A Theory of Non-Linear Elasticity Compatible With the Murnaghan Equation of State |
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Authors: | JR Downes SHB Bosher DJ Dunstan |
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Institution: | 1. Physics Department, Queen Mary , University of London , London , E1 4NS , UK;2. Physics Department, Queen Mary , University of London , London , E1 4NS , UK E-mail: D.J.Dunstan@qmw.ac.uk |
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Abstract: | 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. |
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Keywords: | Murnaghan Non-linear Elastic/elasticity Pressure Semiconductor State |
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