Bulging bifurcation and post-bifurcation of hyperelastic membranes: remarks on two-parameter isotropic solids

Abstract

This article investigates the onset and development of bulging in hyperelastic membranes under internal pressure and axial stretch. We examine several two-parameter isotropic constitutive models—recovering the neo-Hookean model as a special or limiting case—commonly employed for the modelling of the mechanical behaviour of arterial soft tissue. Our analysis shows that the interplay between pressure and stretch, together with the material models, produces a highly non-trivial mechanical response. In particular, we derive necessary and sufficient conditions for the initiation of a bulge and characterize the subsequent post-bifurcation behaviour. Once a bulge forms, either it propagates radially without the increase of the bifurcation pressure, or it may propagate axially, along the tube, as the pressure approaches the Maxwell pressure that defines the ‘two-phase’ propagation state. For further axial propagation of bulging, the inflation pressure must be increased.