Multi-scale Homogenization of Moving Interface Problems with Flux and Field

3 1 Computational Homogenization Approach Micro-scale Boundary Conditions 32 3 2 Micro-Macro linking Transferring Fluxes and Diffusivities 36 3 3 Micro-scale model 37 3 3 1 Description of flow in the porous matrix at micro-scale 38 3 4 Macro scale model 41 3 5 Tracking of the interface using level set method and adaptive meshing 46 3 6 Computational approach and Numerical Results 47 3 6 1 Convergence study 49 3 6 2 Numerical results of the Taylor and Homogenization multi-scale model 51 3 7 Conclusion 56 IV. Multi-scale model validation wi th direct numerical s imulat ions(DNS) 60 4 1 Direct numerical simulation 60 4 2 Computational approach and numerical results 62 4 3 Conclusions 65 V. A 3D multiscale model for property degradation of CMCs: Temperature and stress effects 70 5 1 Matrix and vector transformation 72 5 2 Computational Homogenization Approach Micro-scale Boundary Conditions 73 5 3 Micro-scale model for elasticity 78 5 4 Deformation under mechanical loading 81 5 5 Micro-scale Taylor model for Oi and CO2 diffusion in porous matrix 82 5 5 1 Diffusion properties for pore matrix 84 5 6 Macro-scale model for O2 and CO2 diffusion in C/SiC 88 5 7 Computational approach and numerical Examples 91 5 8 Numerical simulation results 93 5 8 1 Comparison of oxidation behavior in the presence of applied stresses 102 5 9 Conclusion 103 VI. Suggest ions for future research 108 6 1 Modeling UHTCs 109 6 2 Anisotropic diffusion 109 6 3 Modeling microdamage with molecular dynamics 110 6 4 SiC oxidation effect of moisture 113 A P P E N D I C E S 114 B I B L I O G R A P H Y 120