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 (not expressed in the same units); whereas in the context of elasticity, μ is called the shear modulus,[2]: p.333 and is sometimes denoted by G instead of μ.
In homogeneous and isotropic materials, these define Hooke's law in 3D,
where σ is the stress tensor, ε the strain tensor, I the identity matrix and tr the trace function.
Hooke's law may be written in terms of tensor components using index notation as
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 K = λ + 2/3μ.
Relations for other moduli are found in the (λ, G) row of the conversions table at the end of this article.
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.