Instabilities in a compressible hyperelastic cylindrical channel under internal pressure and external constraints

Pressurised cylindrical channels made of soft materials are ubiquitous in biological systems, soft robotics and metamaterial designs. In this paper, we study large deformation and subsequent instability of a thick-walled and compressible hyperelastic cylinder under internal pressure and external constraints. The applied pressure can lead to elastic bifurcations along the axial or circumferential direction. Perturbation 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 instability behaviour. The derived equations are solved numerically using the compound matrix method to evaluate the critical pressure for instability. The effects of the wall-thickness of the cylinder and the compressibility of the material on the critical pressure is 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 circumferential direction for all cases considered herein. Finally, the tuneability of the bifurcation behaviour of transversely isotropic cylinder is demonstrated by considering reinforcements along the cylinder's axis, triggering bifurcation in the circumferential direction in certain cases. The findings of the study indicate that the instability-induced pattern formation will be useful for designing shape changing material systems such as soft robotics and soft metamaterials.

Automated summary

This paper studies the large deformation and subsequent instability of a thick-walled and compressible hyperelastic cylinder under internal pressure and external constraints. Perturbation theory is used to derive the partial differential equations that govern the bifurcation behaviour, and numerical solutions are obtained to evaluate the critical pressure. The results show that the critical pressure is affected by the wall-thickness and compressibility of the material, and for isotropic materials, the axial direction has lower critical pressure.