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In continuum mechanics, the Lamé parameters (also called the Lamé coefficients or Lamé constants) are two material-dependent quantities denoted by λ and μ that arise in strain-stress relationships.〔 In general, λ and μ are individually referred to as ''Lamé's first parameter'' and ''Lamé's second parameter'', respectively. Other names are sometimes employed for one or both parameters, depending on context. For example, the parameter μ is referred to in fluid dynamics as the dynamic viscosity of a fluid; whereas in the context of elasticity, μ is called the shear modulus,〔 and is sometimes denoted by ''G'' instead of μ. Typically the notation G is seen paired with the use of Young's modulus, and the notation μ is paired with the use of λ. In homogeneous and isotropic materials, these define Hooke's law in 3D, : where σ is the stress, ε the strain tensor, the identity matrix and the trace function. 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; for instance, the bulk modulus can be expressed as . 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 parameters are named after Gabriel Lamé. == Further reading == * 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) * W.S. Slaughter, ''The Linearized Theory of Elasticity'', Birkhäuser, ISBN 0-8176-4117-3, (2002) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lamé parameters」の詳細全文を読む スポンサード リンク
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