A catalog of pressure and deformation profile for thin walled hyperelastic tubes conveying inertialess flow and undergoing large deformation.

Slender tubes constituted of hyperelastic materials undergoing large deformations and conveying inertialess flow of Newtonian fluids are a model representation of several systems including those in soft robotics, biology and in industry. In this paper, we undertake a systematic study of this system. The tube's hyperelastic behavior is modeled by five (5) different constitutive laws: Neo-Hookean, Mooney–Rivlin, Fung, Gent and Ogden. Invoking the principles of finite elasticity, we delineate the local pressure — deformation relationship for the tube for each of the hyperelastic models. The structural mechanical field of the tube is then coupled with fluid flow field, which is simplified using the principles of lubrication approximation. The resultant fluid–structure interaction problem then throws up a set of interesting results including the deformation and pressure profile across the tube, and tube laws for five (5) hyperelastic models. Analyzing these results, we posit that the behavior of Neo-Hookean and Mooney–Rivlin tubes is converse of Fung's and Gent's tubes; the latter show a strain hardening behavior whilst the former exhibit a strain softening one. A sensitivity analysis which underscores the relative importance of geometrical nonlinearity in the problem then follows. • Thin walled hyperelastic tubes conveying inertialess flow analyzed. • Five (5) different models of hyperelasticity analyzed and compared. • Tubes undergo large deformations. • Lubrication approximation for fluid flow used to analyze the FSI problem. • Effect of geometric nonlinearity discussed. [ABSTRACT FROM AUTHOR]