## 5 Homogenized Viscoelastic Coefficients
### Future Developments in Homogenization  
Advances in materials science, computer tools, and multiscale modeling methodologies are driving a rapid evolution in the future of homogenization methods used to investigate creep behavior in composites. The following are the most prominent directions of development in future studies:  
* A multiscale or multi-physics modeling approach, a widely used type of analysis, can be considered due to its existing computational possibilities. Currently, directions necessary in current engineering applications are being pursued, such as developing homogenization frameworks (for coupled phenomena, such as thermomechanical, viscoelastic/viscoplastic interactions or damage); coupling creep with oxidation, thermal gradients, and phase transformation; embedding microstructural evolution during creep (grain growth, void formation); or capturing interface behavior and its evolution (e.g., fiber-matrix debonding).
* Further development of numerical calculation methods includes FE2 (finite element squared), applying reduced order modeling (ROM) to reduce high computational costs, incorporating time-dependent behavior (creep laws) into microscale FE models and using adaptive methods to reduce the number of representative volume elements and therefore the dimension of the system [189; 190; 191; 192; 193; 194].
* ML and AI can be used to accelerate the homogenization process using ML-based constitutive models that can evolve with damage and time. This results in a real-time prediction of creep properties from microstructure descriptors. ML can replace or accelerate homogenization processes. Instead of solving the RVE repeatedly, an ML model is trained on pre-computed data to instantly predict effective creep properties.
* Existing homogenization methods should be developed to adapt to creep strain evolution and introduce new internal variables such as creep strain, damage, and history-dependent responses.
* Recognizing the fact that the microstructure of composites is often non-deterministic, stochastic homogenization can be introduced in analysis to quantify uncertainty in creep life prediction. Spectral or Monte Carlo methods can be used to simulate the variability in the distribution of phases in a composite.
* High-resolution experimental data (micro-CT, SEM) can be directly integrated into homogenization. So, using digital volume correlation (DVC), it is possible to validate the creep strain field at different scales, and through direct 3D scans, it is possible to build RVEs directly and introduce them in numerical analysis.
* One important direction of study is the micro-damage evolution (cracking and fiber breakage) within homogenization schemes.  
All these research method developments have wide applicability in CFRPs and GFRPs (aerospace and automotive under high-temperature applications); C/composites, where creep is important in thermal protection systems; metal matrix composites (MMCs) (for high-temp structural uses); and ceramic matrix composites (CMCs). Here, creep and damage are tightly coupled. Validation of the homogenized methods is performed by comparing the values obtained by applying this method with the values obtained by experimental procedures. This is carried out in the paper reviewed in the next section.  
By reducing the system to an equivalent homogeneous material, homogenization theory in composite materials enables scientists and engineers to understand and forecast the behavior of complicated multi-phase materials. This method is crucial for improving composites' performance and design in a range of technical applications.