1. n. [Geophysics]

One of two elastic constants named for French mathematician Gabriel Lamé (1795 to 1870). The first Lamé constant is λ, the bulk modulus (K) less two-thirds of the shear modulus (μ):

λ = K − (2/3)μ

The second Lamé constant is the shear modulus (μ):

μ = τ / γ = (ΔF/A) / (ΔL/L),

where
μ = Shear modulus
τ = Shear stress = ΔF/A
ΔF = Increment of shear force
A = Area acted on by the shear force
γ = Shear strain = ΔL/L
ΔL = Increment of transverse displacement parallel to A
L = Original length.

Lamé constants derived from elastic-wave velocities:

λ = ρ(V_P² − 2V_S²)

μ = ρV_S²

λ/μ = (V_P/V_S)² − 2,

where
λ = Lamé's first constant
μ = Lamé's second constant, the shear modulus
V_P = Compressional-wave (P-wave) velocity
V_S = Shear-wave (S-wave) velocity
ρ = Density.

See: bulk modulus,  elastic constants,  shear modulus,  P-wave,  S-wave