Tensor interpolation in virtual manufacturing chains for fiber reinforced composites

Abstract

Preeminent weight-specific mechanical properties predestine fiber-reinforced plastics for application in structural components. Virtual manufacturing chains (CAE-chains) capture a multi-step process sequence by interlinking models with corresponding constitutive laws for each process step. In common numerical solving techniques, spatial discretization of governing equations yields discrete solutions. Since mesh type and fineness are usually problem-specific, mesh-to-mesh mapping must be embedded in the data interfaces between the individual simulation steps. To receive meaningful data, the underlying averaging and interpolation schemes between non-congruent meshes must be mathematically and physically consistent. In engineering applications, interpolation of tensors is usually carried out component-based, treating each component as an independent scalar-field and thus neglecting the tensorial character. The work at hand gives an overview of sophisticated techniques that preserve specific tensor characteristics in interpolation. Compared to available approaches, an enhanced decomposition-based interpolation method is proposed, allowing for a generalization with more than two basic values. In the context of process simulation for short fiber-reinforced injection molding, the influence of the interpolation techniques is evaluated in a three-stage approach with increasing proximity to application. Firstly, mathematical examples demonstrate that component-based interpolation can result in erroneous, non-monotonous tensor characteristics. Secondly, an analytically resolvable problem is derived, and the solution is compared to reconstructed tensors from different interpolation schemes. Thirdly, a numerical CFD-simulation is conducted. Field recovery via interpolation is performed and systematical errors are statistically evaluated. The results reveal significant biases for certain tensor characteristics induced by conventional component-wise interpolation. Overall, a reduction in systematic interpolation errors is achieved by the proposed decomposition-based interpolation.