High-Pressure Shock Compression of Solids VI pp 215-254 | Cite as

# The Shock Wave as a Nonequilibrium Transport Process

- 8 Citations
- 304 Downloads

## Abstract

Shock-wave propagation involves mass, momentum, and energy transport in a medium. The state of a medium is determined by the exchange processes with surroundings through the interphase boundaries and the transport processes occurring within it. The transport processes in a medium are characterized by their rates, intensity, and the initial state of the medium. There a problem arises: how does one determine the state of the medium under given loading conditions? Following Maxwell, the medium state can be determined only with respect to the applied loading conditions. Under a short-time loading a medium demonstrates its solid properties and, when subject to a long-time force, the same medium behaves more as a liquid. There have been many attempts to describe plastic properties of deformed solids by methods similar to those used for hydrodynamic flow. Classical hydrodynamics, however, is valid only for fluids near thermodynamic equilibrium. From the point of view of nonequilibrium statistical mechanics, the deviation of the state of the system from thermodynamic equilibrium is closely connected with the correlation concept. A solid body subject to a very low velocity impact moves without deformation owing to the rigid correlation among the particles of the medium. All particles are linked together and their typical correlation length corresponds to the size of the body. In this case, we have mechanical transport only at the macroscopic scale. If we have a fluid in thennodynamic equilibrium, and if the applied loading isn’t highrate and intense, its behavior is that of an ideal fluid without relaxation. All particles are moving chaotically without any correlation. The typical correlation length is zero. More intense loading produces nonequilibrium transport characterized by finite space-time correlation scales. In all intermediate cases, we have a finite correlation length within which collective motion of particles of the medium occurs. This means that the medium does not behave as a simple fluid when subjected to load. Rather than being a structure less continuum, it is a medium having a complicated internal structure.

## Keywords

Shock Wave Wave Front Entropy Production Velocity Fluctuation Velocity Dispersion## Preview

Unable to display preview. Download preview PDF.

## References

- [1]S. De Groot and P. Mazur,
*Nonequilibrium thermodynamics*, North-Holland, Amsterdam (1963).Google Scholar - [2]T.K. Shapovalov, “To the initial conditions for equations of rarefied gas hydrodynamics”,
*Aeromekhanika*, pp. 304–306, (1976) (in Russian)Google Scholar - [3]W. Garen, R. Synifzik, and G. Wertberg, “Experimental investigation of weak shock waves in noble gases,” in:
*Rarefied gas dynamics*, 10^{th}Int. Symp, (ed. G. Potter), pp. 519–528 (1978).Google Scholar - [4]M.N. Kogan,
*Rarefied gas dynamics.*Nauka, Moscow, (1967) (in Russian).Google Scholar - [5]L.C. Woods, “Transport processes in dilute gases over the whole range of Knudsen numbers. Part 1. General theory.”
*J. Fluid Mech.***93**, pp. 585–607 (1979).MathSciNetADSzbMATHCrossRefGoogle Scholar - [6]C.R. Doering, M.A. Burshka, W. Horsthenike, “Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics,”
*J. Stat. Phys*.**65**, pp. 953–970 (1991).ADSzbMATHCrossRefGoogle Scholar - [7]D.N. Zubarev and S.V. Ticshenko, “Nonlocal hydrodynamics with memory,”
*Physica***59**, pp. 285–304 (1972).MathSciNetADSCrossRefGoogle Scholar - [8]B.V. Filippov and T.A. Khantuleva,
*Boundary problems of non local hydrodynamiCS*, Leningrad, Leningrad State Univ. (1984) (in Russian).Google Scholar - [9]M. Bixon, J.R. Dorfman, and K.C. Mot, “General hydrodynamic equations from the linear Boltzmann equation,”
*Phys. Fluids***14**, pp. 1049–1057 (1971).ADSzbMATHCrossRefGoogle Scholar - [10]N.N. Bogolyubov,
*Problems of dynamic theory in statistical physics*, Gostekhizdat, Moscow (1946). (in Russian).Google Scholar - [11]L.P. Kadanoff and P.C. Martin, “Hydrodynamic equations and correlation functions,”
*Ann. Phys.***24**, pp. 419–460 (1963).MathSciNetADSzbMATHCrossRefGoogle Scholar - [12]C.H. Chung and S. Yip, “Generalized hydrodynamics and time correlation functions,”
*Phys. Rev*.**182**, pp. 323–338 (1965).ADSCrossRefGoogle Scholar - [13]N. Ailavadi, A. Rahman, and R. Zwanzig, “Generalized hydrodynamics and analysis of current correlation functions,”
*Phys. Rev*.**4a**, pp. 1616–1625 (1971).ADSGoogle Scholar - [14]J.M. Richardson, The hydrodynamical equations of a one-component system derived from nonequilibrium statistical mechanics.
*J. Math. Anal. and Appl.***1**, pp. 12–60 (1960).MathSciNetzbMATHCrossRefGoogle Scholar - [15]R. Piccirelli, “Theory of the dynamics of simple fluid for large spatial gradients and long memory,”
*Phys. Rev*.**175**, pp. 77–98 (1968).ADSCrossRefGoogle Scholar - [16]K. Kawasaki and J.D. Ganton, “Theory of nonlinear transport processes: nonlinear shear viscosity and normal stress effects”
*Phys. Rev. A***8**, pp. 2048–2064 (1973).ADSCrossRefGoogle Scholar - [17]H. Mori, “Transport, collective motion and brownian motion,”
*Progr. Theor. Phys*.**33**, pp. 423–454 (1965).ADSzbMATHCrossRefGoogle Scholar - [18]D.N. Zubarev, “Statistical operator for nonequilibrium systems”
*Doklady Akad. Nauk SSSR***140**, pp. 92–95 (1961) (in Russian).Google Scholar - [19]D.N. Zubarev, “Modern methods of statistical theory of irreversible processes,”
*Itogi nauki i tekhniki. Ser. Sovremennye problemy matematiki***15**, VINITI, Moscow, pp. 128–227 (1980) (in Russian).Google Scholar - [20]V. Ya. Rudyak,
*Statistical theory of dissipative processes in gases and liquids*, Nauka, Novosibirsk (1987) (in Russian).Google Scholar - [21]T.A Khantuleva, “Modern hydrodynamical problems on the basis of nonlocal hydrodynamical equations,”
*Modely mekhaniki sploshnoj sredy*, Vladivostok-Novosibirsk, pp. 158–173 (1991) (in Russian).Google Scholar - [22]A.G. Vershinin and T.A. Khantuleva, “To a nonlocal description of flows with shock waves,”
*Mekhanika reagiruyuschikh sred i eye prilojeniya*, Nauka, Novosibirsk, pp. 89–96 (1989). (in Russian)Google Scholar - [23]A.G. Vershinin and T.A. Khantuleva, “Nonlocal hydrodynamical model of the shock wave front,”
*Fizicheskaya mekhanika***16**, Leningrad State Univ., Leningrad, pp. 21–31 (1990) (in Russian).Google Scholar - [24]S.A. Vavilov, “Geometric methods of studying the solvability of a class of operator equations”
*Russian Acad. Sci. Dokl. Math*.**45**, pp. 276–280 (1992).MathSciNetGoogle Scholar - [25]S.A. Vavilov, “A method of studying the existence of nontrivial solutions to some classes of operator equations with an application to resonance problems in mechanics,”
*Nonlinear Analysis***24**, pp. 747–764 (1995).MathSciNetzbMATHCrossRefGoogle Scholar - [26]T.A. Khantuleva and Yu.I. Mescheryakov, “Nonlocal theory of the high-strain-rate processes in structured media,”
*Int. J. Solids and Structures***36**, pp. 3105–3129 (1999).zbMATHCrossRefGoogle Scholar - [27]T.A. Khantuleva and Yu.I. Mescheryakov, “Kinetics and non-local hydrodynamics of mesostructure formation in dynamically deformed media,”
*Phys. Mesomechanics***2**, pp 5–17 (1999).Google Scholar - [28]T.A. Khantuleva, “Non-local theory of high-rate processes in structured media,” in:
*Shock Compression in Condensed Matter—1999*(ed. M.P. Furnish, L.C. Chhabildas, and R.S. Hixson), American Institute of Physics, New York, pp. 371–374 (2000).Google Scholar - [29]T.A. Khantuleva, “Microstructure formation in the framework of the non-local theory of interfaces,”
*Mater. Phys. Mech*.**2**, pp 51–62 (2000).Google Scholar - [30]Yu. V. Sud’enkov, “Relaxation of the elastic constants in A1 near the loading surface,”
*J. Tech. Phys. Letters*. 9, pp. 1418–1422 (1983) (in Russian).Google Scholar - [31]O.D Baizakov and Yu. V. Sud’enkov, “Relaxation phenomena in materials near the surface of the elastic submicrosecond loading,”
*J. Tech. Phys. Letters*.**11**, pp. 1433–1437 (1985)(in Russian).Google Scholar - [32]Yu. V. Sud’enkov, “Special features of the shock wave propagation in solids near the surface of high-rate loading” In:
*Problems of dynamical processes in heterogeneous media*ed. Kalinin Univ., pp. 120–126 (1987) (in Russia).Google Scholar - [33]Yu.I. Mescheryakov and A.K. Divakov, “Multi-scale kinetics of microstructure and strain-rate dependnence of materials,”
*DYMAT Journal***1**, p. 271 (1994).Google Scholar - [34]Yu.I. Mescheryakov, A.K. Divakov, and N.I. Zhigacheva, “Role of mesostructure effects in dynamic plasticity and strength in ductile steels,”
*Mater. Phys. Mech*.**3**, pp. 63–100 (2001).Google Scholar - [35]Yu.I. Mescheryakov, “Mesoscopic effects and particle velocity distribution in shock compressed solids,” in:
*Shock Compression in Condensed Matter—1999*(ed. M.P. Furnish, L.C. Chhabildas, and R.S. Hixson), American Institute of Physics, New York, pp 1065–1070 (1999).Google Scholar - [36]
*Physical mesomechanics and computer construction of materials*(ed. V.A. Panin), Nauka, Novosibirsk (1995).Google Scholar - [37]
- [38]Yu.I. Mescheryakov, this volume, Chapter 5.Google Scholar