Shocks in thermoelastic rods

American Society of Mechanical Engineers, Applied Mechanics Division, AMD

Volumn 236, Issue , 1999, Pages 105-115

  O'Reilly, Oliver M ^a   Varadi, Peter C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; ENTROPY; FREE ENERGY; PHASE TRANSITIONS; PLASTIC DEFORMATION; SHOCK WAVES; TEMPERATURE; THERMODYNAMICS;

ACCELERATION WAVE; THERMOELASTIC ROD;

THERMOELASTICITY;

EID: 0033300262     PISSN: 01608835     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (32)

1. Abeyaratne, R., and Knowles, J. K., 1993, "Nucleation, Kinetics and Admissibility Criteria for Propogating Phase Boundaries," in Shock Induced Transitions and Phase Structures in Generalized Media, J. E. Dunn, R. Fosdick and M. Slemrod, Eds., Springer-Verlag, Berlin, pp. 1-33.
2. Abeyaratne, R., and Knowles, J. K., 1994a, "Dynamics of Propogating Phase Boundaries: Adiabatic Theory for Thermoelastic Solids, Physica D, Vol. 79, pp. 269-288.
3. Abeyaratne, R., and Knowles, J. K., 1994b, "Dynamics of Propogating Phase Boundaries: Thermoelastic Solids with Heat Conduction," Archive for Rational Mechanics and Analysis, Vol. 126, pp. 203-230.
4. Carlson, D. E., and Tortorelli, D. A., 1996, "On Hyperelasticity with Internal Constraints," Journal of Elasticity, Vol. 42, pp. 91-98.
5. Casey, J., and Carroll, M. M., 1996, "Discussion of 'A Treatment of Internally Constrained Materials' by J. Casey," ASME JOURNAL OF APPLIED MECHANICS, Vol. 63, p. 240.
6. Casey, J., and Krishnaswamy, S., 1998, "A Characterization of Internally Constrained Thermoelastic Materials," Mathematics and Mechanics of Solids, Vol. 3, pp. 71-89.
7. Cohen, H., 1978, "Shock Wave Decay in Elastic Rods," Iranian Journal of Science and Technology, Vol. 7, pp. 83-91.
8. Cohen, H., 1979, "On Wave Propogation and Evolution in Rods," Rendiconti del Seminaro Mathematico: Università e Politecnico Torino, Vol. 47, pp. 97-124.
9. Cohen, H., and Epstein, M., 1979, "Acceleration Waves in Constrained Elastic Rods," Archive for Rational Mechanics and Analysis, Vol. 72, pp. 141-154.
10. Cohen, H., and Whitman, H. B., 1977, "Waves in Elastic Rods," Journal of Sound and Vibration, Vol. 51, pp. 283-302.
11. Courant, R., and Friedrichs, K. O., 1948, Supersonic Flow and Shock Waves, Interscience Publishers, New York.
12. Godlewski, E., and Raviart, P.-A., 1996, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer-Verlag, New York.
13. Green, A. E., and Laws, N., 1966, "A General Theory of Rods," Proceedings of the Royal Society of London, Vol. A293, pp. 145-155.
14. Green, A. E., and Naghdi, P. M., 1977a, "On Thermodynamics and the Nature of the Second Law," Proceedings of the Royal Society of London, Vol. A357, pp. 253-270.
15. Green, A. E., and Naghdi, P. M., 1977b, "A Note on Thermodynamics of Constrained Materials," ASME JOURNAL OF APPLIED MECHANICS, Vol. 44, p. 787.
16. Green, A. E., and Naghdi, P. M., 1978, "A Derivation of Jump Condition for Entropy in Thermomechanics," Journal of Elasticity, Vol. 8, pp. 179-182.
17. Green, A. E., and Naghdi, P. M., 1979, "On Thermal Effects in the Theory of Rods," International Journal of Solids and Structures, Vol. 15, pp. 829-853.
18. Green, A. E., and Naghdi, P. M., 1993, "A Direct Theory of Viscous Fluid Row in Pipes. I: Basic General Developments," Proceedings of the Royal Society of London, Vol. A448, pp. 357-377.
19. Green, A. E., and Naghdi, P. M., 1995, "A Unified Procedure for the Construction of Theories of Deformable Media. II. Generalized Continuua," Proceedings of the Royal Society of London, Vol. A448, pp. 357-377.
20. Gurtin, M. E., 1994, "The Characterization of Configurational Forces," Archive for Rational Mechanics and Analysis, Vol. 126, pp. 387-394.
21. Gurtin, M. E., 1995, "The Nature of Configurational Forces," Archive for Rational Mechanics and Analysis, Vol. 131, pp. 67-100.
22. Hilditch, J., and Colella, P., 1995, "A Front Tracking Method for Compressible Flames in One Dimension," SIAM Journal on Scientific Computing, Vol. 16, pp. 755-772.
23. Lamb, H., 1929, Dynamics, Reprinted Second Edition, Cambridge University Press, Cambridge.
24. Lax, P. D., 1973, Hyperbolic Systems of Conservation Laws and Mathematical Theory of Shocks, SIAM, Philadelphia.
25. Love, A. E. H., 1897, Theoretical Mechanics, Cambridge University Press, Cambridge.
26. Marshall, J. S., and Naghdi, P. M., 1989, "A Thermodynamical Theory of Turbulence. I. Basic Developments," Philosophical Transactions of the Royal Society of London, Vol. A327, pp. 415-448.
27. Naghdi, P. M., 1982, "Finite Deformation of Elastic Rods and Shells," in Proceedings of the IUTAM Symposium on Finite Elasticity, Bethlehem PA 1980, D. E. Carlson and R. T. Shield, Eds., Martinus-Nijhoff, The Hague, pp. 47-103.
28. Nordenholz, T. R., and O'Reilly, O. M., 1997, "On Steady Motions of an Elastic Rod with Application to Contact Problems," International Journal of Solids and Structures, Vol. 34, pp. 1123-1143 and pp. 3211-3212.
29. O'Reilly, O. M., 1998, "On Constitutive Relations of Elastic Rods," International Journal of Solids and Structures, Vol. 35, pp. 1009-1024.
30. O'Reilly, O. M., and Varadi, P. C., 1999, "A Treatment of Shocks in One-Dimensional Thermomechanical Media." Accepted for publication in Continuum Mechanics and Thermodynamics.
31. Rivlin, R. S., 1975, "Thermomechanics of Materials with Fading Memory," in Theoretical Rheology, J. F. Hutton, J. R. A. Pearson and K. Walters, Eds., J. Wiley and Sons, New York, pp. 83-103.
32. Truskinovsky, L. M., 1993, "Shocks and Kinks," in Shock Induced Transitions and Phase Structures in Generalized Media, J. E. Dunn, R. Fosdick and M. Slemrod, Eds., Springer-Verlag, Berlin, pp. 185-229.