Mechanics of a Hyperelastic Inflated Tube with Emphasis on Biological Soft Tissues

Inflated hollow cylinder is an important problem encountered in a variety of fields in
engineering. In industry, tires and fire hoses are pressurized from inside. In biomechanics, veins, arteries
and intervertebral discs can also be modeled using the inflated cylinder problem. The soft ground
substance of biological tissues in question are incompressible and portray large non-linear deformations
under loading. Classical theories of linear elasticity are incapable of modeling such behavior. Instead,
continuum mechanics based large displacement formulation and hyperelasticity are necessary to
understand the deformation and mechanics of soft materials. In this study, inflation of a cylinder
composed of an isotropic neo-Hookean type of material is analyzed in plane strain and generalized plane
strain conditions. First, an analytical solution is established using a continuum mechanical framework.
Second, the finite element method is employed to model the same problem. The numerical approach is
verified by using a mesh sensitivity analysis and validated by using analytical solution. Therefore, the
proposed analytical benchmark can quantify the accuracy of any commercial finite element software
solution of neo-Hookean tube inflation. As a side result, it was also revealed that the hydrostatic pressure
in the tube is more than six times the inflation pressure.