A Theory of Non-Linear Elasticity Compatible With the Murnaghan Equation of State

We present an equation of state for a cubic non-linear elastic material in a general state of finite strain. For hydrostatic pressure, the predictions closely follow Murnaghan's well-known equation of state. At 170 kbar, our model differs from Murnaghan's equation by only 1.3%, which contr...

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Bibliographic Details
Published in:High pressure research 2002, Vol.22 (1), p.231-235
Main Authors: Downes, J.R., Bosher, S.H.B., Dunstan, D.J.
Format: Article
Language:English
Subjects:
Elastic/elasticity
Murnaghan
Non-linear
Pressure
Semiconductor
State
Online Access:Get full text
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Summary:We present an equation of state for a cubic non-linear elastic material in a general state of finite strain. For hydrostatic pressure, the predictions closely follow Murnaghan's well-known equation of state. At 170 kbar, our model differs from Murnaghan's equation by only 1.3%, which contrasts with the currently accepted non-linear elasticity theory that differs by 10% at this pressure. The theory is based on expressing the variation of the elastic constants as a linear function of stress rather than strain. We define a different set of third-order elastic constants, which involve a derivative with respect to stress, and relate these to the conventional third-order elastic constants. We apply the model to GaAs under hydrostatic pressure and we compare the predictions of the conventional non-linear theory with those of the model we present.
ISSN:0895-7959
1477-2299
DOI:10.1080/08957950211352