Finite strain equation of states

Finite strain vs. Birch-Murnaghan

Explicit expression for Birch-Murnaghan equation of states

The explicit expressions for third-order Birch-Murnaghan (BM3) equation of states (EoS) are

where the Eulerian strain is given by

The effect of using of an arbitrary instead of

Since we have and we assume , we have

So we have

Since , we can fit with

So with an arbitrary , the fitting result is equivalent.

Analytical derivatives to obtain

Not easy to do, because

where

But the expression for is a 3rd-order polynomial vs. ,

Gibbs free energy or enthalpy

Usually, these equation of states are for internal energy (), Helmholtz free energy () as a function of volume . It is also possible to think about the form of enthalpy (), Gibbs free energy () as a function of strain.

Because

assuming , from the above statement, is a 3rd-order polynomial of , it is obvious that and will be 3rd order polynomials of too.

References