  Pressurised cylindrical channels made of soft materials are ubiquitous in
biological systems, soft robotics, and metamaterial designs. In this paper, we
study large deformation of a long, thick-walled, and compressible hyperelastic
cylindrical channel under internal pressure. The applied pressure can lead to
elastic bifurcations along the axial or circumferential direction. Incremental
theory is used to derive the partial differential equations that govern the
bifurcation behaviour of the cylindrical channel. Two cases of boundary
conditions on the outer surface of the cylinder, namely, free and constrained
are studied to understand their influence on the buckling behaviour. The
derived equations are solved numerically using the compound matrix method to
evaluate the critical pressure. The effects of the thickness of the cylinder
and the compressibility of the material on the critical pressure are
investigated for both the boundary conditions. The results reveal that for an
isotropic material, the bifurcation occurs along the axial direction of the
cylinder at lower critical pressure compared to the circumferential direction
for all cases considered. Finally, we demonstrate the tailorability of
bifurcation behaviour of the cylinder by adding reinforcements along the length
of cylinder. The anisotropic hyperelastic material behaviour for triggering the
bifurcation in the circumferential direction is studied by varying the material
parameters.
