A mesoscale tensile model for woven fabrics based on Timoshenko beam theory

The yarn weave architectures highly influence the mechanical response of woven fabrics. To provide an accurate prediction of the mechanical behaviors of woven fabrics under tension, a mesoscale model is developed. The model takes into account yarn properties, yarn weaving pattern, and interactions between yarns. The yarn properties such as tensile modulus and yarn strength of yarns are considered as random variables. Each yarn in fabric is modeled as a Timoshenko beam with a weaving shape modeled by a parabolic function. The yarn shape evolution and mechanical response of undulated yarn under tension are computed based on Castigliano’s second theorem. The damage initiation and propagation of a yarn in fabric is introduced through a damage variable. The model is demonstrated on woven jute fabrics. Analytical and numerical analyses are carried out and show good prediction on the macroscopic tensile response of woven jute fabric. The model provides a quantitative understanding between yarn geometrical parameters and the expected material response, and makes it helpful for designing woven structural composites with high performance.