Modelling, Simulation and Software Concepts for Scientific-Technological Problems (eBook)

Table of Contents 6
Preface 8
Martensitic Phase Transformations of Mono and Polycrystalline Shape Memory Alloys – A Theoretically and Numerically Unified Concept 10
Introduction 10
PTs of Monocrystalline SMAs 13
Twinning of Monocrystalline SMAs 13
PT Modeling at Linear and Nonlinear Kinematics 14
Time Integration of Constitutive Equations 17
PT of Polycrystalline SMAs 21
Presumptions for Modeling Polycrystals 21
Modeling of Polycrystals 23
Error Controlled Adaptive Mesh Refinement in Space via Abaqus 25
Averaging Type Error Estimator and Effectivity Index 25
Adaptive Remeshing with Abaqus 26
Numerical Examples 27
Superelastic Polycrystalline NiTi 28
Superelastic Mono and Polycrystalline CuAlNi 30
Dovetail Shaped Specimen 32
Conclusions 34
References 35
Thermo-Hydro-Mechanical Modeling of Coupled Processes in Clay Materials 38
Introduction 39
Theoretical Background 40
Partially Saturated Flow in Poro-Thermo-Elastic Media 41
Anisotropic Material Modeling 43
Non-linear Shrinkage Model 44
Continuum Damage Model 46
Non-linear Compressibility Model 46
Validation 52
Liakopoulos Drainage Test 52
Step-wise Compression Test 53
Application 56
Thermo-Hydro-Mechanical Simulation of a Generic Repository 56
Long-term Saturation Process (TDR-Test) 65
Conclusions and Outlook 78
References 80
Multibody Contact Algorithms for Fracturing Solids 84
Computational Fracture Mechanics 84
Properties of Concrete 85
Continuum Mechanical Fracture Effects 86
Numerical Fracture Approaches 87
Strong Discontinuity Analysis 89
Kinematics 91
Finite Element Approximation 92
Discretized Set of Enhanced Equations 94
Material Model 98
Isotropic Damage Model 98
Identification of the Fracture Plane Normal 99
Numerical Example 101
Continuous-Discontinuous Model 103
Overview of Fragmentation Techniques 104
Adaptive Mesh Refinement 106
Crack Path Continuity 108
Continuity Checks 109
Numerical Example 110
Concept of Weak Nodes 110
Discrete Fracture 111
3D Crack Propagation 112
A Combined Strategy 114
Extension to Explicit Time Integration Schemes 116
Incorporation of SDA Kinematics 117
Numerical Example 118
References 121
New Strategies in Finite Element Analysis of Material Processing 126
Finite Element Analysis of Blanking of Thin Metal Sheets 126
Finite Element Analysis of Forming of Polymer Coated Sheet Metal 131
Finite Element Analysis of Forming of Aluminium in a Semi-Solid State 135
References 139
Computational Techniques for Multiscale Analysis of Materials and Interfaces 141
Introduction 142
Multiscale Methods in Computational Mechanics – A Brief Review 143
A Multiscale Approach for Contact Interfaces 144
A Multiscale Model for AFM Operation 145
A Consistent MD-FE Coupling Approach 151
Biomechanics of Bones 159
Continuum Approach 160
Multiscale Modeling of Cortical Bone Tissue 161
An Adaptive Computational Approach for Interlaminar Micro-Cracks 164
Mechanical Model for Bone Cells 166
Conclusions 169
References 170
Numerical Modelling and Simulation of Atomic Force Microscopes 176
Atomic Force Microscopes 176
Physical Foundations of AFMs 177
Mechanical Foundations 179
Electrostatic Force Microscopes (EFM) 179
Magnetic Force Microscopes (MFM) 182
Conclusion 184
References 186
Finite Element and Boundary Element Approaches to Transmission and Contact Problems in Elasticity 188
Adaptive FE/BE Coupling for Elasticity Problems 189
FE Analysis of a Process with Delamination 197
Contact Problems with Friction 202
Fluid-Structure Interaction 204
References 206
Efficient Solvers for Mixed Finite Element Discretizations of Nonlinear Problems in Solid Mechanics 207
Efficient Solvers and A-posteriori Error Estimators for Mixed Problems in Elastoplasticity 207
Least Squares Mixed Finite Element Methods for Elastoplastic Problems 209
Least Squares Mixed Finite Element Solution of Contact Problems 211
References 214
Computational Differential Geometry Contributions of the Welfenlab to GRK 615 216
Introduction 216
Medial Sets in Euclidean and Riemannian Spaces 220
Medial Computations Since 2000 during the Years of GRK 615 226
Remarks 228
Application of 3D-Medial Axis on Metal Forming Simulation 229
Spectrum of Eigenvalues of the Laplace–Beltrami Operator 231
Laplace Spectra as Shape DNA for Surfaces and Solids 233
Laplace Spectra as Image DNA 235
Conclusions and Prospects 237
References 238
Analysis of a Mathematical Model Describing Necrotic Tumor Growth 241
The Mathematical Model 241
Radially Symmetric Stationary Solutions 245
The Moving Boundary Problem 248
References 253
Author Index 255