Nonlinear reflection of shock shear waves in soft elastic media

The Journal of the Acoustical Society of America
Gianmarco F PintonM Tanter

Abstract

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides ...Continue Reading

References

Feb 1, 2003·The Journal of the Acoustical Society of America·Roger J ZempRichard S C Cobbold
Nov 1, 2003·The Journal of the Acoustical Society of America·François Coulouvrat, Régis Marchiano
Nov 1, 2003·The Journal of the Acoustical Society of America·Régis MarchianoRichard Grenon
Nov 13, 2003·Physical Review Letters·S CathelineM Fink
Mar 12, 2005·The Journal of the Acoustical Society of America·Régis MarchianoJean-Louis Thomas
Oct 2, 2007·The Journal of the Acoustical Society of America·Xavier JacobMathias Fink
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Régis MarchianoJean-Louis Thomas
Feb 6, 2008·The Journal of the Acoustical Society of America·J-L GennissonM Fink
Jun 6, 2008·The Journal of the Acoustical Society of America·Mark S WochnerEvgenia A Zabolotskaya

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Citations

Jan 12, 2011·The Journal of the Acoustical Society of America·Michel Destrade, Raymond W Ogden
Aug 29, 2014·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·Gianmarco PintonFrançois Coulouvrat
Jun 7, 2011·Applied Spectroscopy·Jonathan R Dion, David H Burns
Feb 3, 2016·Journal of Biomechanical Engineering·Bruno GiammarinaroGianmarco Pinton
Mar 13, 2019·International Journal for Numerical Methods in Biomedical Engineering·Bharat B TripathiGianmarco F Pinton
Aug 20, 2019·Proceedings. Mathematical, Physical, and Engineering Sciences·Michel DestradeGiuseppe Saccomandi
Feb 4, 2019·The Journal of the Acoustical Society of America·Maria M KarzovaPhilippe Blanc-Benon

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