An Investigation of Finite Strain in an Isotropic Material Subjected to Hydrostatic Pressure and its Seismological Applications

Keane, A.

doi:10.1071/ph540322

Cited by 99 publications

(42 citation statements)

References 6 publications

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“…In support of the statement, some examples can be given here, the equations of state obtained by Murnaghan [27,28], Keane [29] and Birch [30].…”

Section: Kumari-dass Equation Of Statementioning

confidence: 72%

“…Keane [56] noted that an exact solution of a formula, from a derivation of Murnaghan [28], for the calculation of B and dB/dP at large pressure is impossible to obtain, without the knowledge of the variation of the possible function of pressure which is essentially a combination of second order elastic parameters. This recognition prompted Keane [29] to come up with a new EOS form with an explicit use of the equation of state parameter B ¥ ¢ , the asymptotic limit of B ¥ ¢ as P ® ¥ ,…”

Section: Roy-roy Equation Of Statementioning

confidence: 99%

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Inverted equations of state for solids under high pressures

2011

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In the present communication we have reviewed some inverted type equations of state for solids under high pressures. An inverted equation of state (EOS) gives volume as a function of pressure for a solid under isothermal conditions. We have considered various equations of state proposed by earlier workers which express volume as a function of pressure. Expressions for bulk modulus and its pressure derivatives based on such EOSs are obtained and reported here. It is emphasized here that the high pressure derivative properties are very sensitive to the forms of equations of state representing volume-pressure relationships. We have also studied the thermoelastic properties of solids based on pressure derivatives of bulk modulus. Applications have been extended in the present review article to the solids which are metals as well as non-metals including geophysical minerals present in the lower mantle and core of the Earth.

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“…In support of the statement, some examples can be given here, the equations of state obtained by Murnaghan [27,28], Keane [29] and Birch [30].…”

Section: Kumari-dass Equation Of Statementioning

confidence: 72%

Section: Roy-roy Equation Of Statementioning

confidence: 99%

Inverted equations of state for solids under high pressures

2011

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“…The Mie-Grüneisen Keane equation of state starts with a reference pressure as a function of density, p s (ρ), along an isentrope given by the following form [2]:…”

Section: Materials Modelsmentioning

confidence: 99%

“…Besides the standard Hugoniot data [1], we report on recent multi-shock compression experiments performed at LANL's two-stage gas gun. We model polymethylpentene with a simple Mie-Grüneisen EOS based on a three parameter Keane fitting form for an isentrope [2]. Computational modeling is performed with the use of a 2nd order spatial total variation diminishing, conservative Lagrangian scheme based on an approximate Riemann solver which allows for discontinuous material properties across cell interfaces, without the use of artificial viscosity.…”

Section: Introductionmentioning

confidence: 99%

An equation of state for polymethylpentene (TPX) including multi-shock response

Aslam

Gustavsen

Sanchez

et al. 2012

AIP Conference Proceedings

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The reactants equation of state for the tri-amino-tri-nitro-benzene (TATB) based explosive PBX (TPX) is examined through both single shock Hugoniot data as well as more recent multi-shock compression and release experiments. Results from the recent multi-shock experiments on LANL's two-stage gas gun will be presented. A simple conservative Lagrangian numerical scheme utilizing total variation diminishing interpolation and an approximate Riemann solver will be presented as well as the methodology of calibration. It is shown that a simple Mie-Grüneisen EOS based on a Keane fitting form for the isentrope can replicate both the single shock and multi-shock experiments.

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“…Since it is essential that K' remains positive and finite, while decreasing somewhat with pressure, Keane (1954) proposed an empirical equation whereby K' decreased progressively from its zero pressure value, Ko', toward an asymptotic limit K" at high compressions:…”

Section: Keane's Equationmentioning

confidence: 99%

Finite strain theories and comparisons with seismological data

Stacey

Brennan

Irvine

1981

Geophysical Surveys

184

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Abstract. All the finite strain equations that we are aware of that are worth considering in connection with the interior of the Earth are given, with the assumptions on which they are based and corresponding relationships for incompressibility and its pressure derivatives in terms of density. In several cases, equations which have been presented as new or independent are shown to be particular examples of more general equations that are already familiar. Relationships for deriving finite strain equations from atomic potential functions or vice versa are given and, in particular it is pointed out that the BirchMurnaghan formuIation implies a sum of power law potentials with even powers. All the equations that survive simple plausibility tests are fitted to the lower mantle and outer core data for the PEM earth model. For this purpose the model data are extrapolated to zero temperature, using the MieGrfineisen equation to subtract the thermal pressure (at fixed density) and the pressure derivative of this equation to substract the thermal component of incompressibility. Fitting of finite strain equations to such zero temperature data is less ambiguous than fitting raw earth model data and leads immediately to estimates of the low temperature zero pressure parameters of earth materials. On this basis, using the best fitting ~uations and constraining core temperature to give an extrapolated incompressibility Ko = 1.6 X 10 Pa, compatible with a plausible iron alloy, the following numerical data are obtained: However, an inconsistency is apparent between P(p) and K(p) data, indicating that, even in the PEM model, in which the lower mantle is represented by a single set of parameters, it is not perfectly homogeneous with respect to composition and phase.

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An Investigation of Finite Strain in an Isotropic Material Subjected to Hydrostatic Pressure and its Seismological Applications

Cited by 99 publications

References 6 publications

Inverted equations of state for solids under high pressures

Inverted equations of state for solids under high pressures

An equation of state for polymethylpentene (TPX) including multi-shock response

Finite strain theories and comparisons with seismological data

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