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:

      <path>P = P_0 {T\over T_0} \thinspace{1\over J}

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

Property	Description	Units	Default
E	Tensile modulus	MPa	none

History Variables

None