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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. Also denoted $G$.

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

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

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

The first parameter λ has no physical interpretation, but it serves to simplify the stiffness matrix in Hooke's law. The two parameters together 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.

## ReferencesEdit

• 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)
he:קבועי לאמהuk:Коефіцієнти Ламе