Engineering Constants

• \(E_{i}=\frac{\sigma_{ii}}{\varepsilon_{ii}}\) : 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 \(i, j \in [1, 2, 3]\).

Implications:

• \(G_{ij} = G_{ji}\) due to the symmetry of \(\boldsymbol{\sigma}\) and \(\boldsymbol{\varepsilon}\)

Visualization: