## 2 Materials and Methods
### Preparation of NiAl Sample for DEM Simulations  
The discrete element model was verified by the experimental results of a uniaxial compression test of a cube-shaped sample. Nickel aluminide was selected as a representative porous material. The NiAl sample was manufactured using the powder metallurgy technique based on Spark Plasma Sintering (SPS), related to resistive heating in an electrically conductive matrix. Densification of the material occurs at elevated temperatures in the presence of uniaxial pressure. The process of material compaction occurs due to diffusive mass transport mechanisms because of the generated Joule heat, which is a consequence of the flow of electric current through the usually graphite punches and dies [32]. This type of heating allows for high heating rates (up to 1000 \({}^{\circ}\)C/min), lower sintering temperatures, and much shorter processing times than conventional methods [33]. The method can effectively synthesize materials from metallic, ceramic, and composite powders [34; 35].  
Nickel aluminide (NiAl--Goodfellow) gas-atomized powders with an average particle size of 10 \(\upmu\)m diameter and purity of 99.9% were selected for sintering. The main advantage of the SPS process is that it reduces uncontrolled grain growth at elevated temperatures and avoids undesirable structural changes when sintering reactive materials. The details of the manufacturing procedure are presented in [28]. The powder was loosely filled into a graphite die with an inner diameter of 26.0 mm and closed tightly with graphite punches. Graphite foil that was 0.5 mm thick was used as a die-powder spacer. Then, the NiAl powder was heated at a rate of 100 K/min to the target sintering temperature, reaching 1200 \({}^{\circ}\)C for a sintering time of 10 min. The sintering process conducted in a vacuum atmosphere was supported by an external pressure of 5 MPa. Afterwards, the samples were naturally cooled down. The final 25.0 mm diameter discs were cut and ground for further investigations. The density of the sintered materials was estimated using the Archimedes method. The average density of the NiAl material sintered in presented conditions was determined from 10 measurements and was 4620 kg/m\({}^{3}\). This represents 78.1% of relative density, assuming a theoretical density of 5910 kg/m\({}^{3}\).  
To reconstruct the actual microstructure of the NiAl sample, the X-ray computed tomography (micro-CT) was carried out by the EasyTom system (RX Solutions (Chavanod, France)) using an open transmission X-ray source with a tungsten target and a diamond window at the tube voltage of 160 kV. The CT was performed for the sample volume of 2 \(\times\) 2 \(\times\) 2 mm\({}^{3}\) with a voxel size of about 1.8 \(\upmu\)m. In total, 2880 projections were taken using a PaxScan 2520 DX Varian (Varex Imaging (Salt Lake City, UT, USA)) flat panel detector. The images were acquired in the continuous cone beam single circle acquisition mode with an additional 32 reference images.  
Finally, the NiAl sample was subjected to the uniaxial compression test at room temperature using a Zwick Roell Z005 (ZwickRoell (Ulm, Germany)) universal testing machine equipped with a 1 kN force transducer. The experiments were conducted under displacement control with a strain rate of 10\({}^{-3}\) s\({}^{-1}\). The tests were performed on cubic-shaped samples of 2 \(\times\) 2 \(\times\) 2 mm\({}^{3}\) (Figure 1).