Stability analysis of a hyperelastic tube under large deformation

Hyperelasticity plays a vital role in the advancement of the biological materials used in the medical science. The hyperelastic deformation sometimes leads to an unstable state, and this phenomenon is quite undesirable from a practical standpoint. At the unstable state, the deformation becomes highly non-uniform, and it may result a premature failure. In the present paper, we analyze the stability of a hyperelastic tube subjected to an internal pressure under large deformation. The deformation response of a hyperelastic tube is formulated through a new strain energy density function. An existing energy density function is modified in line with the limiting chain extensibility models. The existence of the modified energy function at its minimum potential state is ensured followed by the principle of polyconvexity. Additionally, we also developed the limiting conditions on the material parameters for a hyperelastic tube under large deformation. The stability criteria of a hyperelastic tube is examined through the distribution curve of the inflation pressure versus volume expansion ratio with the variation of the material parameters. The present study may provide a valid reference to design a hyperelastic tube for its numerous engineering and medical field applications.