Next: Hyperelastic and hyperfoam materials Up: Materials Previous: Linear elastic materials for Contents
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 dp is related to a density change d \rho by
| dp=\frac{d \rho}{\rho_0} \rho_0 r T, | (285) |
where \rho_0 is the density at rest, r is the specific gas constant and T is the temperature in Kelvin. From this one can derive the equations
| t_{11}=t_{22}=t_{33}=(\epsilon_{11}+\epsilon_{22}+\epsilon_{33}) \rho_0 r T | (286) |
and
| t_{12}=t_{13}=t_{23}=0, | (287) |
where \boldsymbol{t} denotes the stress and \boldsymbol{\epsilon} the linear strain. This means that an ideal gas can be modeled as an isotropic elastic material with Lamé constants \lambda=\rho_0 r T and \mu=0. This corresponds to a Young's modulus E=0 and a Poisson coefficient \nu=0.5. Since the latter values lead to numerical difficulties it is advantageous to define the ideal gas as an orthotropic material with D_{1111}=D_{2222}=D_{3333}=D_{1122}=D_{1133}=D_{2233}=\lambda and D_{1212}=D_{1313}=D_{2323}=0.