## 1 Introduction
Generally, there is no multi-scale procedure in this technique and its efficiency has been observed particularly for composites with inclusions that can be separated into several subdomains with the same property. The MFH method has been exploited by various studies (see (2018)  
incremental-secant and integral affine formulation approaches, and they observed that the computational time cost is largely better than the full-field finite element analyses. [PERSON] et al. [24] computed the effective thermal conductivity of three-dimensional braided composites using an original method by combining a meso-micro scale and multistep modeling. The validation of the proposed method has been performed by confrontation with experimental data and to DH method. [PERSON] et al. [25] applied the concept morphology to two types of composite mediums, an elementary cell periodic medium and a representative volume element random medium, to investigate the possibility of replacing different inclusion morphologies with a circular one. Several cases of shapes and the inclusion's position and orientations have been tested and the results revealed that, for all situations tested, there is no equivalence between the different morphologies. Recently, various advanced homogenization techniques have been developed. For example, [PERSON] et al. [26] established a novel homogenization method for the estimation of the effective elastic and thermal behavior of heterogeneous materials. This method is based on the mathematical curve fitting. A mathematical model is deducted through three steps consisting of plotting module curves as functions of the volume fraction and contrast, creating a unified model, and, finally, predicting the bulk, shear, and thermal conductivity moduli by formulating mathematical equations. [PERSON] et al. [27] developed a homogenization scheme to estimate the effective superior mechanical properties, resulting from the inclusion of rigid elements in elastic grid composites, such as extreme auxeticity. The technique has been tested on Chinese lattices, and it has been shown that this method can improve the conception of the architected materials. More recently, the current trend has been for intelligent methods based on the application of neural networks and deep data learning. The homogenization techniques of heterogeneous materials have followed this trend and several works have emerged. For example, to substitute the micro-level finite element (FE) and to reduce computational costs in multi-scale simulations, [PERSON] et al. [28] proposed a data-driven model, based on artificial intelligence, for both linear and nonlinear elastic responses of heterogeneous solids. The originality of the proposed technique is the development of a deep learning model for estimating the mechanical behavior of heterogeneous microstructures. An original technique, named physics-informed deep homogenization networks (DHN), has been proposed by [PERSON] et al. [29]. Based on neural network learning, this method is used to estimate the local stress field and homogenized moduli of heterogeneous materials with two- and three-dimensional periodicity. The proposed model is validated by confrontation, for different composites, with the finite element method, and a good agreement has been observed. [PERSON] et al. [30] presented a transformer neural network architecture, which, through the knowledge of different microstructure components, can predict the history-dependent homogenized response of elastoplastic composites. This technique has the advantage of being a homogenization substitution model that can reduce the computational costs of the arbitrary and nonlinear microstructures analyzed by classical homogenization methods. All multi-scale homogenization methods, aimed at determining the effective properties or, even better, the construction of equivalent homogenous behavior models, are mainly based on a detailed description of different heterogeneities of the microstructure at the study scale.