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: \( \boldsymbol{\tau} = J \boldsymbol{\sigma} \)


More to explore

Extended Tube Model in Ansys Mechanical

The Extended Tube model is one of the most accurate hyperelastic material models available, but it can be difficult to use if you don’t understand how the material parameters influence the predicted stress-strain response. This article will demonstrate that by example.

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