## 4 Conclusions  
In the present paper, the damage evolution of the porous NiAl material is simulated by using the DEM and the micro-CT imaging-based reconstruction of the material microstructure. Based on the performed geometry reconstruction, DEM simulations, and analysis of damage evolution, some observations and concluding remarks may be drawn as follows:  
* The DEM supplemented by the micro-CT imaging-based reconstruction of the porous NiAl microstructure revealed a realistic representation of the damage evolution and stress-strain curve.
* While the count of broken bonds was negligibly small, the elastic behavior of the material was dominant, and the numerical stress-strain curve was linear.
* When the strain increased, the count of broken bonds exponentially grew, and some random microcracks initiated, which led to slow weakening of the sample and small deviations of the macroscopic stress-strain curve from the line.  
Figure 6: Stress–strain dependencies obtained by using different values of the compression strain rate.  
At the end of the investigated strain interval, the formation and propagation of macroscopic cracks caused the fall-down of the stress-strain curve, which indicated the beginning of the sample failure. The numerically obtained stress and strain of the curve peak differed from the experimentally measured values by 0.1% and 4.2%, respectively.
* At a high compression load, the propagation of macrocracks, caused by a high increase of the broken bond count in the whole macrocrack propagation volume, led to fragmentation of the sample into more than two parts, which is common to failure patterns observed in uniaxial compression experiments of brittle materials.
* The developed stress scaling technique, based on scaled-down elastic moduli with bond breakage parameters and scaled-up stress values, allowed a seven times increase of the size of the time step, which reduced the computing time by seven times. The proposed scaling was very accurate until the time interval of fast macrocrack propagation. However, the stress peaks of the original and scaled curves differed by 3.2% of the highest stress obtained in DEM computations with the original values of parameters.
* The analysis of stress-strain dependencies obtained by using different values of the compression strain rate showed that the computations performed with a compression strain rate close to 53 s\({}^{-1}\) approached the quasi-static state and achieved acceptable accuracy within the limits of the available computational resources.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15105260/s1](https://www.mdpi.com/article/10.3390/app15105260/s1)]([https://www.mdpi.com/article/10.3390/app15105260/s1](https://www.mdpi.com/article/10.3390/app15105260/s1)), Dataset S1: AKaceniuskas_dataset.vtp.  
Conceptualization, methodology, formal analysis, and investigation, A.K., E.S., R.P., M.C., A.G., J.R. and S.N.; software, E.S. and R.P.; writing--original draft preparation, A.K., S.N. and E.S.; writing--review and editing, A.K., E.S., S.N. and R.P.; visualization, R.P., M.C. and A.G.; supervision, J.R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Science Centre, Poland, under Grant Agreement No. OPUS 2020/37/B/ST8/03907, for the project \"Multiscale investigation of deformation and damage behaviour of novel hybrid metal matrix composites. Experimental studies and numerical modelling\".  
The original contributions presented in the study are included in the article/Supplementary Materials, further inquiries can be directed to the corresponding author.  
The authors would like to acknowledge the consultation on HPC provided by the Lithuanian NCC in the project \"National Competence Centres in the framework of EuroHPC Phase 2\" (DIGITAL-EUROHPC-JU-2022-NCC-01, No. 101101903).  
The authors declare no conflicts of interest.