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Chapter 1 Atomistic to Continuum Modeling of DNA Molecules 1

1.1 Introduction 2

1.2 Statistical models for DNAs—polymer elasticity 5

1.2.1 The freely jointed chain(FJC)model 6

1.2.2 The worm-like chain(WLC)model 9

1.2.3 Beyond the entropic regime 10

1.2.4 Long-range electrostatic effects 11

1.3 Atomistic modeling of DNA molecules 12

1.3.1 MD basic theory 12

1.3.2 Force fields for nucleic acids 13

1.3.3 Limitations and challenges 14

1.3.4 MD simulation of DNA stretching 15

1.4 Continuum DNA models 17

1.4.1 Kirchhoff's elastic Rod model for DNAs 17

1.4.2 Finite element(FE)analysis of DNAs 20

1.4.3 Director field method for modeling of DNA viral packaging 22

1.5 Multiscale homogenization for simulation of DNA molecules 24

1.5.1 Basics of multiscale wavelet projection method 24

1.5.2 First-level homogenization—wavelet-based coarse-grained DNA model 28

1.5.3 Second-level homogenization—hyperelastic beam formulation for DNA 39

1.5.4 Applications 43

1.6 Conclusion 48

Appendix：Wavelet and decomposition coefficients for linear spline function 49

References 50

Chapter 2 Computational Contact Formulations for Soft Body Adhesion 55

2.1 Introduction 55

2.2 Continuum contact formulation 57

2.3 Finite element formulations 64

2.4 Adhesion examples 72

2.5 Peeling contact 79

2.6 Rough surface contact 83

2.7 Conclusion 87

References 89

Chapter 3 Soft Matter Modeling of Biological Cells 95

3.1 Introduction 95

3.2 Soft matter modeling of cells 97

3.2.1 The future is soft 97

3.2.2 The reasons to use liquid crystal elastomers to model cell and focal adhesion 98

3.2.3 Elasticity of soft contact/cell adhesion and surface material property sensing 100

3.2.4 Cell and ECM modeling 101

3.3 A nanoscale adhesive contact model 105

3.4 Meshfree Galerkin formulation and the computational algorithm 107

3.5 Numerical simulations 109

3.5.1 Validation of the material models 109

3.5.2 Endothelial cell simulations 110

3.5.3 Stem cell simulations 113

3.6 Discussion and conclusions 114

References 115

Chapter 4 Modeling the Mechanics of Semiflexible Biopoly-mer Networks:Non-affine Deformation and Presence of Long-range Correlations 119

4.1 Introduction 119

4.2 Network representation and generation 121

4.3 Affine vs.non-affine deformation 123

4.4 Network microstructure:scaling properties of the fiber density function 127

4.5 Network elasticity:the equivalent continuum and its elastic moduli 131

4.6 Boundary value problems on dense fiber network domains 132

4.6.1 Background:affine and non-affine theories 132

4.6.2 Karhunen-Loeve decomposition 136

4.6.3 Stochastic finite element formulation of 2D problems 137

4.7 Solution of boundary value problems on dense fiber network domains 139

References 141

Chapter 5 Atomic Scale Monte-Carlo Studies of Entropic Elasticity Properties of Polymer Chain Molecules 147

5.1 Introduction 147

5.2 Entropic elasticity of linear polymer molecules 148

5.2.1 Continuum limit 152

5.2.2 Monte-Carlo sampling 154

5.3 Summary 160

References 161

Chapter 6 Continuum Models of Stimuli-responsive Gels 165

6.1 Introduction 165

6.2 Nonequilibrium thermodynamics of neutral gels 166

6.3 A simple material model for neutral gels 171

6.4 Swelling of a spherical gel 174

6.5 Thermodynamics of polyelectrolyte gels 177

6.6 A material model for polyelectrolyte gels 182

6.7 Chemical reactions and pH-sensitive gels 186

6.8 Equilibrium models of polymeric gels 189

6.9 Summary 193

References 194

Chapter 7 Micromechanics of 3D Crystallized Protein Structures 197

7.1 Introduction 197

7.2 3D crystallized protein structures 198

7.3 Thermomechanical properties of protein crystals 199

7.4 A micromechanical model for protein crystals 200

7.5 Application to tetragonal lysozyme as a protein crystal model 202

7.5.1 Elastic deformation in lysozyme crystals 202

7.5.2 Plastic deformation in lysozyme crystals 203

7.5.3 Anisotropic plastic yielding of lysozyme crystals 205

7.5.4 Orientation effect on mechanical behavior of lysozyme crystals 206

References 210

Chapter 8 Micromechanical Modeling of Three-dimensional Open-cell Foams 213

8.1 Introduction 214

8.1.1 Unit cell models 215

8.1.2 Random cell models 217

8.2 Micromechanics model using a tetrakaidecahedral unit cell 218

8.2.1 Formulation 218

8.2.2 Numerical results 232

8.2.3 Summary 235

8.3 Random cell model incorporating cell shape and strut cross-sectional area irregularities 236

8.3.1 Analysis 236

8.3.2 Results and discussion 242

8.3.3 Summary 254

References 256

Chapter 9 Capillary Adhesion of Micro-beams and Plates：A Review 259

9.1 Introduction 259

9.2 Capillary adhesion of micro-beams of infinitesimal deformation 261

9.3 Capillary adhesion of micro-beams of finite deformation 264

9.4 Hierarchical structure of micro-beams induced by capillary force 268

9.5 Capillary adhesion of a plate 270

9.6 Conclusions 273

References 274

Color Plots 277