Inflation and extension of soft fibrous membranes that account for fiber dispersion and pre-stretch: A sensitivity analysis

This article presents a sensitivity analysis aimed at examining the pressure–inflation relation and the axial force within a pressurized and elongated cylindrical tube. The material under consideration is an isotropic ground material that is reinforced by two families of fibers. Within these families, the fibers are taken to be dispersed. The natural configuration of these fibers may not coincide with the one of the ground substance, potentially due to a pre-stretch of the fibers or imperfect bonding between the constituents. The input parameters relevant to the mechanical system, including the fiber dispersion, the azimuthal and axial stretches of the cylinder, the stiffness parameters of the constituents, the fiber winding angle, and the natural configurations of the fibers are presumed to follow two distinct probability distribution functions. In the sensitivity analysis, we utilize the Sobol method to assess how variations of the input parameters influence the necessary inflation pressure and the corresponding axial force, which are the output variables. The application of the Sobol method enables us to consider the interactions among various parameters and to pinpoint the most significant factors affecting both the pressure–inflation relation and the axial force. This analysis highlights these elements, revealing a diverse array of results.