Up to an orthogonal transformation, the second order orientation tensor (see Orientation Tensor and Orientations Averaging) is completely characterized by its two largest principal values, say A₁₁ and A₂₂ , which satisfy the following inequalities:

(2–1)

Figure 2.22: Sampling of the orientation tensor space

As a result, all possible orientation states fall within the triangle highlighted in the figure above. (Those falling outside of this region can be obtained by symmetry.) Therefore, to characterize the homogenized material for a general orientation state, it is enough to compute its mechanical properties for a few sample orientations in the highlighted region. See for example [Cintra et al., (1995)] and [Köbler et al, (2018)] for further details.

When Solve Variable Material is selected, the Short Fiber Wizard button appears in the Options Panel. Click it to launch the interface.

In the Short Fiber Wizard interface shown below, you must first specify the number of sampling points desired when sampling the orientation tensor. Then select additional parameters like the Fiber Volume Fraction and Temperature. (Temperature only applies if any of the constituent materials are temperature dependent.) For each of these parameters, you can specify either a comma separated list of values or n evenly spaced values in the range using the format a-b:n. For example, 0.2-0.7:6 corresponds to 0.2,0.3,0.4,0.5,0.6,0.7.