Empirical hyperelastic modeling of textile fabrics for measuring nonlinear bending rigidity

Measuring and modeling the bending rigidity of textile fabrics is challenging due to the nonlinearity and coupling of the bending and tensile strains, especially in the high-stress ranges. To address this problem, we propose a novel empirical hyperelastic model to measure the nonlinear behaviors of the bending rigidity, including high-stress ranges close to bending rupture. Specifically, we develop the hyperelastic strain energy by generalizing the linear orthotropic constitutive relation, whose nonlinear material parameters can be directly determined by fabric tests through nonlinear curve fitting. To model the nonlinear bending modulus, we introduce fraction factors that quantify the softness of the bending rigidity compared with the tensile rigidity. Based on the proposed hyperelastic model, we performed the finite element method of ball bursting tests to optimize the fraction factors, and found that the bending rigidity is 3-5 times lower than the tensile rigidity in high-stress ranges for cotton woven fabrics (i.e., Sheeting, Ox, and Twill), showing that the nonlinearity of the bending modulus and strain is important for predicting bending stresses during the out-of-plane stretching. Besides, the nonlinearity of the tensile rigidity also affects the measurement of the bending rigidity in high-stress ranges. We anticipate that our hyperelastic modeling of textile fabrics and measurement method of the nonlinear bending rigidity will give new functionalities to product development in the textile industry.