# Traditional Analysis of Nonlinear Wave Propagation in Solids

- 308 Downloads

## Abstract

Before beginning a formal discussion of nonlinear wave propagation, it seems useful to describe some of the basic observations. Most of the work that has been done concerns the response of materials to compression because the experiments are convenient and permit access to states of larger deformation than can be attained in materials under tension. The simplest situation considered is that in which a wave is introduced into the material by applying a compressive force uniformly over the surface of a halfspace. When this force increases smoothly in time, the resulting wave is also smooth. However, it is observed that (with a few exceptions) the gradient in such a wave increases with increasing propagation distance. Eventually, the wavefront evolves into an almost discontinuous jump. One cannot expect formation of a true discontinuity, but this is often a useful mathematical approximation to reality.

## Keywords

Shock Compression Jump Condition Detonation Product Uniaxial Strain Traditional Analysis## Preview

Unable to display preview. Download preview PDF.

## References

- [1]J.N. Johnson and R. Chéret (eds.),
*Classic Papers in Shock Compression Science*, Springer, New York (1998).zbMATHGoogle Scholar - [2]R. Courant and K.O. Friedrichs,
*Supersonic Flow and Shock Waves*, Interscience, New York (1948).zbMATHGoogle Scholar - [3]V.F. Nesterenko,
*iDynamics of Heterogeneous Materials*, Springer-Verlag, New York (2001).CrossRefGoogle Scholar - [4]C. Truesdell and R.A. Toupin, The Classical Field Theories, in
*Handbuch der Physik***III/1**(ed. S. Flügge), Springer-Verlag, Berlin (1960).Google Scholar - [5]L.E. Malvern,
*Introduction to the Mechanics of Continuous Media*, Prentice-Hall, Englewood Cliffs, NJ (1969).Google Scholar - [6]D.S. Drumheller,
*Introduction to Wave Propagation in Nonlinear Fluids and Solids*, Cambridge University Press, Cambridge (1998).CrossRefGoogle Scholar - [7]C. Truesdell and W. Noll, in
*Handbuch der Physik***III/3**(ed. S. Flügge), Springer-Verlag, Berlin (1965).Google Scholar - [8]M.H. Rice, R.G. McQueen, and J.M. Walsh, in
*Solid State Physics***6**(eds. F. Seitz and W. Turnbull), Academic Press, New York, pp. 1–63 (1958).Google Scholar - [9]R.G. McQueen, S.P. Marsh, J.W. Taylor, J.N. Fritz, and W.J. Carter, in
*High Velocity Impact Phenomena*(ed. R. Kinslow), Academic Press, New York, pp. 293–417 with appendices on pp. 515-568 (1970).CrossRefGoogle Scholar - [10]R.N. Thurston, in
*Handbuch der Physik***IVa/4**(ed. S. Flügge), Springer-Verlag, Berlin, pp. 109–308 (1974).Google Scholar - [11]J.R. Asay and M. Shahinpoor, eds.,
*High-Pressure Shock Compression of Solids*, Springer-Verlag, New York (1993).Google Scholar - [12]
*Shock compression of Condensed Matter — 2001*(eds. M.D. Furnish, N.N. Thadhani, and Y. Horie), American Institute of Physics, Melville, NY (2002).Google Scholar - [13]Eleventh International Detonation Symposium, U.S. Office of Naval Research report ONR33300-5 (2000).Google Scholar
- [14]L.M. Barker, M. Shahinpoor, and L.C. Chhabildas, in [11], pp. 43–73.Google Scholar
- [15]L. Davison and M. Shahinpoor, eds.,
*High-Pressure Shock Compression of Solids—III*, Springer-Verlag, New York (1997).Google Scholar - [16]S.K. Sikka, B.K. Godwal, and R. Chidambaram, in [15], pp. 1–35.Google Scholar
- [17]
- [18]
- [19]J.N. Johnson, in [11], pp. 217–264.Google Scholar
- [20]G.T. Gray III, in [11], pp. 187–215.Google Scholar
- [21]T. Mashimo, in [15], pp. 101–146.Google Scholar
- [22]J. Cagnoux and J.-Y. Tranchet, in [15], pp. 147–169.Google Scholar
- [23]J.W. Nunziato, E.K. Walsh, K.W. Schuler, and L.M. Barker, in
*Handbuch der Physik***IVa/4**(ed. S. Flügge), Springer-Verlag, Berlin, pp. 1–108 (1974).Google Scholar - [24]R.A. Graham,
*Solids Under High-Pressure Shock Compression*, Springer-Verlag, New York (1993).Google Scholar - [25]T.H. Antoun, L. Seaman, D.R. Curran, G.I. Kanel, S.V. Razorenov, and A.V. Utkin,
*Dynamic Fracture of Materials*, Springer-Verlag, New York, in press.Google Scholar - [26]L. Davison, D.E. Grady, and M. Shahinpoor, eds.,
*High-Pressure Shock Compression of Solids—II: Dynamic Fracture and Fragmentation*, Springer-Verlag, New York (1996).zbMATHGoogle Scholar - [27]A.K. Zurek and M.A. Meyers, in [26], pp. 25–70.Google Scholar
- [28]L. Davison, Y. Horie, and M. Shahinpoor, eds.,
*High-Pressure Shock Compression of Solids—IV: Response of Highly Porous Solids to Shock Loading*, Springer-Verlag, New York (1997).Google Scholar - [29]L.S. Belmett, K. Tanaka, and Y. Horie, in [28], pp. 105–175.Google Scholar
- [30]R. Engelke and S.A. Sheffield, in [15], pp. 171–239.Google Scholar
- [31]S.A. Sheffield, R.L. Gustavsen, and M.U. Anderson, in [28], pp. 23–61, (1997).Google Scholar
- [32]M.R. Baer in [28], pp. 63–82.Google Scholar
- [33]F.L. Addessio and J.B. Aidun, in [15], pp. 241–275.Google Scholar
- [34]T.J. Ahrens, in [11], pp. 75–113.Google Scholar
- [35]L. Davison, Y. Horie, and T. Sekine, eds.,
*High-Pressure Shock Compression of Solids—V: Shock Chemistry with Application to Meteorite Impacts*, Springer-Verlag, New York (2003).Google Scholar - [36]N.N. Thadhani and T. Aizawa, in [28], pp. 257–287.Google Scholar
- [37]J.M. McGlaun and P. Yarrington, in [11], pp. 323–353.Google Scholar
- [38]