St.Venant-Kirchhoff¶
Module: solid
Category: material
Type string: "St.Venant-Kirchhoff"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
density |
density | 1 | [M/L^3] |
E |
E | 0 | [P] |
v |
v | 0 | [] |
Description¶
The St.Venant-Kirchhoff material is a hyperelastic material that is analogous to a linear elastic material, but uses the Green-Lagrange strain instead of the infinitesimal strain tensor. The second Piola-Kirchhoff stress is defined as,
\[
\mathbf{S} = \lambda \, \text{tr} \left( \mathbf{E}\right) \mathbf{I} + 2\mu\mathbf{E}
\]
Here, \(\lambda\) and \(\mu\) and related to the Young's modulus \(E\) and Poisson's ratio \(\nu\) as follows,
\[
\lambda = \frac{E\,\nu}{\left(1+\nu\right)\left(1-2\nu\right)},\quad \mu=\frac{E}{2\left(1+\nu\right)}
\]
Note that this material can produce non-physical behavior under large deformations and it is better to use a neo-Hookean material.