This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada
The rising importance of Industry 4.0 applications has made its way into the daily life of simulation engineers and the term of a “Closed Simulation Process Chain” is commonly used nowadays. With that, the demand for software tools which not only help to transfer result data from all kinds of process analysis towards structural simulation but also interpret, interpolate, and homogenize the resulting data most accurately has risen constantly. Thereby, one has to overcome the fact that various software tools being used for several simulation tasks do have non-consistent output formats; material formulations do interpret field- or history variables differently – not only between different solvers, but also within a solver itself. Furthermore, different discretization techniques are used for the different simulation disciplines, e.g. result data has to be transferred between beam, shell, thick shell, and solid elements that can be layered, stacked, fully or under-integrated.
Within this work, different averaging techniques such as Shepard’s method [Shepard 1968] for scalar simulation result data will be introduced in the framework of Finite-Element (FE) result data mapping and compared to a standard closest point approach which basically transfers the values between source and target meshes. Using the linear invariant (LI) approach proposed by [Gahm 2014], various sets of tensor invariants are used to interpolate resulting stress tensors. Due to the fact that stress tensors are not a-priori positive-definite, one can rule out two of the three proposed invariant sets for the interpolation of any arbitrary tensor. Instead, it seems to be reasonable to use the Cauchy stress invariants for interpolation and to compare the results with a closest point mapping and a standard Euclidean tensor averaging approach [Usta 2018]. Nevertheless, the invariant sets are still valid for positive tensors such as fiber orientation tensors and therefore need further investigation.
Furthermore, the method has been extended, making use of the shape functions of 2D finite element meshes for a rather simulation related approach. Further methods which could be interesting for an enhanced mapping approach would be to ensure energy conservation through the thickness when transforming plastic strains from source to target mesh, as it is proposed by [Wolf et. al. 2005]. Also, the superconvergent patch recovery method [Zienkiewicz et. al. 1992] which is used to ensure stable mapping when adaptive mesh refinement is used during FE analysis could be an option as well and shall be discussed in this work.