Recent Developments and Innovative Applications in Computational Mechanics (eBook)

Dana Mueller-Hoeppe, Stefan Loehnert, Stefanie Reese (Herausgeber)

eBook Download: PDF

2011 | 2011
XX, 340 Seiten
Springer Berlin (Verlag)
978-3-642-17484-1 (ISBN)

Infos

This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his  60th birthday. It contains contributions from friends and collaborators as well as current and
former PhD students from almost all continents. As a very diverse group of people, the  authors cover a wide range of topics from fundamental research to industrial applications: contact mechanics, finite element technology, micromechanics, multiscale approaches,
particle methods, isogeometric analysis, stochastic methods and further research interests. In  summary, the volume presents an overview of the international state of the art in computational mechanics, both in academia and industry.

Inhalt

Title Page 1
Preface 5
Contents 7
New Applications of Mortar Methodology to Extended and Embedded Finite Element Formulations 19
Introduction 19
Stability Issues Associated with Contact on Enriched Interfaces 20
Adaptation to the Embedded Interface Case 22
Conclusion 25
References 26
Thermo-Mechanical Coupling in Beam-to-Beam Contact 27
Thermo-Mechanical Beam Finite Element 27
Weak Form for Thermo-Mechanical Contact 29
Numerical Example 31
Untitled 33
References 33
On Regularization of the Convergence Path for the Implicit Solution of Contact Problems 35
Introduction 35
Structure of the Consistent Tangent Stiffness 37
Large Penetration Basic Algorithm 38
Strategy Outline 38
Modified Stiffness and Residual during Phase One 39
Limitations of the Strategy 40
Large Penetration Enhanced Algorithm 41
Solution of the Problem for r < 1
Example 43
Conclusions 45
References 46
On Different Variational Formulations of the Nitsche Method 47
Nitsche Formulation 47
Choice of the Lagrange Multiplier Set µ 49
Physical Meaning of the Non-penetration Terms 50
Types of the Nitsche Approach 51
FE Implementation of the Nitsche Approaches 52
Gauss Point-Wise Substituted Formulation 52
Bubnov-Galerkin-Wise Partial Substituted Formulation 53
Numerical Example 54
References 56
Challenges in Computational Nanoscale Contact Mechanics 57
Introduction 57
Nanoscale Contact Challenges 57
Nanoscale versus Macroscale Contact 58
Adhesion Instability 60
Multiscale Contact Modeling 62
Conclusion 63
References 63
On the Four-node Quadrilateral Element 65
Introduction 65
Element Formulation 66
Numerical Example 67
References 67
Stability of Mixed Finite Element Formulations – A New Approach 69
Introduction 69
Linear Elasticity - Mixed Variational Formulation 70
Interpolation 71
Compatible Strain 71
Enhanced Strain 72
Element Stiffness Matrix 72
Eigenvalue Analysis 73
Non-linear Finite Element Technology 73
References 77
A Finite Element Formulation based on the Theory of a Cosserat Point – Modification of the Torsional Modes 79
Motivation 79
A Brief Introduction to the Cosserat Point Element 80
Kinematics 80
Equilibrium 81
Constitutive Equations 82
Torsion 83
Conclusions 86
References 86
A Brick Element for Finite Deformations with Inhomogeneous Mode Enhancement 87
Introduction 87
Theoretical Background 88
Enhanced Strain Assumption 89
Variational Formulation 90
Discretization 90
Numerical Examples 91
Irregularly Meshed Beam 91
Nearly Incompressible Block 92
Conclusions 94
References 94
Automatic Differentiation Based Formulation of Computational Models 96
Introduction 96
Automatic Differentiation 97
Automatic Differentiation in Computational Mechanics 98
Automatic Differentiation Based Computational Models 99
ADB Form of Hyperelastic Models 99
ADB Form of Elasto-plastic Models 99
Numerical Efficiency of ADB Form 100
ADB Form of Contact Formulations 101
ADB Form in Stability Analysis 102
Conclusions 102
References 103
Nonlinear Finite Element Shell Formulation Accounting for Large Strain Material Models 104
Introduction 104
Variational Formulation of the Shell Equations 105
Mixed Hybrid Shell Element 107
Numerical Example: Stretching of a Rubber Sheet 108
Conclusions 111
References 111
Hybrid and Mixed Variational Principles for the Geometrically Exact Analysis of Shells 113
Introduction 113
The Geometrically-Exact First-Order-Shear Shell Model 114
Some Multi-field Variational Principles 119
Principle of Total Potential Energy 119
Three-Field Principle of Veubeke-Hu-Washizu Type 119
Two-Field Principle of Hellinger-Reissner Type 120
Two-Field Principle of Total Complementary Potential Energy 120
Hybrid Principle of Hellinger-Reissner Type 121
References 122
A Shell Theory with Scale Effects, Higher Order Gradients, and Meshfree Computations 123
Introduction 123
Deformation and Strain 124
Generalized Shell Theory 125
Numerical Example 127
References 130
An Electro-mechanically Coupled FE-Formulation for Piezoelectric Shells 131
Introduction 132
Kinematics 132
Constitutive Equations 133
Finite Element Approximation 134
Numerical Example 136
References 139
Non-intrusive Coupling: An Attempt to Merge Industrial and Research Software Capabilities 140
Introduction 141
The General Principles of Non-intrusive Coupling 141
Piecewise Substitution 142
Iterative Coupling 143
Choice of the Interface Boundary Condition for the Local Step 145
Examples Using Abaqus/Standard 145
Conclusion 147
References 147
Constitutive Models and Failure Prediction for Al-Alloys in Industrial Applications 149
Introduction 149
Factors Influencing Properties 150
Work-Hardening of Aluminum Alloys 150
Yield Locus 152
Fracture Prediction 154
Conclusions 155
References 156
A Phenomenological Damage Model to Predict Material Failure in Crashworthiness Applications 157
Introduction 158
The Process Chain of Sheet Metal Part Manufacturing 158
Failure Modelling in Forming and Crashworthiness Simulations 158
A Generalized Scalar Damage Model 160
Failure Prediction 161
Path-Dependent Localization 161
Stress and Strain Measures 162
Nonlinear Accumulation of the Instability Criterion 163
Post Critical Behaviour 164
Damage-Dependent Yield Stress 165
Energy Dissipation and Fadeout 165
Conclusions 166
References 167
A Computational Approach for Mixed-Lubrication Effects in Sealing Applications 168
Introduction 168
Basic Equations 169
Solid Mechanics 169
Fluid Mechanics 170
Coupled Fluid Film Computation 172
Friction Approach 173
Example 175
References 175
Deformations of a Large Hall: Structural Design and Analysis 176
Introduction 176
Steel Construction 177
Bearing Structure 178
Roof 179
Stiffening Components 181
Support of Partial Halls 181
Construction and Computation 184
Summary 190
References 190
Recovering Micropolar Continua from Particle Mechanics by Use of Homogenisation Strategies 191
Introduction 191
The Particle Model 192
Homogenisation Technique 195
Numerical Example 198
Conclusion 200
References 201
Modelling of Microstructured Materials with Micromorphic Continuum Approaches 202
Introduction 202
The Micromorphic Continuum 203
Micromorphic Continuum Framework 203
Hyperelastic Constitutive Framework 204
Numerical Aspects 204
Application to Material Interfaces with Heterogeneous Micromorphic Mesostructure 206
Scale Transition between Interface and Micromorphic RVE 206
A Computational Homogenization Approach for Micromorphic Meso-heterogeneous Material Layers 207
Numerical Examples 207
Conclusion 208
References 209
On Computational Homogenisation of Heterogeneous Media with Debonded Inclusions 210
Introduction and Background 210
Multi-scale Constitutive Theory: Overview 211
RVE Kinematical Constraints 212
Finite Element Approximation 212
Solution Procedure 213
Frictional Contact 213
Boundary Value Problem 213
Constitutive Relations 213
Assessment of Yield Surfaces of Heterogeneous Media with Debonded Inclusions 214
Computational Homogenisation Based Methodology 215
Estimated Yield Surfaces 216
Conclusion and Remarks 217
References 217
Assessment of Homogenization Errors in Transient Problems 218
Introduction 218
Transient Heat Flow – A Model Problem 219
Space-Variational Format 219
Explicit Homogenization Results 220
RVE-Problem 221
Dirichlet Boundary Conditions 221
Neumann Boundary Conditions 222
Computational Results 223
Problem Definition – Substructure Characteristics 223
Conclusions 225
References 225
Multiscale Modeling of Metal Foams Using the XFEM 226
Introduction 227
Modified XFEM for Heterogeneous Materials 227
Incorporation of Finite Plasticity 229
Comparison of Metal Foams with and without Filler Material 229
Conclusions 232
References 232
3D Multiscale Projection Method for Micro-/Macrocrack Interaction Simulations 234
Introduction 234
The Multiscale Technique in Three Dimensions 235
Stress Projection from the Fine Scale to the Coarse Scale 235
Projection of the Displacement Field from the Coarse Scale to the Fine Scale 238
Numerical Investigations 239
Conclusion and Outlook 241
References 241
Goal-Oriented Residual Error Estimates for XFEM Approximations in LEFM 242
Introduction 242
XFEM Approximations in LEFM 243
The Model Problem of LEFM 243
XFEM Approximations 244
A Posteriori Error Estimation in the Energy Norm 245
Error Representation 245
An Implicit Residual Error Estimator 245
Equilibration of Tractions 246
Goal-Oriented Error Estimation in LEFM 247
Linearization of the J-Integral 247
Duality Techniques 247
Numerical Example 248
Conclusions 249
References 249
Multi-field Coupling Strategies for Large Scale Particle-Fluid Problems 250
Introduction 251
LB Formulations for Turbulent Incompressible Fluid Flows 252
Standard LB Formulation 252
Turbulence Modelling 253
Hydrodynamic Forces for Fluid-Particle Interactions 254
Fine Particle Modelling - Non-newtonian Fluid Flow 254
The Thermal Lattice Boltzmann Method 255
Numerical Illustrations 256
Particle Transportation in Turbulent Fluid Flows 256
Fine Particle Migration in a Block Cave 256
Modelling Heat Transfer in (Particle-)Fluid Flows 258
Conclusions 259
References 259
Numerical Simulation of Particle-Fluid Systems 260
Introduction 260
Mathematical Description 261
Equations for Fluid Motion 261
Equations for Particle Motion 261
The Discrete Element Model 262
Collision Model for Normal Contact 262
Frictional Tangential Contact Model 263
Coupling of the Fluid and Particle Phase 264
Evaluation of the Hydrodynamic Forces 264
Coupling Constraints 265
Numerical Example 266
Conclusion 266
References 266
A Concurrent Multiscale Approach to Non-cohesive Granular Materials 268
Introduction 268
Discrete Element Method 269
Homogenization and Elasto-plastic Parameters 270
Coupling 272
Numerical Examples 273
Conclusion 275
References 275
On Some Features of a Polygonal Discrete Element Model 276
Introduction 276
Discrete Element Method with Polygonal Particles 277
Models for Contact 277
Models for Cohesion 279
Examples 280
Model Material without Cohesion 280
Model Material with Cohesion 281
Concrete with Microstructure 282
Conclusions 283
References 283
Isogeometric Failure Analysis 285
Introduction 285
Isogeometric Finite Elements 286
Higher-Order Gradient Damage Formulation 287
Constitutive Behavior 288
L-Shaped Specimen 288
Cohesive Zone Formulation 289
Constitutive Behavior 290
Single-Edge Notched Beam 290
Conclusions 291
References 292
A Method for Enforcement of Dirichlet Boundary Conditions in Isogeometric Analysis 293
Introduction 294
Dirichlet Boundary Conditions 295
Examples from Linear Elasticity 297
Infinite Half-Space 298
Infinite Plate with Circular Hole under Tension 299
Infinite Plate with Elliptical Hole under Tension 301
Closure 302
References 303
Application of Isogeometric Analysis to Computational Contact Mechanics 304
Introduction 304
Contact Boundary Value Problem 305
Isogeometric Treatment with NURBS 305
Knot-to-Surface Contact Algorithm 307
Contact of a Grosch Wheel 308
Contact of Two Deformable Bodies 309
Conclusion 309
References 311
Stochastic Galerkin Method for the Elastoplasticity Problem with Uncertain Parameters 312
Introduction 312
Mathematical Formulation 313
Problem Setting 313
Variational Formulation 314
Numerical Analysis of the Problem 314
Discretisation of Input 315
Stochastic Galerkin Method 315
Numerical Results 316
Conclusion 319
References 319
A Time-Discontinuous Galerkin Approach for the Numerical Solution of the Fokker-Planck Equation 320
Introduction 321
FPE Expression of Stochastic Dynamic Problems 322
Numerical Solution of the Fokker-Planck Equation with TDG Methods 323
Numerical Example 326
Conclusions 326
References 327
Interface Modelling in Computational Limit Analysis 329
Discrete Formulation of Bound Theorems 329
Velocity Discontinuities as a Patch of Thin Elements 331
Stress Discontinuities as a Patch of Thin Elements 332
Interfaces between Material Domains 333
Interfaces at Segments Subject to Loading or Boundary Conditions 334
Moment-Free Interfaces for Modelling of Joints 336
Interfaces for Overlapping Connections 337
Conclusions 338
References 338
On the Coexistence of Intermeshed Hostile Populations 339
Introduction 340
Objectives 341
Direct Interaction Models: Rules of Engagement 341
An Example 342
Identification of System Parameters: Genetic Algorithms 343
An Example of Parity Identification 346
Concluding Remarks 347
References 348

Produkt-Details

• Erscheint lt. Verlag: 11.1.2011
• Zusatzinfo: XX, 340 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 3-642-17484-1 / 3642174841
• ISBN-13: 978-3-642-17484-1 / 9783642174841