Study of bifurcation in a pressurized hyperelastic membrane tube enclosed by a soft substrate

We model a perivascular supported arterial tube as a uniform cylindrical membrane tube enclosed by a soft substrate, and derive the solution bifurcation criterion. We assume the surrounding soft substrate as an elastic foundation with distributed stiffness. We consider the tube to be a neo-Hookean material with isotropic and anisotropic (orthotropic) properties, and study solution bifurcation at a constant axial stretch. In the isotropic case, the surrounding soft substrate can substantially delay the onset of bifurcation through a subcritical jump in circular distension at bifurcation with increasing substrate stiffness. Introduction of anisotropy can significantly change the jump behavior from subcritical to supercritical. •A cylindrical membrane tube enclosed by an elastic substrate is modeled.•The model has relevance to an arterial tube with perivascular support.•Bifurcation criterion for axisymmetric bulging mode is obtained.•Subcritical and supercritical jump phenomena are observed.