Results of the two-scale simulation
For the project, 2 scales for modeling and simulation are observed in order to analyze the influence of micro-structural parameters (such as, for example, fiber length distribution and fiber orientation) on the properties of MDF or building components. For the characterization of the microstructure, a fiber network in a volume element of a few cubic millimeters is used. Three-dimensional μCT images (Fig. 4) with a resolution of 4 µm are suitable for capturing a representative section (at least half the plate thickness) and for a simultaneous sufficiently-good resolution of the individual fibers.
For the modeling of the geometric microstructure, the length and thickness distribution of the fibers is determined from the applied fiber material, and the fiber orientation is determined from the μCT images. To determine the orientation, automatic mathematical algorithms for fiber-direction analysis are applied (Fig. 5). This method also enables the determination of the position of fiber bundles (red region). The result of this process step is a so-called stochastic geometry model.
For the stochastic geometry model, realizations (Fig. 6) in the form of microstructures in volume elements can be generated. In the generated volume element, for each point belonging to a fiber the local orientation this fiber has in this point is clearly defined. In contrast, in a binarized image, only the information as to whether a point belongs to the solid material (cellulose) or to the pore space would be captured.
In the next step, the anisotropic elastic properties and the anisotropic strength properties for the fibers are selected. Following this, 6 non-linear elasticity problems (tension in 3 directions, thrust in 3 directions) are solved using the FeelMath software developed at the ITWM, in order to determine the effective mechanical properties.
These effective material parameters represent the final result of the microstructure analysis and are applied in the second scale (macro-scale or component scale) as a material parameter. The simulation on the macro-scale is executed using a standard method (FEM). In the project, the results of the macro-simulation, e.g. a simulation of the flex test, correlated very well with corresponding measurement results (Fig. 7).
The advantage of the two-scale simulation lies in the fact that in the stochastic geometry model, individual parameters can be systematically selectively varied in order to study their sensitivity to the macroscopic stiffness and strength, without having to produce the relevant material variants. Whilst the computer simulation is elaborate, it takes considerably less time than measurements; a very large number of MDF variants can therefore be simulated. An example of this can be seen in Fig. 8. For the same fiber length distribution and the same fiber volume content, only the orientation has been changed. The result is an improvement in the rigidity in the direction in which the fibers are aligned. The extent of the quantitative improvement is demonstrated in the diagram in Fig. 8.