An analytical approach to the deflection analysis of woven preforms and composites under tensile loading using the Winkler theory of curved beams

• A new analytical modeling framework is presented for the deflection analysis of woven materials.
• Efficiency of the Winkler theory of curved beams is validated for woven fabrics.
• A large deformation analysis framework is presented and compared to FEM results.

In this article, a new analytical approach for the deflection analysis of yarns in woven materials under tensile loading is presented. A unit cell of a warp yarn surrounded by adjacent weft yarns is modeled using curved beams. Next, using the Winkler theory of curved beams, the warp yarn strain energy under tensile loading is derived; followed by the implementation of the variational method to obtain the governing equations as well as related boundary conditions. The exact displacement field solution was found and using the continuity of deflection condition at crossover points, the normal inter-yarn contact force was estimated. In the proposed analytical approach, shear forces and potential slippage of yarns at contact points are neglected. The validation of the solution was checked by comparing results of a benchmark example on steel textile preforms to two sets of finite element simulations. For further evaluation of the approach, the uniaxial extension response of a polypropylene/glass woven fabric composite with a noncircular yarn cross section is also considered under large deformation and predictions are compared to earlier data in the literature.