Numerical Methods for Strong Nonlinearities in Mechanics -

. .

Résumé :

Preface
Jacques Besson, Fr?d?ric Lebon And ?ric Lorentz

Part 1 Contact and Friction 1

Chapter 1 Lagrangian and Nitsche Methods for Frictional Contact 3
Franz Chouly, Patrick Hild And Yves Renard

1.1 Introduction 3

1.2 Small-strains frictional contact between two elastic bodies 4

1.2.1 Contact between two elastic bodies 4

1.2.2 The classical weak inequality form 7

1.2.3 The principle of duality and the weak form with multipliers 8

1.2.4 Proximal augmented Lagrangian: principle and use 9

1.3 Finite element approximation in small deformations 12

1.3.1 State of the art, methods with multipliers 13

1.3.2 Absence of inf-sup condition and stabilized methods 15

1.3.3 Nitsche's method seen as a limit stabilized method model 16

1.3.4 Relationship between Nitsche and proximal augmented Lagrangian 19

1.3.5 The connection between Nitsche and penalty 20

1.4 Large strain finite element approximation 21

1.4.1 About contact pairing and gap function 23

1.4.2 Formulation of contact and friction conditions 26

1.4.3 Augmented Lagrangian and penalization 28

1.4.4 Nitsche's method 33

1.4.5 About the value of the parameter ? 36

1.4.6 Numerical tests 36

1.5 Acknowledgments 41

1.6 References 41

Chapter 2 High-performance Computing in Multicontact Mechanics: From Elastostatics to Granular Dynamics 47
Pierre Alart

2.1 Introduction 47

2.2 Multicontact in elastostatics 49

2.2.1 Development framework 49

2.2.2 Parallel solver preconditioning 51

2.2.3 Domain decomposition: Newton-Schur solver 53

2.3 Diffuse non-smoothness in discrete structures: tensegrity 57

2.3.1 Motivation 57

2.3.2 Domain decomposition: micro-macro LATIN solver 58

2.4 Granular dynamics 61

2.4.1 Velocity-impulse formulation 61

2.4.2 Parallelized and parallelizable solvers 63

2.4.3 Conjugate projected gradient solver 65

2.4.4 Domain decomposition: FETI-NLGS solver 66

2.5 Conclusion 73

2.6 References 75

Chapter 3 Numerical Methods in Micromechanical Contact 79
Vladislav A. Yastrebov

3.1 Introduction 79

3.1.1 Plan 80

3.2 Contact micromechanical problem 80

3.2.1 Surface geometry: mathematical description 80

3.2.2 Surface geometry: examples and discussions 83

3.2.3 Roughness models 85

3.2.4 Contact formalization 86

3.2.5 Laws of friction 88

3.3 Finite element method 90

3.3.1 Convergence, parameters and loading step 91

3.3.2 Convergence of friction problems 92

3.3.3 Quadratic convergence 94

3.3.4 Mesh and computation time 95

3.3.5 Contact constraint 95

3.3.6 Surface regularity 97

3.4 Application I: study of an isolated asperity 98

3.4.1 Elastic asperity 98

3.4.2 Elastoplastic asperity 102

3.5 Application II: rough surface contact 109

3.6 Conclusion 113

3.7 References 114

Part 2 Damage and Cracking 135

Chapter 4 Numerical Methods for Ductile Fracture 137
Jacques Besson

4.1 Introduction 137

4.2 Physical mechanisms of ductile fracture 138

4.3 Some ductile fracture models 139

4.3.1 Rice and Tracey model and fracture criteria 139

4.3.2 The Gurson-Tvergaard-Needleman model 140

4.3.3 Other models 143

4.4 Performing ductile fracture simulations with a finite elements code 143

4.4.1 Calculation parameters 143

4.4.2 Pressure control 145

4.4.3 Application of the Rice and Tracey criterion 146

4.4.4 GT...

Biographie:

Jacques Besson is Research Director at the CNRS, France, where he conducts research into damage and fracture modeling of metallic materials.

Fr?d?ric Lebon is Professor of Solid Mechanics at Aix-Marseille University and the Mechanics and Acoustics Laboratory (LMA), France.

Eric Lorentz is a senior expert at EDF R&D, France, where he conducts studies on damage modeling, applied to the performance of power generation structures.