| Isogeometric Analysis of Phase-Field Models: Application to the Cahn-Hilliard Equation | p. 1 |
| Introduction | p. 2 |
| Phase Transition Phenomena: The Phase-Field Approach | p. 2 |
| Numerical Methods for the Cahn-Hilliard Phase-Field Model | p. 2 |
| The Strong Form of the Cahn-Hilliard Equation | p. 3 |
| Dimensionless Form of the Cahn-Hilliard Equation | p. 4 |
| Numerical Formulation | p. 5 |
| Weak Form | p. 5 |
| Space Discretization | p. 5 |
| Time Discretization | p. 5 |
| Numerical Results | p. 6 |
| Numerical Examples in Two-Dimensions | p. 7 |
| Mesh-Independent Cahn-Hilliard Phase-Field Model | p. 9 |
| Numerical Examples in Three-Dimensions | p. 11 |
| Conclusions | p. 14 |
| References | p. 15 |
| New Computational Challenges in Fluid Structure Interactions Problems | p. 17 |
| Introduction | p. 17 |
| The Discretized Equations to Be Solved in a FSI Problem | p. 19 |
| Monolithic Solution of the FSI Equations by Pressure Segregation | p. 21 |
| Static Condensation of the Pressure | p. 22 |
| Approximation to the Static Condensation | p. 23 |
| Evaluation of the Laplace Matrix <$>{bf L}(tau)<$> for FSI Problems | p. 25 |
| The Partitioned (or Staggered) Scheme | p. 27 |
| Fluid Column Interacting with an Elastic Solid Bottom | p. 28 |
| Conclusions | p. 30 |
| References | p. 31 |
| Brick Elements for Finite Deformations Based on Macro-concepts and on Inhomogeneous Mode Enhancement | p. 33 |
| Introduction | p. 33 |
| Incompressible Macro-element | p. 35 |
| Theory | p. 35 |
| Numerical Examples | p. 38 |
| Enhanced Strain Element | p. 41 |
| Theory | p. 42 |
| Numerical Examples | p. 44 |
| Conclusions | p. 46 |
| References | p. 47 |
| Multi-phase Modelling of Unsaturated Soils | p. 49 |
| Introduction | p. 49 |
| Effective Stress | p. 50 |
| Governing Equations | p. 51 |
| Flow Model | p. 51 |
| Deformation Model | p. 51 |
| Fully Coupled Equations | p. 52 |
| Elastic-Plastic Constitutive Model | p. 52 |
| Bounding and Loading Surfaces | p. 53 |
| The Critical State and Isotropic Compression Lines | p. 54 |
| Plastic Potential | p. 54 |
| Hardening Modulus | p. 55 |
| Suction Hardening | p. 55 |
| Numerical Implementation | p. 56 |
| Finite Element Formulation | p. 56 |
| Stress Integration Scheme | p. 57 |
| Correction of Yield Surface Drift | p. 57 |
| Numerical Results | p. 58 |
| Drying Path (Desaturation) Tests | p. 58 |
| Drained Triaxial Tests | p. 59 |
| Conclusion | p. 60 |
| References | p. 61 |
| Swelling of a Bentonite Plug: A Micromechanical Approach | p. 63 |
| Macro State Equations via Micro-poromechanics | p. 65 |
| General Principles of Linear Micro-poroelasticity | p. 65 |
| When Interactions Solid/Pore Fluid Are Purely Mechanical | p. 67 |
| Swelling Experiment of a Bentonite Plug | p. 70 |
| Conclusions of the First Model of Bentonite Swelling | p. 71 |
| When Interaction Forces Between Platelets Are Addressed | p. 72 |
| Equivalent Behaviour of a Particle: Micro Meso | p. 72 |
| Homogenized Behaviour of a Set of Particles with Mesopores: Meso Macro | p. 73 |
| Swelling Experiment of a Bentonite Plug | p. 75 |
| Conclusions | p. 76 |
| References | p. 77 |
| Solution of Large-Scale Porous Media Problems | p. 79 |
| Introduction | p. 79 |
| Porous Media Problem Formulation | p. 80 |
| Algebraic System Symmetrization | p. 83 |
| Domain Decomposition Solution Methods | p. 84 |
| D-DDM with No Coarse Problem for Implicit Dynamics | p. 85 |
| D-DDM-S and D-DDM-P: D-DDM with an Artificial Coarse Problem Based on Optional Admissible Constraints | p. 86 |
| P-DDM-S and P-DDM-P: P-DDM with an Artificial Coarse Problem Based on Optional Admissible Constraints | p. 87 |
| DDM Computational Issues | p. 88 |
| Numerical Example | p. 89 |
| References | p. 92 |
| A Finite Element Method for Level Sets | p. 95 |
| Introduction | p. 95 |
| Level Set Methods | p. 96 |
| Weak Formulation and Finite Element Implementation | p. 98 |
| Propagation Equation | p. 98 |
| Enforcement of Constant Gradient Norm and Zero-Isolevel Contour | p. 99 |
| Stabilisation | p. 101 |
| The Complete Algorithm | p. 102 |
| Example | p. 104 |
| Concluding Remarks | p. 105 |
| References | p. 105 |
| Modelling of Cementitious Materials by Means of a Multiphysics Approach | p. 107 |
| Introduction | p. 107 |
| Mathematical Model of Concrete Considered as a Multi-phase Porous Material | p. 108 |
| Effective Stress Principle | p. 111 |
| Application of the Model to Prediction of Short/Long Term Performance of Concrete | p. 111 |
| Numerical Simulation of the Russel Experimental Test | p. 114 |
| Application of the Model to the Simulation of Leaching Process | p. 115 |
| Modelling Kinetics of Calcium Leaching Process | p. 115 |
| Numerical Simulation of the Non-isothermal Leaching Process in a Concrete Wall | p. 117 |
| References | p. 119 |
| On the Multiscale Computation of Con"ned Granular Media | p. 121 |
| Introduction | p. 121 |
| RVE Generation | p. 122 |
| Microscale | p. 123 |
| Homogenization - Macroscale | p. 125 |
| Representative Numerical Examples | p. 126 |
| Slope Stability Problem | p. 126 |
| Bi-Axial Compression Test | p. 128 |
| Summary and Discussion | p. 132 |
| References | p. 132 |
| Computational Model Veri"cation and Validation in Structural Mechanics | p. 135 |
| Coupled Verification and Validation in Structural Mechanics | p. 136 |
| AM-FEM for Verification and Validation | p. 136 |
| State of the Art of Discretization and Model Adaptivity | p. 138 |
| Model Verification of Elliptic Problems by Mesh Adaptivity via Explicit and Implicit A Posteriori Error Estimates from Energy Norms and Averaging Techniques | p. 138 |
| Goal-Oriented A Posteriori Error Estimates for Quantities of Interest | p. 138 |
| Model Verification and Validation by Combined Adaptivity via Discretization and Model Error Estimates | p. 139 |
| Strategies for Combined Discretization and Model Adaptivity | p. 140 |
| Variational Formulation of Combined A Posteriori Discretization and Model Error Estimates for Expansive Model Adaptivity via Prolongations | p. 141 |
| Goal-Oriented Error Measures and Their Advantages | p. 143 |
| Duality Techniques and Solutions of Local Neumann Problems for Goal-Oriented A Posteriori Error Estimates | p. 143 |
| Computable Implicit Primal and Dual Error Estimators | p. 144 |
| Adaptive Ansatz Spaces for Plates and Solids | p. 145 |
| Prolongation of Coarse-to-Fine Model Solutions and Orthogonalization of the Discrete Model Error | p. 145 |
| Kinematic Prolongations from Finite Plate Elements to Finite Solid Elements | p. 146 |
| Orthogonalization of the Discrete Model Error on the Finite Element Level | p. 147 |
| Example: Combined Discretization and Model Adaptivity for an Elastic Plate with 3D Boundary Layers | p. 148 |
| References | p. 150 |
| Microstructure-Oriented Modeling and Computational Remodeling of the Collagen Network in Corneo-Scleral Shells | p. 155 |
| Introduction | p. 155 |
| Mechanics of Crimped Collagen Fibrils at the Micro-level | p. 157 |
| Mechanics of Collagen Fibril Networks at the Meso-level | p. 160 |
| Remodeling of the Collagen Fibril Network | p. 161 |
| Numerical Example | p. 162 |
| Discussion | p. 165 |
| References | p. 167 |
| Microstructure Optimization and Identi"cation in Multi-scale Modelling | p. 169 |
| Introduction | p. 169 |
| Computational Homogenization in Multiscale Modelling | p. 170 |
| The Problem Formulation | p. 171 |
| The Evolutionary Algorithm | p. 174 |
| The Numerical Example | p. 175 |
| Shape Optimization | p. 175 |
| Identification of Material Properties | p. 177 |
| Identification of Fibres Shape in the Microstructure | p. 178 |
| Conclusions | p. 179 |
| References | p. 180 |
| Homogenization of Strength A Numerical Limit Analysis Approach | p. 183 |
| Introduction | p. 183 |
| Discretized Form of Limit Analysis | p. 185 |
| Upper-Bound (UB) Formulation - The Kinematic Approach | p. 185 |
| Lower-Bound (LB) Formulation - The Static Approach | p. 187 |
| Failure Criteria and Solution of Optimization Problem | p. 187 |
| Numerical Studies - Effective Strength Properties of Matrix-Inclusion Materials | p. 189 |
| Limit Analysis Applied to Porous Material Structures | p. 189 |
| Limit Analysis Applied to Matrix-Particle Materials | p. 195 |
| Conclusions | p. 198 |
| Appendix | p. 199 |
| References | p. 200 |
| Computable Error Indicators for Approximate Solutions of Elliptic Problems | p. 203 |
| Introduction | p. 204 |
| Error Indicators for Global Errors | p. 206 |
| Indicators for Goal-Oriented Quantities | p. 208 |
| Indicators Based on Solutions of Etalon Problems | p. 214 |
| References | p. 215 |
| Interaction of Incompressible Flows and Thin-Walled Structures | p. 219 |
| Introduction | p. 220 |
| Governing Equations and Basic Assumptions | p. 220 |
| Structural Domain | p. 221 |
| Fluid Domain | p. 221 |
| Modeling and Discretization | p. 222 |
| Nonlinear Shell Dynamics | p. 223 |
| Stabilized Fluid Formulation | p. 224 |
| Coupling Approaches | p. 225 |
| Weakly Coupled Partitioned Approaches and Artificial Added Mass Effect | p. 226 |
| Strongly Coupled Partitioned Approach | p. 228 |
| Iterative Substructuring Scheme Accelerated via the Aitken Method | p. 228 |
| Numerical Simulations and Applications | p. 230 |
| Two-Dimensional Bridge Cross Section | p. 230 |
| Snap Through of a Gasket | p. 231 |
| Conclusions | p. 231 |
| References | p. 233 |
| Advances in Fixed-Grid Fluid Structure Interaction | p. 235 |
| Introduction | p. 235 |
| Formulation of a Coupled Fluid-Structure Problem | p. 237 |
| Fluid | p. 237 |
| Structure | p. 238 |
| Fluid-Structure Interface Conditions | p. 238 |
| XFEM/Lagrange Multiplier Based Techniques for FSI | p. 239 |
| Fixed-Grid Fluid Formulation | p. 239 |
| Direct Fixed-Grid Fluid-Structure Coupling | p. 241 |
| Enhancement of the Flow Field Around the Submersed Structures | p. 243 |
| Adaptive Fixed-Grid Methods | p. 243 |
| A Hybrid Fixed-Grid/ALE Approach | p. 244 |
| Extension to Three-Dimensional Problems | p. 246 |
| Conclusion | p. 247 |
| References | p. 248 |
| Exploring Automatic Multi-objective Turbine Disc Design for Virtual Engines | p. 251 |
| Introduction | p. 252 |
| Overview Virtual Engine Coloration | p. 253 |
| Automatic Single Disc Design Tool Suite | p. 254 |
| Tool Suite Overview | p. 255 |
| Disc Evaluation Results | p. 256 |
| Design Optimisation | p. 258 |
| Conclusions | p. 261 |
| References | p. 262 |
| Modeling of Smart Structures by Meshless Local Integral Equation Method | p. 263 |
| Introduction | p. 263 |
| Local Boundary Integral Equations for 2-D Problems | p. 265 |
| Numerical Examples | p. 271 |
| Conclusions | p. 273 |
| References | p. 274 |
| Meshless Local Petrov Galerkin (MLPG) Formulations for Analysis of Shell-Like Structures | p. 277 |
| Introduction | p. 277 |
| Fully Displacement MLPG Formulation for Shell Analysis | p. 279 |
| Governing Equations | p. 279 |
| Discretization | p. 280 |
| Mixed MLPG Formulation for Plate Analysis | p. 282 |
| Numerical Examples | p. 286 |
| Cylindrical Shell Subjected to Uniform Line Load | p. 286 |
| Simply Supported Plate Under Uniformly Distributed Load | p. 287 |
| Conclusion | p. 288 |
| References | p. 289 |
| Hierarchical Meshing for the Adaptive Finite Elements | p. 291 |
| Introduction | p. 291 |
| Level-of-Detail (LOD) | p. 292 |
| Hierarchical Clustering | p. 293 |
| Cluster analysis | p. 293 |
| Ward s Method | p. 293 |
| Generation of Hierarchical Mesh | p. 294 |
| Adaptive Mesh | p. 295 |
| Posterior Error Estimation | p. 296 |
| Mesh Control | p. 297 |
| Calculation Results | p. 299 |
| Cavity Flow | p. 299 |
| Crack Propagation | p. 301 |
| Future Works | p. 303 |
| References | p. 305 |
| One-Dimensional Shock-Capturing for High-Order Discontinuous Galerkin Methods | p. 307 |
| Introduction | p. 307 |
| The Basics of LDG in 1D | p. 309 |
| Proposed Approach for the Artificial Diffusion | p. 310 |
| RKDG Methods | p. 311 |
| The Nonlinear Limiting Operator | p. 312 |
| Artificial Diffusion | p. 313 |
| Order of the Introduced Diffusion | p. 314 |
| Shock Detection | p. 315 |
| Numerical Examples | p. 315 |
| Linear Advection | p. 316 |
| A Steady-State Convection-Diffusion Problem | p. 318 |
| Nonlinear Conservation Law | p. 319 |
| Euler Equations | p. 321 |
| Concluding Remarks | p. 323 |
| References | p. 324 |
| Computing Interfaces in Diverse Applications | p. 327 |
| Introduction | p. 327 |
| Survey of Methods for Moving Interfaces | p. 328 |
| Front-Tracking Methods | p. 328 |
| Front-Capturing Methods | p. 329 |
| The Level Set Method | p. 329 |
| The Level Set Equation | p. 330 |
| Velocity Extension | p. 330 |
| Distance Function and Re-initialization of the Level Set Function | p. 331 |
| Composite Grid | p. 332 |
| Local Grid Refinement and Derefinement | p. 332 |
| The Cut-Cell Method | p. 333 |
| Applications | p. 334 |
| Precipitate Dissolution Under Homogenization Conditions | p. 334 |
| Epidermal Wound Closure | p. 337 |
| Conclusions | p. 339 |
| References | p. 340 |
| New Aerospace Design Challenges: Robust Multidisciplinary Evolutionary Techniques | p. 343 |
| Introduction | p. 344 |
| Methodology | p. 344 |
| Uncertainty | p. 345 |
| Analysis Tools | p. 345 |
| Aerodynamic Analysis Tools (FLO22 + FRICTION) | p. 345 |
| Electromagnetic Analysis Tools (POFACETs software) | p. 346 |
| Analysis and Formulation of Problem | p. 346 |
| Representation of Design Variables | p. 347 |
| Real World Design Problems | p. 349 |
| Multi-objective Design Optimisation of UCAS | p. 349 |
| Robust Multidisciplinary Design Optimisation of UCAS | p. 352 |
| Conclusions | p. 357 |
| References | p. 357 |
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