Lamé parameters

Summary

The Lamé parameters $\lambda$ and $\mu$ are the two constants that describe a homogeneous isotropic linear elastic material. In terms of them the stress–strain law reads $\sigma = \lambda (\tr \varepsilon) I + 2\mu \varepsilon$. The second parameter $\mu$ is the shear modulus. Every other isotropic elastic constant, such as Young's modulus or Poisson's ratio, is a function of $\lambda$ and $\mu$. They are the natural constants in the Lamé equations for the displacement.