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Slender tubes constituted of hyperelastic materials undergoing largedeformations and conveying inertialess flow of Newtonian fluids at steady stateare a model representations of complex systems in both biomechanics andbio-inspired technology. In this paper, we undertake a systematic study of thissystem. The tube's hyperelastic behavior is modeled by five (5) differentconstitutive laws: neo Hookean, Mooney Rivlin, Fung, Gent and Ogden. Invokingthe principles of finite elasticity, we delineate the local pressure -deformation relationship for the tube for each of the hyperelastic models. Thestructural mechanical field of the tube is then coupled with fluid flow field,which is simplified using the tenets of lubrication approximation. Theresultant fluid-structure interaction problem then throws up a cohort ofinteresting results including the deformation and pressure profile across thetube, and tube laws for five ($5$) hyperelastic models. Analysing theseresults, we posit that the behavior of neo Hookean and Mooney Rivlin tubes usconverse of Fung's and Gent's tubes; the latter show a strain hardeningbehavior whilst the former exhibit a strain softening one. A sensitivityanalysis which underscores the relative importance of geometrical nonlinearityin the problem then follows.

A catalog of pressure drop, deformation profile and tube laws for slender hyperelastic tubes conveying Newtonian flow at steady state