The modelling 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 a 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 permit to obtain a mesh of weaves 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 behaviour and whatever the method of homogenisation 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 that will enable us to take into account the geometry as well as the characteristic mechanics of the yam, as well as the applied stresses.

The application of this method requires first 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.

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