The task and planned approach of this research project were described in our blog “Calibrating anisotropic material models with AI support” (08/2023) and are briefly summarized here:
Determining parameters of anisotropic material models typically requires multiple FEM simulations. A filling simulation determines fiber orientations, while structural simulations generate stress–strain curves for the given parameter set of a material model. Parameters are optimized until experimental tensile tests are reproduced accurately.
The aim was to replace FE solvers with AI models to predict orientation profiles and mechanical behavior without simulation effort. The project has now been successfully completed and prototypically implemented in user software.
Generation or Training Data
In most cases, providing a sufficiently large amount of training data that adequately describes the problem at hand is a challenge in the development of AI models. In the anisotroKI project, the focus was clearly on replacing time-consuming FE simulations. This applied both to predicting the fiber orientation in a test specimen (filling simulation) and to predicting the calculated stress-strain curve using a given material model and the determined fiber orientation (structural simulation). This means that the target values of the training data are NOT actual measured properties of the test specimen, but exclusively simulated data. This significantly simplifies the generation of training data.
AI-Modell „Prozess“
The AI model “Process” was developed by the project partner aiXtrusion. The goal was not to simulate the entire filling process, but solely to predict the fiber profile resulting from the filling process at specific measurement points. The orientation profile that develops in a test specimen depends primarily on the viscosity of the melt, the shear rate, and possibly the flow path length. These parameters, in turn, are influenced by the temperature, the injection speed, and the wall thickness or the test specimen geometry. In reality, the fiber content and the aspect ratio of the fibers certainly also play a role.
For the AI model “Process”—that is, the model designed to replace the filling simulation—a range of commercial materials with the widest possible viscosity spectrum was therefore selected.
For each material, a series of filling simulations with varying process parameters and two different thicknesses (2 mm and 4 mm) were performed for plate geometries, and the resulting fiber orientation was measured at several points. Figure 1 shows a test plate used with 3 measurement points and example results for the orientation profile and tensile tests. A total of 378 different data sets were generated in this way during the first project phase. Two different FE solvers were used. Figure 2 shows the spectrum of the orientation profiles used. To validate the simulation results, corresponding plates were additionally manufactured for three materials at the project partner SKZ, the actual orientation profiles were determined from CT scans, and tensile tests were conducted.
For the filling simulation, the project partner aiXtruison developed and trained a corresponding AI model. As is standard practice, 80% of the training data was used to train the model, and the remaining 20% for validation.
Figure 3 shows, by way of example, an orientation profile calculated in the filling simulation and one predicted by the AI model. The average error of the predicted values was approximately 3%. However, the AI model was unable to predict the results of both injection molding solvers, which in some cases differed significantly despite identical input data. Furthermore, the model’s validity is currently limited to specific plate geometries.
AI Model “Structure”
Training datasets were also generated for the AI model “Structure” by simulating and evaluating tensile tests with various orientation profiles and material models. Each dataset always consisted of tensile tests in 4 different directions (0°, 30°, 45°, and 90° to the flow direction). Orientation and model parameters served as the input data for the AI model to be trained, while the simulated stress-strain curves represented the target variables.
The behavior at different temperatures was treated separately in each case, i.e., as a distinct material. A total of 389 datasets were generated in this manner. Figure 2 shows the complete set of stress-strain curves used.
Input Data for the AI Model
The AI model in question was developed and trained by project partner SKZ in Würzburg. Figure 4 shows some representative results. Here, too, the model generally provided good predictions of the simulation results. However, as the project progressed, the AI model proved to be sensitive to the input data and did not always produce meaningful results.
Workflow
In an initial beta version of the MatScape software, both AI models were implemented as prototypes. The “Process” AI model can be used as an alternative to the conventional method of importing orientation profiles from measurements or simulations. In a later version of MatScape, the required rheological data will be stored in the material database, so that the user will only need to specify the material and the specimen geometry to obtain a prediction of the resulting orientation profile. Figure 5 shows a possible result of this step.
The orientation profile of the “Process” AI model is used in a first step to determine the parameters of the anisotropically elastic material model.
In a second step, various parameters of the material model can be varied in an optimization process to match measured test data as closely as possible with the simulation of the tensile test. However, instead of actual simulation results, the outputs of the “Structure” AI model are now used for the individual parameter sets. In this way, parameter optimization can be performed without external solvers and in a fraction of the time that would otherwise be required.
Figure 6 shows the calibration tool, which at this stage was still an external software module.
The workflow was validated using a demonstration component as an example. This component is a so-called mask base, which serves as a support for filter mats in protective masks. The results of a filling simulation on the component were transferred to the structural model using Converse. The material model was calibrated both manually and using the two AI models as described above. Figure 7 shows the force-displacement curve measured on the component as well as the simulation result using the AI-based material model. The result of the AI calibration is not better than the manually calibrated model, but rather comparable. However, it was created in a fraction of the time and without additional solvers.
This investigation was funded by the German Federal Ministry of Education and Research via the DLR Project Management Agency as part of the “KMU-innovativ program” (project No. 01IS23042) on the basis of a decision by the German Bundestag.
Autor: Dr. Marcus Stojek, Managing Director, PART Engineering GmbH, Bergisch Gladbach, Germany
