Difference between revisions of "Ideal Gas Material"
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<math>P = P_0 {T\over T_0} | <math>P = P_0 {T\over T_0} {1\over J}</math> | ||
where ''J'' is determinant of the deformation tensor (''J'' = ''V''/''V''<sub>0</sub>), ''T'' is temperature, and ''P''<sub>0</sub> and ''T''<sub>0</sub> are reference conditions. The pressure P is stored in the normal stresses or σ<sub>xx</sub> =σ<sub>yy</sub> = σ<sub>zz</sub> = -''P''. All shear stresses are zero. This material is equivalent to a hyperelastic material with strain energy function of | where ''J'' is determinant of the deformation tensor (''J'' = ''V''/''V''<sub>0</sub>), ''T'' is temperature, and ''P''<sub>0</sub> and ''T''<sub>0</sub> are reference conditions. The pressure P is stored in the normal stresses or σ<sub>xx</sub> =σ<sub>yy</sub> = σ<sub>zz</sub> = -''P''. All shear stresses are zero. This material is equivalent to a hyperelastic material with strain energy function of | ||
Revision as of 11:55, 28 December 2013
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
| Property | Description | Units | Default |
|---|---|---|---|
| E | Tensile modulus | MPa | none |
History Variables
None