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v • d • e Elastic moduli for homogeneous isotropic materials |
Bulk modulus (K) | Young's modulus (E) | Lamé's first parameter (λ) | Shear modulus (μ) | Poisson's ratio (ν) | P-wave modulus (M)
K = | λ + 2μ / 3 | Eμ / (3(3μ − E) | λ(1 + ν) / (3ν) | 2μ / 3(1 + ν) / (1 − 2ν) | E / (3(1 − 2ν))
E = | μ(3λ + 2μ) / (λ + μ) | 9K(K − λ) / (3K − λ) | 9Kμ / (3K + μ) | λ(1 + ν)(1 − 2ν) / ν | 2μ(1 + ν) | 3K(1 − 2ν)
λ = | K − 2μ / 3 | μ(E − 2μ) / (3μ − E) | 3K(3K − E) / (9K − E) | 2μν / (1 − 2ν) | 3Kν / (1 + ν) | Eν / (1 + ν) / (1 − 2ν)
ν = | λ / (2(λ + μ)) | λ / (3K − λ)| (3K − 2μ) / (2(3K + μ)) | E / (2μ) − 1 | (3K − E) / (6K)
M = | λ + 2μ | 3K − 2λ | K + 4μ / 3 | μ(4μ − E) / (3μ − E) | 3K(3K + E) / (9K − E) | λ(1 − ν) / ν | μ(2 − 2ν) / (1 − 2ν) | 3K(1 − ν) / (1 + ν) | E(1 − ν) / (1 + ν) / (1 − 2ν)
μ = | 3(K − λ) / 2 | 3KE / (9K − E) | λ(1 − 2ν) / (2ν) | 3K(1 − 2ν) / (2 + 2ν) | E / (2 + 2ν)
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