## 1 Introduction  
When designing heterogeneous materials, it is of great importance to take the microscale geometric arrangement of their constituents into consideration, in order to make confident assumptions about their macroscopic mechanical performance. During the last few decades, the practice of building digital 3D representative volume elements (RVEs) has been employed for the consideration of the microstructure of polycrystals (alloys [1; 2; 3; 4; 5; 6; 7; 8; 9] and ceramics [10]), polymer matrix composites [11; 12; 13; 14], metal matrix composites [15; 16; 17; 18; 19], and ceramic matrix composites [20; 21; 22; 23]. In many instances, and especially for metals and alloys, experimental methods are used to obtain information on the microstructure of the material, primarily electron backscattering diffraction (EBSD) and scanning electron microscopy (SEM). However, the use of pure experimental data regarding the geometry of the specimens may result in severe numerical drawbacks during the simulation of the RVEs. This occurs as these data exhibit geometrical complexity and, consequently, an extremely high number of degrees of freedom (DOFs) [24]. Therefore, the construction of RVEs is commonly accomplished by resorting to alternative methods, such as Voronoi diagrams [3; 15; 16; 17; 25; 26; 27] or by applying statistical simulations (e.g., Monte Carlo) [11; 14]. The utilization of simpler RVEs in terms of geometry, which, despite their simplicity, represent the material's microstructure and respond adequately to simulations in terms of the material's macroscopic properties, is also desirable [24]. These elements, often referred to as statistically similar RVEs (SSRVEs), are obtained by minimizing the differences in statistical and mechanical behavior compared to the actual microstructure [24, 28]. This optimization process is executed to ensure statistical similarity, as well as to render the SSRVEs and the real microstructure comparable, in terms of mechanical properties. The performance of SSRVEs may vary depending on the statistics used and on the parameterization of the microstructure. It is also important for the efficient construction of SSRVEs to retrieve the statistics in a reasonable time frame and provide sufficient and valid information about the actual microstructure [28]. One way to construct SSRVEs is to segment images obtained by a microscopy technique (e.g., SEM, TEM, tomography) based on the brightness of its segments. These segments depict different phases of the material and segmentation is used to obtain information about the statistics of each phase [24, 29]. The objective of this study is to establish a framework for constructing 3D digital volumes that simulate, based on microstructure statistics, a complex material. These volumes can be used to perform simulations of mechanical loading to evaluate their macroscopic mechanical properties. The framework is designed by employing experimental data of the microstructure of its individual phases and their mechanical properties. Having developed such a framework, one can design novel materials and predict their mechanical performance at the macroscale by combining different constituents (matrix and reinforcing phases) and by altering the parameters that describe the microstructure, such as volume fractions, size distributions, particle geometry, and inter-phase interactions. The benefit of replacing experimental mechanical testing (e.g., tension, compression, hardness measurements) with simulation analyses lies in the significant cost reduction in the material design process. The present study was performed, as a first step, on a metal matrix composite (MMC), namely the aluminum alloy composite AA7075 with a T700S-type carbon fiber reinforcing phase. This alloy was chosen as it is one of the most studied alloys, with applications in fields where high mechanical stresses are applied (e.g., aerospace, aeronautics, machinery, pressure vessels) [4, 30, 31, 32, 33].