Nonlinear viscoelastic analysis of a cylindrical balloon squeezed between two rigid moving plates

A nonlinear model of visco-elastic balloon, interposed between a couple of moving rigid bodies, is formulated. The pneumatic structure is modeled as a thin, infinitely long cylindrical membrane, pre-stressed by an internal pressure. External pressure is assumed to be zero. The pushing bodies are modeled as a couple of frictionless rigid parallel plates, approaching each other normally, and causing squeezing of the pneumatic body. Motion is assumed to be slow, in such a way that any inertial effects are negligible. Both cases of long and short plates are considered, the latter entailing the possibility of puncture of the deformable body. A thermoplastic polyurethane material behavior is considered, and proper constitutive relationships adopted. Several models are formulated, which differ for constitutive laws (inextensible, elastic, linearly or non linearly visco-elastic) and/or for kinematic description (small strains and displacements or finite kinematics). The governing mixed differential-algebraic equations are analytically or numerically integrated for several impressed motion time-histories and the main features of the phenomenon are investigated.