2-DIMENSIONAL MODELS OF FABRICS

The aim of this work is to study different two-dimensional models of a fabric (coated or uncoated) where shearing between warp and weft is taken into account. In the first section, a model is described in which we introduce two two-dimensional displacement fields in the areas where warp and weft are superposed. The second section shows in a classical study of functional analysis that, if warp and weft interact through elastic forces, the boundary value problem has one unique solution, wether there are Neumann, Dirichlet or periodicity boundary conditions on the edge of the sample. The third section is devoted to the homogenization method of periodic media which is applied to the considered model. It yields different macroscopic models according to the strength of the coupling between warp and weft and the possible presence of coating. The last section sums up briefly the previous ones and gives future possibilities of development from this work.