## 2 Materials and Methods
### Development of a Geometrical Model of the NiAl Microstructure Based on Micro-CT Images  
A geometrical model, realistically representing the material microstructure, is especially important because the properties of the material strongly depend on the particle packing used. Generation of a well-connected densely packed irregular assembly of particles is the key to successful DEM simulations. In the present research, particle packings of porous NiAl material are generated by the adapted advancing front algorithm according to micro-CT images. The proposed reconstruction procedure of the porous NiAl microstructure consists of four main steps, illustrated in Figure 2:  
* Process the micro-CT scan for geometrical reconstruction of the NiAl sample (Figure 2a). * Define the boundaries of the solid phase by the particles (Figure 2b). * Fill the volume of the solid phase by irregular highly dense particle packing (Figure 2c). * Remove the temporal particles from the pores (Figure 2d). In the first step, the geometry of the NiAl sample is reconstructed by segmenting micro-CT images. Defining the representative volume element (RVE) also requires careful consideration to ensure statistical homogeneity of the microstructural elements (solid and pores). Based on the homogeneity analysis of sintered NiAl, we selected a sample comprising 100 \(\times\) 100 \(\times\) 100 voxels (183 \(\times\) 183 \(\times\) 183 \(\upmu\)m\({}^{3}\)). Confirmation of the reliability of the images obtained is provided by the high agreement of the sinter porosity obtained by density measurement and volumetric image analysis, 21.8% and 21.9%, respectively. The solid and pore phases are identified by using phase masks and applying the threshold value. Figure 2a shows the segmented 3D model obtained from processing the initial micro-CT scan. Figure 1: NiAl sample subjected to uniaxial compression at (**a**) the beginning of the loading stage (initial state), and (**b**) the end of the loading stage (damaged state). In the second step, the boundaries of the solid phase are defined by the particles. Pores are regularly filled by temporal particles of equal size (blue particles in Figure 2b). Each particle is placed in a voxel center of the micro-CT scan. Naturally, the accuracy of pore geometry is limited by the voxel size. The top and bottom boundaries of the sample are represented by regularly located particles (red particles in Figure 2b) to obtain smooth boundary surfaces that are loaded by moving two rigid plates during simulations. In our experience, rough surfaces produced by irregular packing of particles cause intensive initiation of microcracks on the loaded boundary, which might lead to premature sample failure. Other boundaries of the sample are traditionally represented by using planes, which causes rough surfaces formed from irregularly located particles in the final packing. In the third step, the volume of the solid phase is filled by irregularly packed particles of defined size or radius distribution. A well-connected highly dense sphere packing (Figure 2c) is generated by using the adapted advancing front algorithm [36] for filling arbitrarily complex geometries. In the fourth step, regularly packed particles are removed from the pores. These temporal particles were generated to define surfaces between the pores and solid phase in the second step. The generated porous NiAl sample of 183 \(\times\) 183 \(\times\) 183 \(\upmu\)m\({}^{3}\) is represented by an assembly of 188,190 irregularly packed particles of radius 1.5 \(\upmu\)m (Figure 2d, Dataset S1). The radius of particles is not strictly limited by the voxel size, which is a great advantage of the proposed geometry reconstruction procedure. A larger size of particles allows performing simulations of the considered RVE with a smaller number of particles, which can significantly shorten the computing time.