## 6 Finite Element Method
### Future Developments of FEM  
Although the FEM is frequently used to investigate creep behavior in fiber-reinforced composites, there are still considerable untapped research potential in this area. Some encouraging directions for further research on using FEM to examine creep in fiber composites are described below. Creep occurs at multiple scales (fiber, matrix, and interface). As a consequence, the multiscale modeling of creep becomes a perfect method to study these phenomena. So, it is possible to develop hierarchical or concurrent multiscale FEM models and to connect microscale material behavior with macroscale performance. A direction of research is to incorporate micromechanical models for fiber-matrix interactions during long-term creep. Creep is a behavior that extends over a period of time, resulting in changes in the interface; it often degrades over time under creep conditions. It is necessary to develop a time-dependent interface model and to implement cohesive zone models or other interfacial degradation models within FEM frameworks that evolve over time due to creep. The development of nonlinear and viscoelastic/viscoplastic constitutive models is necessary to integrate advanced time-dependent constitutive models (e.g., Schapery, Findley, or Anand-type models) into FEM codes for better prediction accuracy under various loading histories. Another direction is by introducing thermocreep coupling in FEM. Creep is highly sensitive to temperature, especially in high-performance composites. Developing thermomechanical FEM models that couple heat transfer and creep deformation, including anisotropic thermal conductivity and expansion, is a goal to pursue. Long-term creep can cause damage such as matrix cracking, fiber breakage, and delamination. So, it is useful to incorporate continuum damage mechanics (CDM) or progressive failure models in FEM to simulate damage accumulation due to creep. Because creep simulations can be computationally intensive, it can be beneficial to use machine learning or surrogate models trained on FEM results to speed up predictions, particularly for design optimization or real-time structural health monitoring. The results of long-term models established to develop benchmark datasets should be validated, and FEM-experiment hybrid studies should be promoted, especially with digital image correlation (DIC) and in situ microscopy techniques. Additive manufacturing (3D Printing) can introduce complex fiber orientations and voids. The use of FEM to study how non-traditional fiber architectures affect creep and optimize them for long-term reliability using simulation can be beneficial. Natural fiber composites have different creep behavior and are gaining popularity. It is necessary to adapt FEM tools to model creep in biocomposites, accounting for environmental effects like moisture and biodegradation. Finite element squared (FE\({}^{2}\)) is a computational homogenization technique that integrates two levels of finite element analyses. The first level is at the macroscopic scale, which represents the overall structural behavior of the composite material. The second level, at the microscopic scale, captures the detailed behavior of the material's microstructure, such as fiber-matrix interactions. FE\({}^{2}\) provides a detailed, physics-based approach to modeling creep behavior by capturing both macroscopic and microscopic responses. The method is used to numerically homogenize materials whose behavior depends on complex microstructures. It does this by solving finite element models at both the macro- and microscales simultaneously. To do this, the following procedure is applied: First, the macromodel is discretized using standard finite elements. Then, it is assigned an RVE at each Gauss point considered in the discretization. This is a microscale model showing the material's internal layout (fibers, voids, etc.). The boundary conditions are applied to the RVE. The stress response at the microscale is computed (which may include creep, damage, plasticity, etc.).