# Convert Elastic Constants

## 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: $$\boldsymbol{\tau} = J \boldsymbol{\sigma}$$

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