Nonlinear waves and shock calculations for hyperelastic fluid-filled tubes

Moodie, T. Bryant; Swaters, Gordon E.

doi:10.1090/qam/1031686

Authors: T. Bryant Moodie and Gordon E. Swaters
Journal: Quart. Appl. Math. 47 (1989), 705-722
MSC: Primary 76B99; Secondary 73D99, 73G05, 73K70, 73P05, 76B15, 76L05, 76Z05
DOI: https://doi.org/10.1090/qam/1031686
MathSciNet review: MR1031686
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Abstract: The propagation of both finite amplitude and weakly nonlinear waves in fluid-filled hyperelastic tethered tubes subjected to axial strain is investigated in some detail. Procedures based upon the methods of characteristics and relatively undistorted waves are deployed to compute the time and location of first shock formation in tubes having both constant and variable properties ahead of the wave. The influence of wall thickness changes in shock formation is explored and it is further found that if the transmural pressure ahead of the wave is zero then no shock can form on the lead characteristic for any model based on a rational theory of finite elasticity. This latter result is in disagreement with several earlier studies.

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