Calculation of effective mechanical properties of textiles by asymptotic approach

We consider plates with 2-D periodic rod or fabric structure, used as geotextiles or textiles. The period of structure as well as the hight of a plate are much smaller compared to its depth and width. This makes a direct numerical computation of boundary value or contact elasticity problem too expensive. Three small parameters are introduced for the asymptotic analysis: the first one connected with the period of structure, the second one with the thickness of fibers or beams inside the periodicity cell and the last one - with the hight of a plate. The overcoming to the limit with respect to period of structure provides equivalent homogenized plate of the finite hight. Calculation of its outer-plane stiffness is a new aspect of this work. The next overcoming to the limit with respect to the hight reduces the 3-D problem to the homogenized equations, fourth order PDEs. The effective elasticity moduli and outer-plane stiffness can be obtained numerically solving cell experiments.