Inflation of residually stressed Fung-type membrane models of arteries

Elastic arteries are idealised as being incompressible orthotropic nonlinearly elastic cylinders. They are further idealised as being membranes in order to analyse the effect of the experimentally observed pre-stressing of arterial tissue on inflation. The pre-stress is modelled here using the opening-angle method. It is shown that there can be multiple unloaded states of arterial segments of Fung materials, suggesting the corresponding set of material parameters will not yield reliable predictions of arterial stress in three dimensions as there is no experimental evidence to support this non-uniqueness. It is also shown that the circumferential pre-strain has a simple magnifying scaling effect on the pressure-radial strain relation and on the axial force needed to maintain the membrane length during inflation; the effect of the axial pre-strain is more nuanced.