Investigation on Mie-Grüneisen type shock Hugoniot equation of state for concrete


  • M Katayama
  • A Abe
  • A Takeba



This paper ascertains that the bilinear shock Hugoniot equation of state (EOS) can model the plasticizing process of the porous media like concrete material for high-velocity impact problems successfully. The negative slope of the bilinear Hugoniot for low particle velocity regime can simulate the process that the porosity of concrete may be compressed to form shock wave in concrete, through a series of numerical analyses over the investigation on the physical phenomena. The results of particle velocity for the concrete material are also discussed to be compared with those of non-porous aluminum alloy for 100 and 1000 m/s impact velocities. All the numerical simulations were carried out by applying the bilinear shock Hugoniot EOS to concrete which was linked to the binary object of a hydrocode: ANSYS Autodyn®[1−3] through a user’s subroutine.


ANSYS Autodyn Theory Manual Revision 4.3, Century Dynamics Inc., 2005.

ANSYS Autodyn User’s Manual, Release 15.0, ANSYS, Inc., November 2013.

ANSYS Autodyn User’s Subroutines Tutorial, Release 15.0, ANSYS, Inc., November 2013.

Marsh, S. P. (Ed.), LASL shock Hugoniot data, University of California Press, Berkeley, 1980.

Thiel, M. van, Compendium of Shock Wave Data, UCRL-50108, Lawrence Livermore Laboratory, Livermore, 1977.

Kohn, B. J., Compilation of Hugoniot equations of state, AFWL-TR-69-38, Air Force Weapons Laboratory, New Mexico, 1969.

Trunin, R. F., Shock compression of condensed materials, Cambridge University Press, Cambridge, 1998.

Ahrens, T. J. and Johnson, M. L., Shock wave data for rocks, in Mineral Physics and Crystallography, A Handbook of Physical Constants, Vol.3 (ed. by T. J. Ahrens), Amer. Geophys. Union, Washington, D. C., 1995: p. 35-44.

Riedel, W., Wicklein, M. and Thoma, K., Shock properties of conventional and high strength concrete: Experimental and mesomechanical analysis, International Journal of Impact Engineering, 2008, 35, p. 155-171.

Grady, D. E., Impact compression properties of concrete, The 6th International Symposium on Interaction of Nonnuclearmunitions with Structures, Panama City, FL, 1993: p. 172-175.

Grady D.E., Dynamic decompression properties of concrete from Hugoniot states — 3-25 GPa, Experimental Impact Physics Department Technical Memorandum, TMDG0396, February 1996.

Hall, C. A., Chhabildas, L. C. and Reinhart W. D., Shock Hugoniot and release in concrete with different aggregate size from 3 to 23 GPa., International Journal of Impact Engineering, 1999, 23: p. 341-351.

Kipp, M. E. and Chhabildas, L. C., Elastic shock response and spall strength of concrete, CP 429 Shock Compression of Condensed Matter, 1997: p. 557-560.

Gebbeken, N. and Ruppert, M., A new concrete material model for high dynamic hydrocode simulations., Archive of Applied Mechanics, 2000, 70: p. 463-78.

Gebbeken, N., Greulich, S. and Pietzsch, A., Hugoniot properties for concrete determined by full-scale detonation experiments and flyerplate-impact tests, International Journal of Impact Engineering, 2006, 32: p. 2017-2031.

Ockert, J., Ein Stoffgesetz für die Schockwellenausbreitung, Beton PhD thesis, Technische Hochschule Karlsruhe, 1997.

Tsembelis, K., Millett, J. C. F., Proud W. G. and Field J. E., The shock Hugoniot Properties of cement paste up to 5 GPa, CP505 Shock Compression of Condensed Matter, 1999: p. 1267-70.

Tsembelis, K., Proud, W. G. and Field, J. E., The dynamic strength of cement paste under shock compression, CP620 Shock Compression of Condensed Matter, 2001: p. 1414-1417.

Tsembelis, K., Proud, W. G., Willmott, G. R. and Cross, D. L.A., The shock Hugoniot properties of cement paste & mortar up to 18 GPa, CP706 Shock Compression of Condensed Matter, 2003: p. 1488-1491.

Ishiguchi, M., Yoshida, M., Nakayama, Y., Matsumura, T., Takahashi, I., Miyake, A., et al., A study of the Hugoniot of mortar, Journal of Japanese Explosives Society — Kayaku Gakkaishi, 2000, 61(6): p. 249-253.

Selected Hugoniots, Group GMX-6, LA-4167-MS, Los Alamos Scientific Laboratory, 1969.

Johnson, G. R. and Cook, W. H., A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures. Proceedings of 7th International Symposium on Ballistics, The Hague, The Netherlands, 1983: p. 541-547.



How to Cite

Katayama, M., Abe, A. and Takeba , A. (2017) “Investigation on Mie-Grüneisen type shock Hugoniot equation of state for concrete”, The International Journal of Multiphysics, 11(3), pp. 255-264. doi: 10.21152/1750-9548.11.3.255.