Ideal Gas Material
Constitutive Law
This MPM material models an ideal gas implemented as a large-deformation, isotropic, hyperelastic material at finite deformations. Its contitutive law for pressure is:
[math]\displaystyle{ P = P_0 {T\over T_0} {1\over J} }[/math]
where J is determinant of the deformation tensor (J = V/V0), T is temperature, and P0 and T0 are reference conditions. The pressure P is stored in the normal stresses or σxx =σyy = σzz = -P. All shear stresses are zero. This material is equivalent to a hyperelastic material with strain energy function of
[math]\displaystyle{ W = -P_0{T\over T_0} \ln J }[/math]
This energy function is equivalent to the energy per unit initial volume for isothermal compression or expansion of an ideal gas.
Material Properties
The ideal gas properties are set with
| Property | Description | Units | Default |
|---|---|---|---|
| P0 | Reference pressure at reference temperature and reference density. This must be a positive value greather than zero. | MPa | none |
| T0 | Reference temperature | K | none |
| rho | Density at reference conditinos. | g/cm^3 | none |
| Cv | Instead of head capacity, this parameter just determined is the gas is monatomic or diatomic. If this term is omitted or is less than or equal 1, CV is set to (3/2)R for a monotonic gas. If the entered value is greater than 1, CV is set to (5/2)R for a diatomic gas. | none | 0 |
| (other) | Properties common to all materials | varies | varies |
When using gas particles, the stress free temperature must be set to the desired temperature in Kelvin. The material properties refer to gas state at any reference conditions. For example, air might have reference pressure of 1 atm = 0.101325 MPa at any temperature T0. The density of air (or any gas) is then given by
[math]\displaystyle{ \rho = {P_0 M_g\over R T_0} }[/math]
where Mg is the molecular weight of the gas (such as 28.97 g/mol for air) and R is the gas constant, R = 8.3144621 J/k/mol.
History Variables
None