Table Of ContentContents Contents
Material Modeling in Finite
Element Analysis
Material Modeling in Finite
Element Analysis
Z. Yang
CRC Press
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Contents
Preface .....................................................................................................................xv
Author ..................................................................................................................xvii
1. Introduction .....................................................................................................1
Part I Metal
2. Structure and Material Properties of Metal..............................................7
2.1 Structure of Metal .................................................................................7
2.2 Elasticity and Plasticity of Metal ........................................................7
Reference .........................................................................................................10
3. Some Plastic Material Models of Metals and Definition
of Their Parameters ......................................................................................11
3.1 Introduction of Plasticity ...................................................................11
3.2 Isotropic Hardening Models and Definition of Material
Parameters for 304 Stainless Steel.....................................................12
3.2.1 Multilinear Isotropic Hardening (MISO) ...........................12
3.2.2 Voce Law Nonlinear Isotropic Hardening .........................16
3.3 Nonlinear Kinematic Hardening ......................................................19
3.4 Summary ..............................................................................................21
References .......................................................................................................21
4. Simulation of Metal Forming ....................................................................23
4.1 Introduction of Metal Forming .........................................................23
4.2 Simulation of Forming of a Sheet .....................................................24
4.2.1 Finite Element Model ............................................................24
4.2.2 Material Properties ................................................................26
4.2.3 Contact Definition ..................................................................26
4.2.4 Loadings and Boundary Conditions ..................................26
4.2.5 Solution Setting ......................................................................26
4.2.6 Results .....................................................................................27
4.2.7 Summary .................................................................................27
References .......................................................................................................30
5. Simulation of Ratcheting ............................................................................31
5.1 Introduction of Ratcheting ................................................................31
5.2 Simulation of Ratcheting in a Notched Bar .....................................31
5.2.1 Finite Element Model ............................................................31
v
vi Contents
5.2.2 Material Properties ................................................................33
5.2.3 Loadings and Boundary Conditions ..................................33
5.2.4 Results .....................................................................................33
5.2.5 Summary .................................................................................36
References .......................................................................................................36
6. Influence of Temperature on Material Properties .................................37
6.1 Temperature Dependency of Material Properties ..........................37
6.2 Simulation of Combustion Chamber under Different
Temperatures .......................................................................................38
6.2.1 Finite Element Model ............................................................38
6.2.2 Material Properties ................................................................38
6.2.3 Loadings and Boundary Conditions ..................................40
6.2.4 Results .....................................................................................40
6.2.5 Discussion ...............................................................................40
6.2.6 Summary .................................................................................45
References .......................................................................................................45
7. Simulation of Creep .....................................................................................47
7.1 Introduction of Creep .........................................................................47
7.1.1 Creep ........................................................................................47
7.1.2 Creep Constitutive Law ........................................................47
7.1.3 Subroutine UserCreep ...........................................................49
7.2 Simulation of Creep of a Bolt under Pretension .............................53
7.2.1 Finite Element Model ............................................................53
7.2.2 Material Properties ................................................................53
7.2.3 Loadings and Boundary Conditions ..................................54
7.2.4 Solution Setting ......................................................................55
7.2.5 Results .....................................................................................55
7.2.6 Discussion ...............................................................................55
7.2.7 Summary .................................................................................57
References .......................................................................................................57
Part II Polymers
8. Structure and Features of Polymer ...........................................................61
8.1 Structure of Polymer ...........................................................................61
8.2 Features of Polymer ............................................................................61
References .......................................................................................................62
9. Hyperelasticity ..............................................................................................63
9.1 Some Widely Used Hyperelastic Models ........................................63
9.1.1 Neo-Hookean Model .............................................................63
Contents vii
9.1.2 Mooney–Rivlin Model ..........................................................63
9.1.3 Yeoh Model .............................................................................64
9.1.4 Polynomial Model ..................................................................64
9.1.5 Gent Model .............................................................................64
9.1.6 Ogden Model ..........................................................................64
9.1.7 Arruda–Boyce Model ............................................................65
9.2 Stability Discussion ............................................................................66
9.3 Curve-fitting of Material Parameters from
Experimental Data ..............................................................................67
9.4 Simulation of a Rubber Rod under Compression...........................69
9.4.1 Finite Element Model ............................................................69
9.4.2 Material Parameters ..............................................................69
9.4.3 Loadings and Boundary Conditions ..................................70
9.4.4 Results .....................................................................................70
9.4.5 Discussion ...............................................................................70
9.4.6 Summary .................................................................................71
9.5 Simulation of Breast Implant in ANSYS ..........................................72
9.5.1 Finite Element Model ............................................................73
9.5.2 Material Models .....................................................................74
9.5.3 Loading and Solution Setting .............................................75
9.5.4 Results .....................................................................................75
9.5.5 Discussion ...............................................................................75
9.5.6 Summary .................................................................................77
References .......................................................................................................77
10. Viscoelasticity of Polymers ........................................................................79
10.1 Viscoelasticity of Polymers ................................................................79
10.2 Linear Viscoelastic Models ................................................................79
10.2.1 Maxwell Model ......................................................................80
10.2.2 Kelvin–Voigt Model ...............................................................80
10.2.3 Burgers Model ........................................................................81
10.2.4 Generalized Maxwell Model ................................................81
10.3 Viscoplasticity Models .......................................................................83
10.4 Simulation of Viscoelasticity of Liver Soft Tissues ........................84
10.4.1 Finite Element Model ............................................................84
10.4.2 Material Properties ................................................................85
10.4.3 Contact Definition ..................................................................85
10.4.4 Loadings and Boundary Conditions ..................................85
10.4.5 Results .....................................................................................86
10.4.6 Discussion ...............................................................................87
10.4.7 Summary .................................................................................87
References .......................................................................................................87
11. Mullins Effect ................................................................................................89
11.1 Introduction of Mullins Effect ..........................................................89
viii Contents
11.2 Ogden–Roxburgh Mullins Effect Model .........................................90
11.3 Simulation of a Rubber Tire with the Mullins Effect .....................90
11.3.1 Finite Element Model ............................................................91
11.3.2 Material Properties ................................................................91
11.3.3 Loadings and Boundary Conditions ..................................91
11.3.4 Results .....................................................................................92
11.3.5 Discussion ...............................................................................92
11.3.6 Summary .................................................................................98
References .......................................................................................................99
12. Usermat for Hyperelastic Materials .......................................................101
12.1 Introduction of Subroutine UserHyper .........................................101
12.2 Simulation of Gent Hyperelasticity ...............................................101
12.2.1 Subroutine UserHyper for Gent Material .........................102
12.2.2 Validation ..............................................................................103
12.2.3 Summary ...............................................................................104
References .....................................................................................................104
Part III Soil
13. Soil Introduction .........................................................................................107
13.1 Soil Structure .....................................................................................107
13.2 Soil Parameters ..................................................................................107
References .....................................................................................................108
14. Cam Clay Model .........................................................................................109
14.1 Introduction of Modified Cam Clay Model ..................................109
14.2 Cam Clay Model in ANSYS .............................................................111
14.2.1 Elastic Component ...............................................................111
14.2.2 Plastic Component ...............................................................112
14.3 Simulation of a Tower on the Ground by Cam Clay Model .......113
14.3.1 Finite Element Model ..........................................................113
14.3.2 Material Properties ..............................................................113
14.3.3 Contact Definition ................................................................114
14.3.4 Loadings and Boundary Conditions ................................114
14.3.5 Results ...................................................................................114
14.3.6 Discussion .............................................................................118
14.3.7 Summary ...............................................................................118
References .....................................................................................................118
15. Drucker–Prager Model ..............................................................................119
15.1 Introduction of Drucker–Prager Model .........................................119
15.2 Study of a Soil–Arch Interaction .....................................................120
Contents ix
15.2.1 Finite Element Model ..........................................................120
15.2.2 Material Properties ..............................................................121
15.2.3 Boundary Conditions and Loadings ................................122
15.2.4 Results ...................................................................................122
15.2.5 Discussion .............................................................................124
15.2.6 Summary ...............................................................................124
References .....................................................................................................125
16. Mohr–Coulomb Model ..............................................................................127
16.1 Introduction of Mohr–Coulomb Model .........................................127
16.2 Mohr–Coulomb Model in ANSYS ..................................................130
16.3 Study of Slope Stability ....................................................................131
16.3.1 Finite Element Model ..........................................................131
16.3.2 Material Properties ..............................................................132
16.3.3 Loadings and Boundary Conditions ................................133
16.3.4 Results ..................................................................................133
16.3.5 Discussion .............................................................................135
16.3.6 Summary ...............................................................................136
References .....................................................................................................136
17. Jointed Rock Model ....................................................................................139
17.1 Jointed Rock Model ...........................................................................139
17.2 Definition of the Jointed Rock Model in ANSYS ..........................140
17.2.1 Defining the Base Material .................................................140
17.2.2 Defining the Joints ...............................................................141
17.3 Simulation of Tunnel Excavation ....................................................141
17.3.1 Finite Element Model ..........................................................141
17.3.2 Material Properties ..............................................................141
17.3.3 Loadings and Boundary Conditions ................................142
17.3.4 Solution ..................................................................................142
17.3.5 Results ...................................................................................142
17.3.6 Discussion .............................................................................145
17.3.7 Summary ...............................................................................146
References .....................................................................................................146
18. Consolidation of Soils ...............................................................................149
18.1 Consolidation of Soils .......................................................................149
18.2 Modeling Porous Media in ANSYS ................................................149
18.3 Simulation of Consolidation of Three-Well Zone.........................150
18.3.1 Finite Element Model ..........................................................150
18.3.2 Material Properties ..............................................................150
18.3.3 Boundary Conditions and Loadings ................................152
18.3.4 Solutions ................................................................................152
18.3.5 Results ...................................................................................152
