LAMé PARAMETERS

In linear elasticity, the 'Lamé parameters' are the two parameters

★ $lambda$, also called ''Lamé's first parameter''.

★ $mu$, the shear modulus or ''Lamé's second parameter''.
which in homogenous, isotropic materials satisfy Hooke's law in 3D,
:
where $sigma$ is the stress, $epsilon$ the strain tensor, the $I$ the identity matrix and $tr(cdot)$ the trace function.
The first parameter $lambda$ has no physical interpretation, but it serves to simplify the stiffness matrix in Hooke's law above. Both parameters constitute a parametrization of the elastic moduli for homogeneous isotropic media, and are thus related to the other elastic moduli. Hooke's law is a two parameter material model. Depending on the point of interest the two parameters can be chosen from the table below.
The parameters are named after Gabriel Lamé.

Contents

References

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)