von-Mises-2d¶
Module: solid
Category: materialprop
Type string: "von-Mises-2d"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
b |
concentration | 0 | [] |
Description¶
The fiber density distribution type von-Mises-2d models an orthotropic 2D distribution. This distribution corresponds to
\[
R\left(\mathbf{n}\right)=\frac{\exp\left[b\left(2n_{1}^{2}-1\right)\right]}{2\pi I_{0}\left(b\right)}
\]
where \(\left(n_{1},n_{2},n_{3}\right)\) are the components of \(\mathbf{n}\) in the local Cartesian basis \(\left\{ \mathbf{e}_{1},\mathbf{e}_{2},\mathbf{e}_{3}\right\}\) of each element or the global basis by default, with the distribution lying in the \(\left\{ \mathbf{e}_{1},\mathbf{e}_{2}\right\}\) plane; and \(b\) is the concentration parameter \((b>0)\). \(I_{0}\) is the modified Bessel function of the first kind of order 0.
Figure 1. Illustration of the von-Mises-2d distribution function.
Example:
<distribution type="von-Mises-2d">
<b>3</b>
</distribution>