Branching of stretch histories in biaxially loaded nonlinear viscoelastic fiber-reinforced sheets

This work considers an experiment in which a nonlinear viscoelastic square sheet, subjected to uniformly distributed tensile forces on its edge surfaces, undergoes a homogeneous biaxial extensional creep history. The sheet is fiber-reinforced with the direction of reinforcement either normal to the midplane of the sheet or parallel to one of its edges. The possibility is considered that when the governing equations are solved for the biaxial creep response, there may be a time during the deformation when a second solution branch can form. Thus, if equal biaxial forces are applied to the sheet, its deformed states are squares until some time when they become rectangular. The material is modeled using the Pipkin–Rogers nonlinear single integral constitutive equation for a transversely isotropic material. A condition is derived to determine the time when the solution to the governing equations forms a new branch. Numerical examples are presented for fibers oriented normal to the sheet and in the plane of the sheet.