For the first time, the problem of the inflation of a
nonlinear viscoelastic
thick-walled spherical shell is considered. Specifically, the wall has
quasilinear viscoelastic
constitutive behaviour, which is of fundamental importance in a wide range of applications, particularly in the context of biological systems such as hollow viscera, including the lungs and bladder. Experiments are performed to demonstrate the efficacy of the model in fitting relaxation tests associated with the volumetric inflation of
murine bladders
. While the associated
nonlinear elastic
problem of inflation of a balloon has been studied extensively, there is a paucity of studies considering the equivalent
nonlinear viscoelastic
case. We show that, in contrast to the elastic scenario, the peak pressure associated with the inflation of a neo-Hookean balloon is
not
independent of the shear modulus of the medium. Moreover, a novel numerical technique is described in order to solve the
nonlinear Volterra integral equation
in space and time originating from the fundamental problem of inflation and deflation of a thick-walled nonlinear viscoelastic shell under imposed pressure.
Rotation of a synchronous viscoelastic shell
