Mie-Gruneisen equation of state
Encyclopedia
The Mie-Gruneisen equation of state
is a relation between the pressure and the volume of a solid at a given temperature. It is often used to determine the pressure in a shock-compressed solid. Several variations of the Mie-Gruneisen equation of state are in use.
(see also , p.61)
where
is the bulk speed of sound,
is the initial density, 
is the current density, 
is the Gruneisen's gamma at the reference state, 
is a linear Hugoniot slope coefficient, 
is the shock wave velocity, 
is the particle velocity, and 
is the internal energy per unit reference specific volume.
A rough estimate of the change in internal energy can be computed using
where
is the reference specific volume at temperature 
, and 
is the specific heat at constant volume. In many simulations, it is assumed that 
and 
are equal.
Equation of state
In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...
is a relation between the pressure and the volume of a solid at a given temperature. It is often used to determine the pressure in a shock-compressed solid. Several variations of the Mie-Gruneisen equation of state are in use.
Expressions for the Mie-Gruneisen equation of state
A temperature-corrected version that is used in computational mechanics has the form(see also , p.61)
where
is the bulk speed of sound, is the initial density, is the current density, is the Gruneisen's gamma at the reference state, is a linear Hugoniot slope coefficient, is the shock wave velocity, is the particle velocity, and is the internal energy per unit reference specific volume.A rough estimate of the change in internal energy can be computed using
where
is the reference specific volume at temperature , and is the specific heat at constant volume. In many simulations, it is assumed that and are equal.Parameters for various materials
| Copper Copper Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish... |
3933 | 1.5 | 1.99 | 2.12 | 700 |
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