Structure-based modeling of artificial leather used in sports with non-symmetric fiber distribution

In artificial leather, which is used in sports as a fiber-reinforced material, the distribution of the fiber family in the tangential plane is more dispersed than that perpendicular to the tangential plane. According to previous studies, its mechanical response is different in the two axisymmetric directions with respect to the main direction of the fiber family. This non-symmetric fiber distribution can significantly affect the mechanical properties of artificial leather, but the currently applied fiber dispersion models cannot accurately describe this anisotropic property. Therefore, we propose a novel anisotropic hyperelasticity constitutive model which describes the mechanical behavior of fiber-reinforced material by using a generalized structure tensor in the form of separated in-plane and out-of-plane fiber distribution and by applying the sine-skewed von Mises distribution function as the in-plane fiber distribution function. Our approach consists of developing a construction form of a generalized structure tensor with non-symmetric components, introducing it into the strain energy function and providing explicit expressions for the corresponding second Piola-Kirchhoff stress tensor and the related elasticity tensor. As specific examples, the distribution and material parameters of the model were identified by fitting fiber distribution data and tensile data, respectively, of artificial leather to the model’s theoretical results. The mechanical behavior of artificial leather specimens under uniaxial extension at various tensile angles was simulated through finite element computations. The differences in mechanical response in two axisymmetric directions about the main direction of the fiber family were captured, breaking through the limitations of the currently applied fiber dispersion models. Moreover, inhomogeneous stress distribution under maximum stretch and inhomogeneous deformation were observed. This constitutive model provides a more accurate method for the description of the mechanical behavior of fiber-reinforced material and provides a theoretical reference for the simulation of the three-dimensional deformation of artificial leather.