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A continuum description of failure waves

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Języki publikacji
EN
Abstrakty
EN
Shattering of a brittle material such as glass occurs dynamically through a propagating failure wave, which however, can not be assigned to any of the classical wave. In this paper, we build a thermodynamically consistent theory based on the idea that a failure wave is analogous to a deflagration wave. Our theory admits, as special cases, the classical models of Feng and Clifton. Two fundamental thermodynamic functions form the basis of our theory. This approach allows for the construction of a new variational principle and a Lagrangian formulation. Finally, the theory is linearized to interpret specific experimental observations.
Rocznik
Strony
657—674
Opis fizyczny
Bibliogr. 37 poz., rys., tab.
Twórcy
autor
  • Stony Brook University, Department of Applied Mathematics and Statistics, Stony Brook, USA
autor
  • Stony Brook University, Department of Applied Mathematics and Statistics, Stony Brook, USA
Bibliografia
  • 1. Beardsley C.L., Anderson D.D., Marsh J.L., Brown T.D., 2005, Interfragmentary surface area as an index of comminution severity in cortical bone impact, Journal of Orthopaedic Research, 23, 3, 686-690
  • 2. Bebernes J., Eberly D., 2013, Mathematical Problems from Combustion Theory, Applied Mathematical Sciences, Vol. 83, Springer Science & Business Media
  • 3. Biot M.A., 1955, Variational principles in irreversible thermodynamics with application to viscoelasticity, Physical Review, 97, 6, 1463
  • 4. Biot M.A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics, 27, 3, 240-253
  • 5. Biot M.A., 1970, Variational Principles in Heat Transfer: a Unified Lagrangian Analysis of Dissipative Phenomena, DTIC Document
  • 6. Bless S.J., Brar N.S., 2007, Failure waves and their effects on penetration mechanics in glass and ceramics, [In:] Shockwave Science and Technology Reference Library, 105-141, Springer
  • 7. Bourne N.K., Rosenberg Z., 1996, The dynamic response of soda-lime glass, Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, 370, 1, 567-572
  • 8. Callister W.D., Rethwisch D.G., 2011, Materials Science and Engineering, Vol. 5, John Wiley & Sons, NY
  • 9. Chen Z., Feng R., Xin X., Shen L., 2003, A computational model for impact failure with shear-induced dilatancy, International Journal for Numerical Methods in Engineering, 56, 14, 1979-1997
  • 10. Chorin A.J., Marsden J.E., 1990, A Mathematical Introduction to Fluid Mechanics, 3rd edit., Springer
  • 11. Clavin P., Searby G., 2016, Combustion Waves and Fronts in Flows: Flames, Shocks, Detonations, Ablation Fronts and Explosion of Stars, Cambridge University Press
  • 12. Clifton R.J., 1993, Analysis of failure waves in glasses, Applied Mechanics Reviews, 46, 12, 540-546
  • 13. Courant R., Friedrichs K.O., 1991, Supersonic Flow and Shock Waves, Applied Mathematical Sciences, Vol. 21, Springer Science & Business Media
  • 14. Dafermos C., 2005, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Berlin
  • 15. Feng R., 2000, Formation and propagation of failure in shocked glasses, Journal of Applied Physics, 87, 4, 1693-1700
  • 16. Feng X.W., Liu Z.F., Chen G., Yao G.W., 2012, Experimental investigation on delayed failure of alumina under shock compression, Advances in Applied Ceramics, 111, 4, 237-242
  • 17. Fung Y.-C., Tong P., 2001,Classical and Computational Solid Mechanics, Vol. 1, World Scientific
  • 18. Goldstein H., 1965, Classical Mechanics, Pearson Education India
  • 19. Gurtin M.E., Fried E., Anand L., 2010, The Mechanics and Thermodynamics of Continua, Cambridge University Press
  • 20. Kanel G.I., Rasorenov S.V., Fortov V.E., 1991, The failure waves and spallations in homogeneous brittle materials, Shock Compression of Condensed Matter, 199, 1, 451-454
  • 21. Kanel G.I., Razorenov S.V., Savinykh A.S., Rajendran A., Chen Z., 2005, A study of the failure wave phenomenon in glasses compressed at different levels, Journal of Applied Physics, 98, 11, 113523 22. Lebon G., Jou D., Casas-V´azquez J., 2008, Understanding Non-Equilibrium Thermodynamics, Springer
  • 23. Lee J.J.-W., Constantino P.J., Lucas P.W., Lawn B.R., 2011, Fracture in teeth a diagnostic for inferring bite force and tooth function, Biological Reviews, 86, 4, 959-974
  • 24. Liebe T., Steinmann P., Benallal A., 2001, Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage, Computer Methods in Applied Mechanics and Engineering, 190, 49, 6555-6576
  • 25. Marsden J.E., Hughes T. Jr., 1994, Mathematical Foundations of Elasticity, Courier Corporation
  • 26. Maugin G.A., 1990, Internal variables and dissipative structures, Journal of Non-Equilibrium Thermodynamics, 15, 2, 173-192
  • 27. Maugin G.A., 1992, The Thermomechanics of Plasticity and Fracture, Vol. 7, Cambridge University Press
  • 28. Murakami S., 2012, Continuum Damage Mechanics: a Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer
  • 29. Nedjar B., 2002, A theoretical and computational setting for a geometrically nonlinear gradient damage modelling framework, Computational Mechanics, 30, 1, 65-80
  • 30. Neuberg J.W., Tuffen H., Collier L., Green D., Powell T., Dingwell D., 2006, The trigger mechanism of low-frequency earthquakes on Montserrat, Journal of Volcanology and Geothermal Research, 153, 1, 37-50
  • 31. Partom Y., 1998, Modeling failure waves in glass, International Journal of Impact Engineering, 21, 9, 791-799
  • 32. Rayleigh L., 1945, Theory of Sound, Vol. 1, Macmillan, London, reprinted 1945 by Dover, New York
  • 33. Sapozhnikov O.A., Maxwell A.D., MacConaghy B., Bailey M.R., 2007, A mechanistic analysis of stone fracture in lithotripsy, The Journal of the Acoustical Society of America, 121, 2, 1190-1202
  • 34. Walley S.M., 2013, An introduction to the properties of silica glass in ballistic applications, Strain, 50, 470-500
  • 35. Wei H., Samulyak R., 2014, Mass-conservative network model for brittle fracture, Journal of Coupled Systems and Multiscale Dynamics, 2, 2, 79-90
  • 36. Zhang Z.-X., 2016, Rock Fracture and Blasting: Theory and Applications, Butterworth-Heinemann
  • 37. Ziegler H., 2012, An Introduction to Thermomechanics, Vol. 21, Elsevier
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-37126367-c604-4ebf-9844-e8be4c9869f9
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