An expert and up-to-date discussion of the properties and design of soft active material modeling
In Multi-Field Modeling of Soft Active Materials: Properties and Design, distinguished researcher Rui Xiao delivers an up-to-date exploration of the multi-field modeling of soft active materials, including shape-memory polymers, liquid crystal elastomers, dielectric elastomers, magnetic elastomers, and hydrogels. The book discusses the modeling, simulation, and theoretical progress on each covered soft active material.
The author provides guidance on future development of the theoretical approaches for active materials, as well as efficient tools to design functional soft machines composed of active materials. He offers a deep understanding of the underlying mechanisms of stimulus-response behaviors.
Readers will also find:
- A thorough introduction to the basics of continuum mechanics
- Comprehensive explorations of hyperelastic and viscoeleastic models
- Practical discussions of an electro-mechanical coupled model for dielectric elastomers
- A complete treatment of a chemo-mechanical model for hydrogels
Perfect for materials scientists, polymer chemists, analytical chemists, and theoretical chemists, Multi-Field Modeling of Soft Active Materials will also benefit computer analysts with an interest in functional soft machines.
Table of Contents:
Foreword vii
Preface ix
Acknowledgments xi
1 Basics of Continuum Mechanics 1
1.1 Vectors and Tensors 1
1.1.1 Vector 1
1.1.2 Index Notation 2
1.1.3 Tensor 3
1.1.4 Gradient, Divergence, and Curl 4
1.2 Kinematics 5
1.2.1 Deformation Gradient 5
1.2.2 Strain Tensor 7
1.3 Stress 8
1.4 Balance Principles 9
1.4.1 Material Derivative and Spatial Derivative 10
1.4.2 Reynolds Transport Theorem 10
1.4.3 Conservation of Mass 11
1.4.4 Balance of Momentum 11
1.4.5 Balance of Angular Momentum 12
1.4.6 Balance of Mechanical Energy 13
1.4.7 Balance of Energy 14
1.4.8 Entropy Inequality 15
References 17
2 Hyperelastic, Viscoelastic, and Damage Models 19
2.1 Introduction 19
2.2 Hyperelastic Models 21
2.2.1 Constitutive Equations of Hyperelastic Materials 21
2.2.2 Hyperelastic Models 24
2.2.3 Results 29
2.3 Viscoelastic Models 31
2.3.1 One-dimensional Small Strain Viscoelastic Models 31
2.3.2 Finite Deformation Viscoelastic Models 33
2.3.3 Results 38
2.3.4 Finite Element Simulation 39
2.4 Damage Models 41
2.4.1 Continuum Damage Model 41
2.4.2 Network Alteration Theory 42
2.4.3 Progressively Damage Model 42
2.4.4 Extended Network Alteration Theory 43
2.4.5 Extended Progressively Damage Model 45
2.4.6 Results 47
2.5 Conclusion 51
References 53
3 A Thermomechanical Coupled Model for Amorphous Shape-memory Polymers 57
3.1 Introduction 57
3.2 Thermodynamics 59
3.2.1 Kinematics 59
3.2.2 Thermodynamic Framework 60
3.2.3 Constitutive Relationships 64
3.2.4 A Reduced Version of the Constitutive Model 67
3.3 Parameter Determination 68
3.4 Results 68
3.4.1 Performance of the Viscoelastic Model 68
3.4.2 Performance of the Effective Temperature Model 71
3.5 Discussion 73
3.6 Conclusion 74
References 75
4 An Electromechanical Coupled Model for Dielectric Elastomers 79
4.1 Introduction 79
4.2 Theory 80
4.2.1 Thermodynamic Framework 81
4.2.2 An Electro-hyperelastic Model 84
4.2.3 An Electro-hyper-viscoelastic Model 86
4.2.4 Electromechanical Instability of Dielectric Elastomers 86
4.3 Finite Element Implementation 90
4.3.1 Constitutive Relation 90
4.3.2 Weak Forms 91
4.4 Conclusion 94
References 95
5 A Magnetomechanical Coupled Model for Magnetoactive Soft Materials 99
5.1 Introduction 99
5.2 A Magnetomechanical Coupled Model for h-MREs 101
5.2.1 Kinematics 101
5.2.2 F-based Model 102
5.2.3 R-based Model 103
5.2.4 Comparing R-based and F-based Models 104
5.3 Magnetic Activated Shape-memory Polymers 105
5.3.1 Constitutive Theory 106
5.3.2 Parameter Determination 109
5.3.3 Simulation Results 111
5.4 Conclusion 112
Appendix 113
References 114
6 Multi-field Modeling of Liquid Crystal Elastomers 117
6.1 Introduction 117
6.2 General Theory for Liquid Crystal Elastomers 119
6.2.1 Liquid Crystal 119
6.2.2 Nematic Polymers 121
6.2.3 Neoclassical Model 122
6.3 Thermomechanical Coupled Model for Monodomain Liquid Crystal Elastomers 123
6.4 A Viscoelastic Micropolar Theory for Monodomain Liquid Crystal Elastomers 125
6.4.1 Kinematics 126
6.4.2 Balance of Linear and Angular Momentum 126
6.4.3 Balance of Energy and the Second Law of Thermodynamics 127
6.4.4 Constitutive Equations 128
6.4.5 Simplification for the Non-gradient Case 130
6.4.6 Free Energy Density 132
6.5 Theory for Polydomain Liquid Crystal Elastomers 134
6.6 Conclusion 139
References 140
7 A Chemomechanical Model for Hydrogels 143
7.1 Introduction 143
7.2 Thermodynamics 145
7.3 Constitutive Relations 148
7.3.1 Neutral Gels 148
7.3.2 Fiber-reinforced Gels 149
7.3.3 Diffusion in Glassy Elastomers 150
7.3.4 Numerical Method 152
7.4 Results 153
7.4.1 Neutral Gels and Fiber-reinforced Gels 153
7.4.2 Diffusion in Glassy Polymers 155
7.5 Conclusion 157
References 157
Index 161
About the Author :
Rui Xiao, PhD, is a Professor in the Department of Engineering Mechanics at Zhejiang University. His research focuses on the constitutive relationship of polymers, smart materials and structures, and the mechanics of soft materials.
