Wackerle, S.S.WackerleOrlik, J.J.OrlikHauck, M.M.HauckLykhachova, O.O.LykhachovaSteiner, K.K.Steiner2022-03-062022-03-062020https://publica.fraunhofer.de/handle/publica/26359710.1016/j.promfg.2020.04.169In many textiles and fiber structures, the behavior of the material is determined by the structural arrangements of the fibers, their thickness and cross-section as well as the properties of the fibers themselves. However, this is only valid for materials, where the tension, bending and torsion deformation of yarns can be decomposed. In fibrous materials, this is the case when either bending or tension of the fibers is negligible. In textiles, it is the case when the friction between yarns is small. This theory is based on the mathematical modeling and homogenization approach and is illustrated by examples on woven structures and a spacer fabric. This paper summarizes rigorous results of asymptotic analysis and provides (1) an algorithm for computation of the shear, tension, torsion and bending properties of the textile as an orthotropic plate based on the elastic properties of yarns and the textile structure; (2) critical for its buckling force or pre-stress (thermal, swelling, etc.) computed by a simple formula from the effective textile elastic bending and tension properties; and (3) critical shear angles for the textile given in form of a simple formula in terms of the distance between yarns and their cross-section. All the theoretical results are given in terms of simple formulas and are validated in the paper by mechanical experiments.en003006519journal article