### Ideal gas for quasi-static calculations

A special case of a linear elastic isotropic material is an ideal gas for small pressure deviations. From the ideal gas equation one finds that the pressure deviation is related to a density change by

 (303)

where is the density at rest, is the specific gas constant and is the temperature in Kelvin. From this one can derive the equations

 (304)

and

 (305)

where denotes the stress and the linear strain. This means that an ideal gas can be modeled as an isotropic elastic material with Lamé constants and . This corresponds to a Young's modulus and a Poisson coefficient . Since the latter values lead to numerical difficulties it is advantageous to define the ideal gas as an orthotropic material with and .