Multi-field Modeling of Soft Active Materials

Chapter 1: Basics of Continuum Mechanics

• • 1.1 Vectors and Tensors
• • 1.1.1 Vector
• • 1.1.2 Index Notation
• • 1.1.3 Tensor
• • 1.1.4 Gradient, Divergence, and Curl
• • 1.2 Kinematics
• • 1.2.1 Deformation Gradient
• • 1.2.2 Strain Tensor
• • 1.3 Stress
• • 1.4 Balance Principles
• • 1.4.1 Material Derivative and Spatial Derivative
• • 1.4.2 Reynolds Transport Theorem
• • 1.4.3 Conservation of Mass
• • 1.4.4 Balance of Momentum
• • 1.4.5 Balance of Angular Momentum
• • 1.4.6 Balance of Mechanical Energy
• • 1.4.7 Balance of Energy
• • 1.4.8 Entropy Inequality
• • References

Chapter 2: Hyperelastic, Viscoelastic, and Damage Models

• • 2.1 Introduction
• • 2.2 Hyperelastic Models
• • 2.2.1 Constitutive Equations of Hyperelastic Materials
• • 2.2.2 Hyperelastic Models
• • 2.2.3 Results
• • 2.3 Viscoelastic Models
• • 2.3.1 One-dimensional Small Strain Viscoelastic Models
• • 2.3.2 Finite Deformation Viscoelastic Models
• • 2.3.3 Results
• • 2.3.4 Finite Element Simulation
• • 2.4 Damage Models
• • 2.4.1 Continuum Damage Model
• • 2.4.2 Network Alteration Theory
• • 2.4.3 Progressively Damage Model
• • 2.4.4 Extended Network Alteration Theory
• • 2.4.5 Extended Progressively Damage Model
• • 2.4.6 Results
• • 2.5 Conclusion
• • References

Chapter 3: A Thermomechanical Coupled Model for Amorphous Shape-memory Polymers

• • 3.1 Introduction
• • 3.2 Thermodynamics
• • 3.2.1 Kinematics
• • 3.2.2 Thermodynamic Framework
• • 3.2.3 Constitutive Relationships
• • 3.2.4 A Reduced Version of the Constitutive Model
• • 3.3 Parameter Determination
• • 3.4 Results
• • 3.4.1 Performance of the Viscoelastic Model
• • 3.4.2 Performance of the Effective Temperature Model
• • 3.5 Discussion
• • 3.6 Conclusion
• • References

Chapter 4: An Electromechanical Coupled Model for Dielectric Elastomers

• • 4.1 Introduction
• • 4.2 Theory
• • 4.2.1 Thermodynamic Framework
• • 4.2.2 An Electro-hyperelastic Model
• • 4.2.3 An Electro-hyper-viscoelastic Model
• • 4.2.4 Electromechanical Instability of Dielectric Elastomers
• • 4.3 Finite Element Implementation
• • 4.3.1 Constitutive Relation
• • 4.3.2 Weak Forms
• • 4.4 Conclusion
• • References

Chapter 5: A Magnetomechanical Coupled Model for Magnetoactive Soft Materials

• • 5.1 Introduction
• • 5.2 A Magnetomechanical Coupled Model for h-MREs
• • 5.2.1 Kinematics
• • 5.2.2 F-based Model
• • 5.2.3 R-based Model
• • 5.2.4 Comparing R-based and F-based Models
• • 5.3 Magnetic Activated Shape-memory Polymers
• • 5.3.1 Constitutive Theory
• • 5.3.2 Parameter Determination
• • 5.3.3 Simulation Results
• • 5.4 Conclusion
• • Appendix
• • References

Chapter 6: Multi-field Modeling of Liquid Crystal Elastomers

• • 6.1 Introduction
• • 6.2 General Theory for Liquid Crystal Elastomers
• • 6.2.1 Liquid Crystal
• • 6.2.2 Nematic Polymers
• • 6.2.3 Neoclassical Model
• • 6.3 Thermomechanical Coupled Model for Monodomain Liquid Crystal Elastomers
• • 6.4 A Viscoelastic Micropolar Theory for Monodomain Liquid Crystal Elastomers
• • 6.4.1 Kinematics
• • 6.4.2 Balance of Linear and Angular Momentum
• • 6.4.3 Balance of Energy and the Second Law of Thermodynamics
• • 6.4.4 Constitutive Equations
• • 6.4.5 Simplification for the Non-gradient Case
• • 6.4.6 Free Energy Density
• • 6.5 Theory for Polydomain Liquid Crystal Elastomers
• • 6.6 Conclusion
• • References

Chapter 7: A Chemomechanical Model for Hydrogels

• • 7.1 Introduction
• • 7.2 Thermodynamics
• • 7.3 Constitutive Relations
• • 7.3.1 Neutral Gels
• • 7.3.2 Fiber-reinforced Gels
• • 7.3.3 Diffusion in Glassy Elastomers
• • 7.3.4 Numerical Method
• • 7.4 Results
• • 7.4.1 Neutral Gels and Fiber-reinforced Gels
• • 7.4.2 Diffusion in Glassy Polymers
• • 7.5 Conclusion
• • References