ellipsoidal

Module: solid

Category: materialprop

Type string: "ellipsoidal"

Parameters

Name	Description	Default	Units
spa	spa		[]

Description

The fiber density distribution type ellipsoidal models a generally orthotropic 3D distribution. It corresponds to

\[ R\left(\mathbf{n}\right)=C^{-1}\left[\left(\frac{n_{1}}{a}\right)^{2}+\left(\frac{n_{2}}{b}\right)^{2}+\left(\frac{n_{3}}{c}\right)^{2}\right]^{-1/2}\,, \]

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, when specified or the global basis by default; and \(C\) is calculated to satisfy the integration constraint on \(R\left(\mathbf{n}\right)\). The parameters \(\left(a,b,c\right)\) represents the semi-principal axes of the ellipsoid and must be positive.

The value of \(C\) is automatically adjusted to account for the values of the semi-principal axes \(\left(a,b,c\right)\). Therefore, only the relative ratios of these parameters matter.

Figure 1. Illustration of the ellipsoidal fiber distribution function.

Example:

<distribution type="ellipsoidal">
  <spa>3,2,1</spa>
</distribution>