Kumari-Dass equation of state

Kumari and Dass presented a model based on a linear bulk modulus equation, in the spirit of the Murnaghan equation of state. The equation of state does not correctly model the bulk modulus as the pressure, \(p\), tends towards infinity, as it remains bounded. This is apparent in the equation relating the bulk modulus to pressure:

\[B=B_0+\frac{B_0'}{\lambda}\left(1-e^{-\lambda p}\right)\]

where \(B_0\) is the isothermal bulk modulus, \(B_0'\) is the pressure derivative of the bulk modulus and \(\lambda\) is a softening parameter for the bulk modulus. This leads to a equation for pressure dependent on these parameters of the form:

\[p=\frac{1}{\lambda}\left[\frac{\lambda B_0 \left(V/V_0\right)^{-\lambda B_0 + B_0'}+B_0'}{\lambda B_0 + B_0'}\right]\]