Journal of Engineering Mathematics

, Volume 68, Issue 3–4, pp 269–277 | Cite as

Determining the equation of state of highly plasticised metals from boundary velocimetry: part I

  • H. Ockendon
  • J. R. Ockendon
  • J. D. PlattEmail author


Assuming that a highly plasticised metal has an equation of state that relates pressure to density, an inverse problem is set up to determine this equation of state from boundary velocity measurements. A transformation into the hodograph plane then leads to an overdetermined Goursat problem, which is used to find the polytropic equation of state that is in best agreement with the measurements.


Equation of state Highly stressed materials Murnaghan model 


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  1. 1.
    Rothman SD, Davis J-P, Maw J, Robinson CM, Parker K, Palmer J (2005) Measurement of the principal isentropes of lead and lead-antimony alloy to 400 kbar by quasi-isentropic compression. J Phys D Appl Phys 38: 733–740CrossRefADSGoogle Scholar
  2. 2.
    Pack DC, Evans WM, James HJ (1948) The propagation of shock waves in steel and lead. Proc Phys Soc 60: 1–8CrossRefADSGoogle Scholar
  3. 3.
    Morland LW (1959) The propagation of plane irrotational waves through an elastoplastic medium. Philos Trans R Soc Lond A 257: 341–383CrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Ockendon J, Ockendon H (2004) Waves and compressible flow. Texts in applied mathematics. Springer, New YorkGoogle Scholar
  5. 5.
    Chester CR (1971) Techniques in partial differential equations. Mcgraw-Hill, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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