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 referred to as G)
The first parameter λ is related to the bulk modulus and the shear modulus via in three-dimensions and for two-dimensional solids, and serves to simplify the stiffness matrix in Hooke's law. Although the shear modulus, μ, must be positive, the Lamé's first parameter, λ, can be negative, in principle; however, for most materials it is also positive. The two parameters together constitute a parameterization of the elastic moduli for homogeneous isotropic media, popular in mathematical literature, and are thus related to the other elastic moduli.
The parameters are named after Gabriel Lamé.
- K. Feng, Z.-C. Shi, 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)
|Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these; thus, given any two, any other of the elastic moduli can be calculated according to these formulas.|
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