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### 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

| (46)

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

| (47)

and

| (48)

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 .

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