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$E_{i}=\frac{\sigma_{ii}}{\varepsilon_{ii}}$ : Youngs modulus along direction i. -
$G_{ij}=\frac{\sigma_{ij}}{2\varepsilon_{ij}}$ : Shear modulus in plane with normal i and load in direction j. -
$\nu_{ij}=-\frac{\varepsilon_{jj}}{\varepsilon_{ii}}$ : Poisson's ratio due to load applied in direction i and measured response in direction j. Please note, that some textbooks use different definitions.
with i, j ∈ [1, 2, 3].
Implications:
- Gij = Gji due to the symmetry of σ and ε
Visualization:
