Computational Methods in Applied Sciences

New Computational Challenges in Materials, Structures, and Fluids

By: Josef Eberhardsteiner (Editor), Christian Hellmich (Editor), Herbert A. Mang (Editor)

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Hardcover | 16 January 2009

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This book contains 23 papers presented at the ECCOMAS Multidisciplinary Jubilee Symposium - New Computational Challenges in Materials, Structures, and Fluids (EMJS08), in Vienna, February 18-20, 2008. The main intention of EMJS08 was to react adequately to the increasing need for interdisciplinary research activities allowing ef?cient solution of complex problems in engineering and in the applied sciences. The 15th anniversary of ECCOMAS (European Community on Computational Methods in Applied Sciences) provided a suitable frame for taking the afo- mentioned situation into account by inviting distinguished colleagues from d- ferent areas of engineering and the applied sciences, encouraging them to choose multidisciplinary topics for their lectures. The main themes of EMJS08 have a long tradition in engineering and in the applied sciences: materials, structures, and ?uids. The solution of scienti?c pr- lems involving ?uids together with solids and structures, not to forget the materials the structures are made of, is of paramount importance in a technical world of rapidly increasing sophistication, referred to as the Leonardo World by the eminent German philosopher Ju¨rgen MittelstraŸ. More recently, the main themes of EMJS08 have gained considerable mom- tum, owing to signi?cant progress in nanotechnology. It enables resolution of a multitude of materials into their micro- and nanostructures. Covering aspects such as â¢ Physical and chemical characterization â¢ Multiscale modeling concepts, continuum micromechanics, and computational homogenization, as well as â¢ Applications in various engineering ?elds the individual contributions to this book ?ow along different tracks of ?uids, materials, and structures.

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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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Computational Methods in Applied Sciences

New Computational Challenges in Materials, Structures, and Fluids

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Hardcover

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