated nonlinear response for two important materials (glass, carbon) is due to the change of the geometry, namely the crimp variation and the change of contact area during increased loading. The contact area increases with the applied tensile force and is comparable to the yarn diameter. Only the contribution of the displacement due to flexion is shown to be sensitive to the distribution of the forces on the contact surface. A good agreement between the model predictions and tensile measurements of the response of plain weave fabric has been obtained. (C) 2014 Elsevier Ltd. All rights reserved.