View source for 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.



====Comments====


====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  E.M. Lifshitz,   "Theory of elasticity" , Pergamon  (1959)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  I.S. [I.S. Sokolnikov] Sokolnikoff,   "Mathematical theory of elasticity" , McGraw-Hill  (1956)  (Translated from Russian)</TD></TR>
<TR><TD valign="top">[a3]</TD> <TD valign="top">  S.C. Hunter,   "Mechanics of continuous media" , Wiley  (1976)</TD></TR>
</table>

{{TEX|done}}