## 1 Introduction  
The characterization of the effective properties and behaviors of composites is a very delicate task that has preoccupied researchers for several years. During the last two decades, the prediction of the effective mechanical and physical properties of composite materials has developed considerably thanks to the development of several analytical homogenization models and, especially, to numerical homogenization techniques based on the finite element method. The availability of these increasingly efficient homogenization methods has opened up numerous perspectives for the characterization of composite materials, even with complex morphologies, offering the possibility of developing heterogeneous materials meeting very demanding specifications. For example, in a statistical and numerical approach, [PERSON] et al. [1] proposed an original homogenization methodology to determinate the representative volume element (RVE) size for elastic and thermal effective properties of heterogeneous materials. The RVE size is controlled by introducing the statistical integral range notion. [PERSON] et al. (2018), based on a finite element analysis, developed a multi-scale computational model for determining the elastic-plastic behavior of a multi-phase metal. A single crystal plasticity constitutive model that can capture the shear deformation and the associated stress field on the slip planes is employed at the microstructural length scale. The generalized method of the cell micromechanics model is then used for homogenizing the local field quantities. As part of the development of new environmentally friendly materials, [PERSON] et al. (2018) developed a multi-scale homogenization approach accounting for the shape and orientation of pores and particles to model the effective thermal conductivity and anisotropy of hemp shives, which are used as bio-based insulation material. [PERSON] et al. (2018) developed a new homogenization model for the macroscopic behavior of three-scale porous polycrystals consisting of large pores randomly distributed in a fine-grained polycrystalline matrix. In continuation of this first work, [PERSON], et al. (2018) used the same model developed in (2018) to investigate both the instantaneous effective behavior and the finite-strain macroscopic response of porous FCC and HCP polycrystals for axisymmetric loading conditions. To ensure the safe and stable operation of the high-temperature superconducting magnet, [PERSON], et al. (2018) developed a numerical homogenization scheme to simulate the coupled electromagnetic-thermal-mechanical behaviors of high-field magnets. The representative volume element (RVE) based on micromechanics was created to predict the homogenization properties of the magnets. A very interesting study was developed by [PERSON] et al. (2018) using multistep homogenization for the determination of the effective mechanical properties of ultra-high-performance fiber-reinforced concrete. This study mainly considers the influence of the coarse aggregate content and steel fiber volume fraction on the effective mechanical properties. In the first step, an equivalent damage constitutive model of the UHPFRC composite is established at the mesoscale, according to the Mori-Tanaka homogenization method and progressive damage theory. In the second step, to study the influence of mesoscopic components of UHPFRC on its macroscopic mechanical properties, the mesoscopic material properties obtained in the first step are input into the finite element model for numerical simulation. The mean field homogenization (MFH) technique is a multistep method, which is based on separating the heterogeneities of the considered composite to subdomains and homogenizing the effective property of each one in the first step; the complete composite effective property is then homogenized in the second step.