Abstract
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.
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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: 733–740
Pack DC, Evans WM, James HJ (1948) The propagation of shock waves in steel and lead. Proc Phys Soc 60: 1–8
Morland LW (1959) The propagation of plane irrotational waves through an elastoplastic medium. Philos Trans R Soc Lond A 257: 341–383
Ockendon J, Ockendon H (2004) Waves and compressible flow. Texts in applied mathematics. Springer, New York
Chester CR (1971) Techniques in partial differential equations. Mcgraw-Hill, New York
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Ockendon, H., Ockendon, J.R. & Platt, J.D. Determining the equation of state of highly plasticised metals from boundary velocimetry: part I. J Eng Math 68, 269–277 (2010). https://doi.org/10.1007/s10665-010-9401-0
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DOI: https://doi.org/10.1007/s10665-010-9401-0