# Lamé constants

Quantities that connect the components of an elastic stress at some point of a linearly-elastic (or solid deformable) isotropic body with the components of the deformation at this point: $$\sigma_x = 2 \mu \epsilon_{xx} + \lambda(\epsilon_{xx} + \epsilon_{yy} + \epsilon_{zz}) \ ,$$ $$\tau_{xy} = \mu \epsilon_{xy} \ ,$$ where $\sigma$ and $\tau$ are the normal and tangential constituents of the stress, $\epsilon$ are the components of the deformation and the coefficients $\lambda$ and $\mu$ are the Lamé constants. The Lamé constants depend on the material and its temperature. The Lamé constants are connected with the elasticity modulus $E$ and the Poisson ratio $\nu$ by $$\mu = G = \frac{E}{2(1+\nu)} \ ,$$ $$\lambda = \frac{E\nu}{(1+\nu)(1-2\nu)} \ ;$$ $E$ is also called Young's modulus and $G$ is the modulus of shear.

The Lamé constants are named after G. Lamé.