IsotropicNonlinearElastic3D
General Nonlinear Elastic Isotropic 3D Material Framework
The IsotropicNonlinearElastic3D class is an abstract general purpose framework.
It offers an interface to allow users to define arbitrary strain energy potential based on volumetric strain and equivalent strain (squared), that is
\[
W=f\left(\varepsilon_v,\varepsilon_p^2\right),
\]
where
\[
\varepsilon_v=\text{trace}\left(\varepsilon\right),\qquad\varepsilon_p=\sqrt{\dfrac{2}{3}\varepsilon_d:
\varepsilon_d}.
\]
Note it is normally expressed in terms of equivalent strain rather than its square. However, the derivation of tangent stiffness would be too cumbersome.
Overridden Method
The IsotropicNonlinearElastic3D provides a method that shall be overridden.
| C++ | |
|---|---|
The first argument is \(\varepsilon_v\). The second argument is \(\varepsilon_s=\varepsilon_p^2\).
The method shall return a vector of size six with following values computed.
| index | value |
|---|---|
| \(0\) | \(\dfrac{\partial{}W}{\partial\varepsilon_v}\) |
| \(1\) | \(\dfrac{\partial{}W}{\partial\varepsilon_s}\) |
| \(2\) | \(\dfrac{\partial^2W}{\partial\varepsilon_v^2}\) |
| \(3\) | \(\dfrac{\partial^2W}{\partial\varepsilon_s^2}\) |
| \(4\) | \(\dfrac{\partial^2W}{\partial\varepsilon_v\partial\varepsilon_s}\) |
| \(5\) | \(\dfrac{\partial^2W}{\partial\varepsilon_s\partial\varepsilon_v}\) |