Autodesk Simulation Moldflow Insight is routinely used to predict the spatial distribution of fiber orientations in short fiber filled, injection molded plastic parts. The 2nd order fiber orientation tensor essentially provides a statistical description (in the continuum sense) of the orientation of fibers that lie in the immediate neighborhood of the point in question [3]. The eigenvectors of the fiber orientation tensor provide the principal material directions of the fiber filled plastic which is idealized as an orthotropic material.
The eigenvalues of the fiber orientation tensor provide a measure of the degree of orthotropy of the fiber filled plastic (i.e., the degree of randomness or alignedness of the reinforcing fibers). For example, a completely 3-D random fiber orientation would yield fiber orientation tensor eigenvalues of (1/3, 1/3, 1/3), while a perfectly aligned fiber orientation tensor would yield eigenvalues of (1, 0, 0).
The fiber orientation tensor can be used to operate on the constitutive matrix of a comparable composite material that contains perfectly aligned fibers to compute the anisotropic stiffness matrix of the actual composite material with the specified fiber orientation distribution (a process referred to as fiber orientation averaging [1]). It has been demonstrated [4] that anisotropic stiffness matrices predicted with fiber orientation averaging compare very well with the anisotropic stiffness matrices obtained from finite element models containing actual fiber distributions corresponding to the specified fiber orientation tensor.
Since the fiber orientation averaging process is quite reliable, one can develop complex nonlinear material models (e.g., plasticity, damage, rupture) for a single, much simpler, perfectly aligned material. Then, the fiber orientation averaging process can be used to compute the tangent constitutive matrix for the real composite material with the specified fiber orientation distribution.
In a simulation of the mechanical loading of a fiber filled plastic, knowledge of the fiber orientations at each point in the model is critical to the accuracy of the solution. Generally, the finite element mesh used to simulate the structural response of the part is different from the mesh used to simulate the injection molding. Thus, it is necessary to interpolate the predicted fiber orientation tensor from the Moldflow model to the structural model. Advanced Material Exchange provides a method to 'map' the fiber orientations to the structural model and compare the distribution of fiber orientations. For more information on this topic, refer to the Mapping Results section of the User's Guide.