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.