Local and Global Influence of Second-Order Tensor Interpolation within Virtual Manufacturing Chains for Fiber-Reinforced Composites

Due to their outstanding weight-specific properties, fiber-reinforced plastics (FRPs) are ideally suited for application in structural and semi-structural components.
To account for potential manufacturing effects and defects, accurate structural simulation requires upstream process simulation \cite{Kaerger, Goerthofer}. Linking these modules within digital twins referred to as CAE-chains, introduces new challenges resulting from changes in physics, considered scale, constitutive laws, boundary conditions, and spatial discretizations. If those differ in terms of fineness or topography, the interface between the involved simulation modules has to be extended by a mesh-to-mesh mapping operation, in which scalar fields such as temperature, fiber volume content, etc., but also direction-dependent fields, e.\,g. stresses or fiber orientation tensors (FOT), have to be transferred. This transfer-step involves the interpolation of discrete result values from the donor mesh. In the general case, this operation is associated with loss of information, which can be reduced by choosing physically and mathematically consistent interpolation schemes. ... mehrYet, for common engineering applications, established interpolation approaches for scalar fields are directly adapted to components of tensorial field data \cite{Arsigny, Gahm}. In this work, available alternative interpolation methods for tensorial field data from other research areas are introduced. While preserving specific tensorial properties, extensions and generalizations to those methods remain mandatory for utilizing them in the context of CAE-chains for FRPs. The implementation of those measures is discussed and assessed. Subsequently, the influence of the chosen tensor interpolation methods is evaluated by means of a virtual FRP-processes and components. Results reveal how the component-based interpolation scheme locally overestimates tensor isotropy. Furthermore, global, mechanical properties such as artificially induced strain energy and homogenization results are influenced by the applied interpolation scheme. In both cases, more sophisticated techniques proof to be superior to the conventional scheme.