Mueller-Hoeppe / Loehnert / Reese Recent Developments and Innovative Applications in Computational Mechanics

1. Auflage 2011
ISBN: 978-3-642-17484-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 340 Seiten

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.

Autoren/Hrsg.

Mueller-Hoeppe, Dana

Loehnert, Stefan

Reese, Stefanie

Inhaltsverzeichnis

1;Title Page;1
2;Preface;5
3;Contents;7
4;New Applications of Mortar Methodology to Extended and Embedded Finite Element Formulations;19
4.1;Introduction;19
4.2;Stability Issues Associated with Contact on Enriched Interfaces;20
4.3;Adaptation to the Embedded Interface Case;22
4.4;Conclusion;25
4.5;References;26
5;Thermo-Mechanical Coupling in Beam-to-Beam Contact;27
5.1;Thermo-Mechanical Beam Finite Element;27
5.2;Weak Form for Thermo-Mechanical Contact;29
5.3;Numerical Example;31
5.4;Untitled;33
5.5;References;33
6;On Regularization of the Convergence Path for the Implicit Solution of Contact Problems;35
6.1;Introduction;35
6.2;Structure of the Consistent Tangent Stiffness;37
6.3;Large Penetration Basic Algorithm;38
6.3.1;Strategy Outline;38
6.3.2;Modified Stiffness and Residual during Phase One;39
6.3.3;Limitations of the Strategy;40
6.4;Large Penetration Enhanced Algorithm;41
6.4.1;Solution of the Problem for r < 1;41
6.5;Example;43
6.6;Conclusions;45
6.7;References;46
7;On Different Variational Formulations of the Nitsche Method;47
7.1;Nitsche Formulation;47
7.1.1;Choice of the Lagrange Multiplier Set µ;49
7.1.2;Physical Meaning of the Non-penetration Terms;50
7.2;Types of the Nitsche Approach;51
7.3;FE Implementation of the Nitsche Approaches;52
7.3.1;Gauss Point-Wise Substituted Formulation;52
7.3.2;Bubnov-Galerkin-Wise Partial Substituted Formulation;53
7.4;Numerical Example;54
7.5;References;56
8;Challenges in Computational Nanoscale Contact Mechanics;57
8.1;Introduction;57
8.2;Nanoscale Contact Challenges;57
8.3;Nanoscale versus Macroscale Contact;58
8.4;Adhesion Instability;60
8.5;Multiscale Contact Modeling;62
8.6;Conclusion;63
8.7;References;63
9;On the Four-node Quadrilateral Element;65
9.1;Introduction;65
9.2;Element Formulation;66
9.3;Numerical Example;67
9.4;References;67
10;Stability of Mixed Finite Element Formulations – A New Approach;69
10.1;Introduction;69
10.2;Linear Elasticity - Mixed Variational Formulation;70
10.3;Interpolation;71
10.3.1;Compatible Strain;71
10.3.2;Enhanced Strain;72
10.4;Element Stiffness Matrix;72
10.5;Eigenvalue Analysis;73
10.6;Non-linear Finite Element Technology;73
10.7;References;77
11;A Finite Element Formulation based on the Theory of a Cosserat Point – Modification of the Torsional Modes;79
11.1;Motivation;79
11.2;A Brief Introduction to the Cosserat Point Element;80
11.2.1;Kinematics;80
11.2.2;Equilibrium;81
11.2.3;Constitutive Equations;82
11.3;Torsion;83
11.4;Conclusions;86
11.5;References;86
12;A Brick Element for Finite Deformations with Inhomogeneous Mode Enhancement;87
12.1;Introduction;87
12.2;Theoretical Background;88
12.2.1;Enhanced Strain Assumption;89
12.2.2;Variational Formulation;90
12.3;Discretization;90
12.4;Numerical Examples;91
12.4.1;Irregularly Meshed Beam;91
12.4.2;Nearly Incompressible Block;92
12.5;Conclusions;94
12.6;References;94
13;Automatic Differentiation Based Formulation of Computational Models;96
13.1;Introduction;96
13.2;Automatic Differentiation;97
13.3;Automatic Differentiation in Computational Mechanics;98
13.4;Automatic Differentiation Based Computational Models;99
13.4.1;ADB Form of Hyperelastic Models;99
13.4.2;ADB Form of Elasto-plastic Models;99
13.4.3;Numerical Efficiency of ADB Form;100
13.4.4;ADB Form of Contact Formulations;101
13.4.5;ADB Form in Stability Analysis;102
13.5;Conclusions;102
13.6;References;103
14;Nonlinear Finite Element Shell Formulation Accounting for Large Strain Material Models;104
14.1;Introduction;104
14.2;Variational Formulation of the Shell Equations;105
14.3;Mixed Hybrid Shell Element;107
14.4;Numerical Example: Stretching of a Rubber Sheet;108
14.5;Conclusions;111
14.6;References;111
15;Hybrid and Mixed Variational Principles for the Geometrically Exact Analysis of Shells;113
15.1;Introduction;113
15.2;The Geometrically-Exact First-Order-Shear Shell Model;114
15.3;Some Multi-field Variational Principles;119
15.3.1;Principle of Total Potential Energy;119
15.3.2;Three-Field Principle of Veubeke-Hu-Washizu Type;119
15.3.3;Two-Field Principle of Hellinger-Reissner Type;120
15.3.4;Two-Field Principle of Total Complementary Potential Energy;120
15.3.5;Hybrid Principle of Hellinger-Reissner Type;121
15.4;References;122
16;A Shell Theory with Scale Effects, Higher Order Gradients, and Meshfree Computations;123
16.1;Introduction;123
16.2;Deformation and Strain;124
16.3;Generalized Shell Theory;125
16.4;Numerical Example;127
16.5;References;130
17;An Electro-mechanically Coupled FE-Formulation for Piezoelectric Shells;131
17.1;Introduction;132
17.2;Kinematics;132
17.3;Constitutive Equations;133
17.4;Finite Element Approximation;134
17.5;Numerical Example;136
17.6;References;139
18;Non-intrusive Coupling: An Attempt to Merge Industrial and Research Software Capabilities;140
18.1;Introduction;141
18.2;The General Principles of Non-intrusive Coupling;141
18.2.1;Piecewise Substitution;142
18.2.2;Iterative Coupling;143
18.2.3;Choice of the Interface Boundary Condition for the Local Step;145
18.3;Examples Using Abaqus/Standard;145
18.4;Conclusion;147
18.5;References;147
19;Constitutive Models and Failure Prediction for Al-Alloys in Industrial Applications;149
19.1;Introduction;149
19.2;Factors Influencing Properties;150
19.3;Work-Hardening of Aluminum Alloys;150
19.4;Yield Locus;152
19.5;Fracture Prediction;154
19.6;Conclusions;155
19.7;References;156
20;A Phenomenological Damage Model to Predict Material Failure in Crashworthiness Applications;157
20.1;Introduction;158
20.2;The Process Chain of Sheet Metal Part Manufacturing;158
20.3;Failure Modelling in Forming and Crashworthiness Simulations;158
20.3.1;A Generalized Scalar Damage Model;160
20.3.2;Failure Prediction;161
20.4;Path-Dependent Localization;161
20.4.1;Stress and Strain Measures;162
20.4.2;Nonlinear Accumulation of the Instability Criterion;163
20.5;Post Critical Behaviour;164
20.5.1;Damage-Dependent Yield Stress;165
20.5.2;Energy Dissipation and Fadeout;165
20.6;Conclusions;166
20.7;References;167
21;A Computational Approach for Mixed-Lubrication Effects in Sealing Applications;168
21.1;Introduction;168
21.2;Basic Equations;169
21.2.1;Solid Mechanics;169
21.2.2;Fluid Mechanics;170
21.3;Coupled Fluid Film Computation;172
21.4;Friction Approach;173
21.5;Example;175
21.6;References;175
22;Deformations of a Large Hall: Structural Design and Analysis;176
22.1;Introduction;176
22.2;Steel Construction;177
22.2.1;Bearing Structure;178
22.2.2;Roof;179
22.2.3;Stiffening Components;181
22.2.4;Support of Partial Halls;181
22.3;Construction and Computation;184
22.4;Summary;190
22.5;References;190
23;Recovering Micropolar Continua from Particle Mechanics by Use of Homogenisation Strategies;191
23.1;Introduction;191
23.2;The Particle Model;192
23.3;Homogenisation Technique;195
23.4;Numerical Example;198
23.5;Conclusion;200
23.6;References;201
24;Modelling of Microstructured Materials with Micromorphic Continuum Approaches;202
24.1;Introduction;202
24.2;The Micromorphic Continuum;203
24.2.1;Micromorphic Continuum Framework;203
24.2.2;Hyperelastic Constitutive Framework;204
24.2.3;Numerical Aspects;204
24.3;Application to Material Interfaces with Heterogeneous Micromorphic Mesostructure;206
24.3.1;Scale Transition between Interface and Micromorphic RVE;206
24.3.2;A Computational Homogenization Approach for Micromorphic Meso-heterogeneous Material Layers;207
24.3.3;Numerical Examples;207
24.4;Conclusion;208
24.5;References;209
25;On Computational Homogenisation of Heterogeneous Media with Debonded Inclusions;210
25.1;Introduction and Background;210
25.2;Multi-scale Constitutive Theory: Overview;211
25.2.1;RVE Kinematical Constraints;212
25.2.2;Finite Element Approximation;212
25.2.3;Solution Procedure;213
25.3;Frictional Contact;213
25.3.1;Boundary Value Problem;213
25.3.2;Constitutive Relations;213
25.4;Assessment of Yield Surfaces of Heterogeneous Media with Debonded Inclusions;214
25.4.1;Computational Homogenisation Based Methodology;215
25.4.2;Estimated Yield Surfaces;216
25.5;Conclusion and Remarks;217
25.6;References;217
26;Assessment of Homogenization Errors in Transient Problems;218
26.1;Introduction;218
26.2;Transient Heat Flow – A Model Problem;219
26.2.1;Space-Variational Format;219
26.2.2;Explicit Homogenization Results;220
26.3;RVE-Problem;221
26.3.1;Dirichlet Boundary Conditions;221
26.3.2;Neumann Boundary Conditions;222
26.4;Computational Results;223
26.4.1;Problem Definition – Substructure Characteristics;223
26.5;Conclusions;225
26.6;References;225
27;Multiscale Modeling of Metal Foams Using the XFEM;226
27.1;Introduction;227
27.2;Modified XFEM for Heterogeneous Materials;227
27.3;Incorporation of Finite Plasticity;229
27.4;Comparison of Metal Foams with and without Filler Material;229
27.5;Conclusions;232
27.6;References;232
28;3D Multiscale Projection Method for Micro-/Macrocrack Interaction Simulations;234
28.1;Introduction;234
28.2;The Multiscale Technique in Three Dimensions;235
28.2.1;Stress Projection from the Fine Scale to the Coarse Scale;235
28.2.2;Projection of the Displacement Field from the Coarse Scale to the Fine Scale;238
28.3;Numerical Investigations;239
28.4;Conclusion and Outlook;241
28.5;References;241
29;Goal-Oriented Residual Error Estimates for XFEM Approximations in LEFM;242
29.1;Introduction;242
29.2;XFEM Approximations in LEFM;243
29.2.1;The Model Problem of LEFM;243
29.2.2;XFEM Approximations;244
29.3;A Posteriori Error Estimation in the Energy Norm;245
29.3.1;Error Representation;245
29.3.2;An Implicit Residual Error Estimator;245
29.3.3;Equilibration of Tractions;246
29.4;Goal-Oriented Error Estimation in LEFM;247
29.4.1;Linearization of the J-Integral;247
29.4.2;Duality Techniques;247
29.5;Numerical Example;248
29.6;Conclusions;249
29.7;References;249
30;Multi-field Coupling Strategies for Large Scale Particle-Fluid Problems;250
30.1;Introduction;251
30.2;LB Formulations for Turbulent Incompressible Fluid Flows;252
30.2.1;Standard LB Formulation;252
30.2.2;Turbulence Modelling;253
30.2.3;Hydrodynamic Forces for Fluid-Particle Interactions;254
30.2.4;Fine Particle Modelling - Non-newtonian Fluid Flow;254
30.3;The Thermal Lattice Boltzmann Method;255
30.4;Numerical Illustrations;256
30.4.1;Particle Transportation in Turbulent Fluid Flows;256
30.4.2;Fine Particle Migration in a Block Cave;256
30.4.3;Modelling Heat Transfer in (Particle-)Fluid Flows;258
30.5;Conclusions;259
30.6;References;259
31;Numerical Simulation of Particle-Fluid Systems;260
31.1;Introduction;260
31.2;Mathematical Description;261
31.2.1;Equations for Fluid Motion;261
31.2.2;Equations for Particle Motion;261
31.3;The Discrete Element Model;262
31.3.1;Collision Model for Normal Contact;262
31.3.2;Frictional Tangential Contact Model;263
31.4;Coupling of the Fluid and Particle Phase;264
31.4.1;Evaluation of the Hydrodynamic Forces;264
31.4.2;Coupling Constraints;265
31.5;Numerical Example;266
31.6;Conclusion;266
31.7;References;266
32;A Concurrent Multiscale Approach to Non-cohesive Granular Materials;268
32.1;Introduction;268
32.2;Discrete Element Method;269
32.3;Homogenization and Elasto-plastic Parameters;270
32.4;Coupling;272
32.5;Numerical Examples;273
32.6;Conclusion;275
32.7;References;275
33;On Some Features of a Polygonal Discrete Element Model;276
33.1;Introduction;276
33.2;Discrete Element Method with Polygonal Particles;277
33.2.1;Models for Contact;277
33.2.2;Models for Cohesion;279
33.3;Examples;280
33.3.1;Model Material without Cohesion;280
33.3.2;Model Material with Cohesion;281
33.3.3;Concrete with Microstructure;282
33.4;Conclusions;283
33.5;References;283
34;Isogeometric Failure Analysis;285
34.1;Introduction;285
34.2;Isogeometric Finite Elements;286
34.3;Higher-Order Gradient Damage Formulation;287
34.3.1;Constitutive Behavior;288
34.3.2;L-Shaped Specimen;288
34.4;Cohesive Zone Formulation;289
34.4.1;Constitutive Behavior;290
34.4.2;Single-Edge Notched Beam;290
34.5;Conclusions;291
34.6;References;292
35;A Method for Enforcement of Dirichlet Boundary Conditions in Isogeometric Analysis;293
35.1;Introduction;294
35.2;Dirichlet Boundary Conditions;295
35.3;Examples from Linear Elasticity;297
35.3.1;Infinite Half-Space;298
35.3.2;Infinite Plate with Circular Hole under Tension;299
35.3.3;Infinite Plate with Elliptical Hole under Tension;301
35.4;Closure;302
35.5;References;303
36;Application of Isogeometric Analysis to Computational Contact Mechanics;304
36.1;Introduction;304
36.2;Contact Boundary Value Problem;305
36.3;Isogeometric Treatment with NURBS;305
36.4;Knot-to-Surface Contact Algorithm;307
36.4.1;Contact of a Grosch Wheel;308
36.4.2;Contact of Two Deformable Bodies;309
36.5;Conclusion;309
36.6;References;311
37;Stochastic Galerkin Method for the Elastoplasticity Problem with Uncertain Parameters;312
37.1;Introduction;312
37.2;Mathematical Formulation;313
37.2.1;Problem Setting;313
37.2.2;Variational Formulation;314
37.3;Numerical Analysis of the Problem;314
37.3.1;Discretisation of Input;315
37.3.2;Stochastic Galerkin Method;315
37.4;Numerical Results;316
37.5;Conclusion;319
37.6;References;319
38;A Time-Discontinuous Galerkin Approach for the Numerical Solution of the Fokker-Planck Equation;320
38.1;Introduction;321
38.2;FPE Expression of Stochastic Dynamic Problems;322
38.3;Numerical Solution of the Fokker-Planck Equation with TDG Methods;323
38.4;Numerical Example;326
38.5;Conclusions;326
38.6;References;327
39;Interface Modelling in Computational Limit Analysis;329
39.1;Discrete Formulation of Bound Theorems;329
39.2;Velocity Discontinuities as a Patch of Thin Elements;331
39.3;Stress Discontinuities as a Patch of Thin Elements;332
39.4;Interfaces between Material Domains;333
39.5;Interfaces at Segments Subject to Loading or Boundary Conditions;334
39.6;Moment-Free Interfaces for Modelling of Joints;336
39.7;Interfaces for Overlapping Connections;337
39.8;Conclusions;338
39.9;References;338
40;On the Coexistence of Intermeshed Hostile Populations;339
40.1;Introduction;340
40.1.1;Objectives;341
40.2;Direct Interaction Models: Rules of Engagement;341
40.3;An Example;342
40.4;Identification of System Parameters: Genetic Algorithms;343
40.5;An Example of Parity Identification;346
40.6;Concluding Remarks;347
40.7;References;348