This study presents an extended numerical approach based on GeoMicro3D to simulate the reaction kinetics and three-dimensional (3D) microstructure evolution of alkali-activated fly ash (AAFA). Dissolution experiments were conducted under varying NaOH concentrations and temperatures to formulate predictive rate functions for Si and Al release. These experimentally derived kinetic functions, alongside a thermodynamic dataset for N-(C-)A-S-H gels, were incorporated into the GeoMicro3D model to capture the chemical reactions and 3D microstructure evolution of AAFA. The model well captured reaction degree of fly ash, formation of solid products, evolution of pore solution compositions, and porosity over time. Notably, it is the first to predict the time-dependent spatial distribution of phases within the 3D AAFA microstructure by integrating kinetic and microstructural modeling. Dual validation using both dissolution data and microstructural metrics demonstrates the model's reliability and robustness. This integrated framework provides new insights into the coupled chemical–microstructural evolution of alkali-activated materials.

The demand for composites is rising in industries for instance, in aircraft and automobile engines. In these applications, composites encounter high thermal gradients service condition, and composites exhibit material discontinuous gradient field. It is essential to study how high thermal gradients and material discontinuities influence on the composites’ behavior. Composites are usually modelled with the standard finite element method (FEM), but mesh refinement is required near material interfaces and regions with high thermal gradients to obtain accurate solutions. Enriched finite element procedures are able to solve this issue. The Generalized Finite Element Method (GFEM) can approximate high thermal gradients by adding enriched degrees of freedom (DOFs) to original mesh nodes. In addition, the Interface-enriched Generalized Finite Element Method (IGFEM) can cope with material discontinuities by creating nodes at the intersection between discontinuities and edges of elements in the mesh. Yet, GFEM and IGFEM have their own limitations when implemented: while GFEM needs extra enrichments to resolve the material interfaces in composites, and IGFEM requires mesh refinement if thermal gradients are too high in cut elements. Then we can combine the best of both methods.

In this thesis, a new Generalized Finite Element Method with spread and discrete enrichments (GFEM^sd) is developed to simulate heat transfer problems with high thermal gradients in composites. By combining GFEM and IGFEM formulations, GFEM^sd is capable of dealing with high thermal gradients and material discontinuities simultaneously in an effective manner. We show that GFEM^sd obtains accurate results when compared with analytical solutions in numerical examples. A convergence study illustrates that fewer DOFs are required in GFEM^sd for achieving the same level of accuracy comparable to that of IGFEM. We then apply GFEM^sd to simulate a twill pattern composite and derive effective heat conductivity values. Lastly, based on the composite’s minimum effective heat conductivity, fiber shape optimization is conducted to obtain the best design for a fixed fiber volume fraction.