The paper is dedicated to the asymptotic investigation of textiles as an elasticity problem on beam structures. The structure is subjected to a simultaneous homogenization and dimension reduction with respect to the asymptotic behavior of the beams' thickness and periodicity. Important for the problem are the contact conditions between the beams, which yield multiple limits depending on the order. In this paper two limiting cases are presented: a linear case and a Leray-Lions-type problem.
