Convert Elastic Constants Table
Here is a table with conversions between different elastic constants (Young’s modulus, Poisson’s ratio, shear modulus, bulk modulus, Lame’s constant)
Other Common Definitions and Equations
Green-Lagrange Strain: \( \mathbf{E} = \frac{1}{2} \left[ \mathbf{C} – \mathbf{I} \right] = \frac{1}{2} \left[ \mathbf{U}^2 – \mathbf{I} \right] = \frac{1}{2} \left[ \mathbf{F}^\top \mathbf{F} – \mathbf{I} \right] \)
Convert between true (Cauchy) stress and second Piola-Kirchhoff stress: \( \mathbf{S}^{PK2} = J \mathbf{F}^{-1} \boldsymbol{\sigma} \mathbf{F}^{-\top} \)
Convert between second Piola-Kirchhoff stress and true (Cauchy stress): \( \boldsymbol{\sigma} = \frac{1}{J} \mathbf{F} \mathbf{S}^{PK2} \mathbf{F}^{\top} \)
The Kirchhoff stress is given by: \( \boldsymbol{\tau} = J \boldsymbol{\sigma} \)
