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The arrangement, properties and structure of the fibers within the yarn and the yarns within the fabric, generate a complex mechanism of deformation. Therefore the present work intends to develop a theoretical model of the mechanical behavior of the plain weave. The modeling of textile structures by the finite element method is a new approach based on the combination of geometric and mechanical models. The finite element method permits a construction and representation of fabrics by taking into consideration the yarn undulation, the existence or not of symmetries in the basic cell and the type of contact between warp and weft yarns. These different parameters allow the mesh of weaves to be obtained, the closest to the reality, without any restriction and any simplifying assumption. In every model defined by its partial derivative equation of the fabric mechanical behavior, and whatever the method of homogenization employed to obtain a homogeneous model, we will be brought to solve a cellular problem. The three-dimensional structure of the basic cell of the various fabrics is very complex. Therefore, the mathematical study starts by meshing the different fabrics, which will enable us to take the geometry as well as the mechanical characteristics of the yarn into account, as well as the stresses applied. The application of this method first requires a mathematical formulation of the problem and then a mesh of the basic cell. The next step is the simulation of shearing and tensile tests. The analysis of the results has proved to be very hard and, thus, has demanded a study of the stress field in the basic cell. From the analysis of the plain weave behavior under those different tests we can assess that the yarn cross-section is one of the crucial factors that influences the mechanical behavior of fabrics, and the phenomenon of stress concentration appears to be located at the level of contact surfaces between warp and weft yarns. For all models that deal with the mechanical behavior of textile structures and regardless of the method of homogenization, the problem has to be solved at the basic cell level before moving on to the global model. The geometry of the textile structures is very complex due to the nonsymmetrical aspect of the majority of weaves. After having defined the geometrical form and completed the meshes of the basic cells of the plain weave, we have carried on the treatment of the problem from the mechanical point of view by the finite element method. |
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