Johannes Mitsch, Constantin Krauß, Luise Kärger

Computer Methods in Applied Mechanics and Engineering 2024, 430, Interpolation methods for orthotropic fourth-order fiber orientation tensors in context of virtual composites manufacturing

Abstract:
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.