Modeling the Behavior of Materials

Part of the Scientific Computation book series (SCIENTCOMP)


The first requirement in the calculation of problems in mechanics is a formulation of the material behavior. The material description should include elastic, elastic-plastic, and hydrodynamic flow. Appropriate yield criteria must be employed. The literature includes many complicated forms to describe material behavior, some of which have been developed to aid the mathematics in the analytical solution of the equations of motion. However, since numerical techniques are considered here, the equations of motion are completely independent of equations that describe material behavior, and any mathematical form may be used. The objective of the material models is to provide a theoretical description applicable to a wide class of practical problems, but using simple idealizations of the outstanding features of the real phenomena.


Plastic Strain Flow Stress Yield Surface Fracture Initiation Equivalent Plastic Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [3.1]
    G. Maenchen, J. Nuckolls: Calculations of Underground Explosions, Proceedings of the Geophysical Laboratory, Lawrence Radiation Laboratory Cratering Symposium, Lawrence Radiation Laboratory, Report UCRL-6438, Part I I (1961)Google Scholar
  2. [3.2]
    R. von Mises: Z. Angew Math. u. Mech. 8, 161–185 (1928)zbMATHCrossRefGoogle Scholar
  3. [3.3]
    D.C. Drucker: A Definition of Stable Inelastic Material, J. Appl. Mech., 26, 101–106 (1959)MathSciNetzbMATHGoogle Scholar
  4. [3.4]
    W.L. Bradley: Strain Hardening in the HEMP Code, Lawrence Livermore National Laboratory report UCID-16328 (1973)Google Scholar
  5. [3.5]
    M.L. Wilkins, J.E. Reaugh: Plasticity Under Combined Stress Loading, American Society of Mechanical Engineers Publication 80-C2/ PVP-106 (August 1980)Google Scholar
  6. [3.6]
    D.J. Steinberg, S.G. Cochran, M.W. Guinan: J. Appl. Phys 51, 1498 (1980)ADSCrossRefGoogle Scholar
  7. [3.7]
    J.J. Gilman, W.G. Johnston: Dislocation and Mechanical Properties of Crystals, ed. by J.G. Fisher, W.G. Johnston, R. Thompson, T. Vreeland ( Wiley, New York 1957 )Google Scholar
  8. [3.8]
    G.I. Taylor: Proc. R. Soc. A. 194, 289 (1948)ADSCrossRefGoogle Scholar
  9. [3.9]
    M.L. Wilkins, M.W. Guinan: J. Appl. Phys. 44, No. 3, 1200 (1973)ADSCrossRefGoogle Scholar
  10. [3.10]
    W. Gust: J. Appl. Phys. 53, No. 5, 3566 (1982)ADSCrossRefGoogle Scholar
  11. [3.11]
    G.C. Sih: Handbook of Stress-Intensity Factors, Institute of Fracture and Solid Mechanics, Leigh University, Bethlehem, Pennsylvania (1973)Google Scholar
  12. [3.12]
    G.R. Irwin: Trans ASME, Ser. D 82, 417 (1960)CrossRefGoogle Scholar
  13. [3.13]
    V.M. Vainshelbaum, R.V. Goldshtein: On the Material Scale Length as a Measure of the Fracture Toughness of Plastic Materials and its Role in Fracture Mechanics, Institute of Problems of Mechanics, USSR Academy of Sciences, Moscow (1976)Google Scholar
  14. [3.14]
    W.F. Brown, Jr., J.E. Srawley: Plane Strain Crack Toughness Testing of High Strength Metallic Materials, ASTM STP 410, American Society for Testing and Materials, Philadelphia (1966)Google Scholar
  15. [3.15]
    F.R. Tuler, B.M. Butcher: A Criterion for the Time Dependence of Dynamic Fracture, Int. J. Fracture Mechanics 4, No. 4, 431 (1968)Google Scholar
  16. [3.16]
    F.A. McClintock, A.S. Argon: Developments in Mechanics, Proceedings of the 11th Midwestern Mechanics Conference, Iowa State University, Ames, Iowa (1969). Also cited: Mechanical Behavior of Materials, (Addison-Wesley, Reading, Massachusetts 1965 ), 524Google Scholar
  17. [3.17]
    K. Mogi: Rock Fracture, in Annual Review of Earth and Planetary Science, ed. F.A. Donath, (Annual Reviews, Palo Alto, CA), Vol. 1, 63–84 (1973)Google Scholar
  18. [3.18]
    M.L. Wilkins, R.D. Streit, J.E. Reaugh: Cumulative-Strain-Damage Model of Ductile Fracture: Simulation and Prediction of Engineering Fracture Tests, Lawrence Livermore National Laboratory report UCRL-53058 (October 3, 1980 )Google Scholar
  19. [3.19]
    M.L. Wilkins, B. Squier, B. Halperin: Equation of State for Detonation Products of PBX 9404 and LX-04–01, Tenth Symposium ( International) on Combustion. ( The Combustion Institute 1965 ), 769–778Google Scholar
  20. [3.20]
    R. Cole: Underwater Explosions, Princeton University Press Princeton N.J. (1948)Google Scholar
  21. [3.21] J.W. Kury, H.C. Hornig, E.L. Lee, J.L. McDonnel, D.L. Ornellas, M. Finger, F.M. Strange, M.L. Wilkins: Metal Acceleration by Chemical Explosives, Fourth Symposium (International)
    on Detonation, Office of Naval Research, U.S. Naval Ordnance Laboratory, White Oak, MD. ACR 126- Office of Naval Research/Department of the Navy, (October 12–15, 1965 )Google Scholar
  22. [3.22]
    E.L. Lee, H.C. Hornig, J.W. Kury: Adiabatic Expansion of High Explosive Detonation Products, Lawrence Livermore National Laboratory report UCRL-50422 (May 2, 1968 )Google Scholar
  23. [3.23]
    B.M. Dobratz: Properties of Chemical Explosives and Explosive Simulants, Lawrence Livermore National Laboratory Explosives Handbook (March 16, 1981 )Google Scholar
  24. [3.24] M.L. Wilkins: The Use of One-and Two-Dimensional Hydrodynamic Mechanics Calculations in High Explosive Research, Fourth Symposium (International)
    on Detonations, Office of Naval Research, U.S. Naval Ordnance Laboratory, White Oak, MD. ACR 126- Office of Naval Research/Department of the Navy (October 12–15 1965 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA

Personalised recommendations