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### Linear elastic materials

Linear elastic materials are characterized by an elastic potential of which only the quadratic terms in the strain are kept. It can be defined in a isotropic, orthotropic or fully anisotropic version. Isotropic linear elastic materials are characterized by their Young's modulus and Poisson's coefficient. Common steels are usually isotropic. Orthotropic materials, such as wood or cubic single crystals are characterized by 9 nonzero constants and fully anisotropic materials by 21 constants. For elastic materials the keyword *ELASTIC is used.

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

| (47)

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

| (48)

and

| (49)

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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