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 σ_xx =σ_yy = σ_zz = -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	Reference density at reference temperature.	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

History Variables

None