Lamé parameters

In linear elasticity, the Lamé parameters are the two parameters

* λ, also called "Lamé's first parameter".
* μ, the shear modulus or "Lamé's second parameter".

which in homogenous, isotropic materials satisfy Hooke's law in 3D,

:$sigma=2mu\; varepsilon\; +lambda\; ;\; mathrm\{tr\}(varepsilon)I$

where σ is the stress, ε the strain tensor, the $scriptstyle\; I$ the identity matrix and $scriptstylemathrm\{tr\}(cdot)$ the trace function.

The first parameter λ has no physical interpretation, but it serves to simplify the stiffness matrix in Hooke's law. Both parameters constitute a parametrization of the elastic moduli for homogeneous isotropic media, and are thus related to the other elastic moduli.

The parameters are named after Gabriel Lamé.

References

* F. Kang, S. Zhong-Ci, "Mathematical Theory of Elastic Structures", Springer New York, ISBN 0-387-51326-4, (1981)
* G. Mavko, T. Mukerji, J. Dvorkin, "The Rock Physics Handbook", Cambridge University Press (paperback), ISBN 0-521-54344-4, (2003)