Magic angles for fiber reinforcement in rubber-elastic tubes subject to pressure and swelling

The synthetic fibers in a fire hose are specially oriented so as to minimize the jerk when the hose is suddenly pressurized – at other fiber orientations the hose would either extend abruptly or shorten abruptly. This is one example of a magic angle that separates different response directions in a deformation mode as some driving mechanism is varied. Here we investigate magic angles for winding fibers around a tube with an otherwise rubbery matrix by providing a hyperelastic analysis. While the driving mechanism of pressurization is well known in this regard, we also consider the driving mechanism of matrix swelling. Magic angles of fiber orientation are considered for axial deformation and for channel constriction.