Interpolation of orthotropic fourth-order fiber orientation tensor fields in virtual composite process chains

The strong interrelation between underlying microstructure and effective macroscopic properties in discontinuous fiber-reinforced polymers (DiCoFRP) is well understood and captured in numerous homogenization schemes. Process-induced reorientation is commonly modeled statistically in terms of fiber orientation tensors (FOT) and yields an inhomogeneous orientation state distribution across the considered component. This distribution has to be transferred from the process simulation to the, typically, non-congruent discretization of the structural simulation.

In our previous work, we have discussed the interpolation of second-order FOT fields. However, for the accurate directional average of stiffness or viscosity tensors, FOT of order four are imperative. Consequently, we address the interpolation of fourth-order FOT fields in this contribution. We focus on fiber orientation states of orthotropic material symmetry, discussing the limitations of StoA techniques and the general portability of decomposition-based second-order techniques with respect to preservation of normalization, intrinsic and extrinsic symmetries, and tensor structure. ... mehr

Finally, we quantitatively assess the fourth-order interpolation schemes using an example from short fiber-reinforced injection molding.
Results reveal a superior performance of the novel techniques.