Interpolation methods for orthotropic fourth-order fiber orientation tensors in context of virtual composites manufacturing

The objective of this work is to develop and investigate interpolation methods for fourth-order fiber orientation tensors. The developed methods aim to minimize information loss during mapping in the virtual manufacturing process for fiber-reinforced composites. The strategy of decomposing features that describe tensor shape and orientation, followed by separate interpolation, has been found to be a suitable approach for interpolating second-order fiber orientation tensors. Thus, in this work, decomposition-based approaches are also applied to fourth-order fiber orientation tensors. The decomposition of orthotropic fourth-order tensors into shape- and orientation-describing features with respect to three-dimensional space is presented. Various proposals for shape interpolation are described and evaluated. The developed interpolation methods are then applied to the numerical solution of a continuous problem from fluid mechanics. The continuous solution is used to generate data for the associated discrete problem and to evaluate the interpolation results of the different methods. The evaluation results demonstrate that the proposed interpolation methods are clearly superior to the conventional interpolation methods. Separating shape- and orientation-describing features with respect to three-dimensional space also proves to be useful for fourth-order tensors. The developed methods can significantly reduce the loss of information during mapping in virtual manufacturing process chains.