Title Page
Abstract
Contents
Chapter 1. Introduction 16
1.1. Liquid Crystal Elastomer 16
1.2. Stimuli-Responsive Behavior of LCE 19
1.3. Design and Engineering Capability of LCE 22
1.4. Design-oriented simulation of LCE devices with topology optimization and contact mechanics 26
1.5. Numerical Characterization of LCE Material Behavior 27
1.6. Thesis Outline 32
Chapter 2. Computational Design and Simulation of Liquid Crystal Elastomers 33
2.1. Introduction 33
2.2. Topology Optimization for Strain Pattern Modeling 36
2.2.1. Thermal & Photo-Responsive LCE 38
2.2.2. Nonlinear Corotational FEM 39
2.2.3. Optimization Theory and Sensitivity Analysis 43
2.2.4. Numerical Results for Topology Optimization 50
2.3. Contact Simulation for LCE Application Modeling 69
2.3.1. Weak Energy Formulation of the Frictional Contact Problem 71
2.3.2. Discretized Formulation of the Contact Problem 75
2.3.3. Augmented Lagrangian Formulation of the Frictional Contact Problem 79
2.3.4. Time Stepping Algorithm of the Contact Problem 83
2.3.5. Numerical Results for Contact Simulation 86
2.4. Conclusion 103
Chapter 3. Material Modeling of Nematic Liquid Crystal Elastomer 105
3.1. Energy Formulation of Nematic LCE 105
3.2. Free Energy Model of Monodomain Nematic LCE 108
3.3. Constitutive Modeling of LCE 111
3.3.1. Stress Formulation of Monodomain LCE 111
3.3.2. Tangent Moduli Formulation of Monodomain LCE 114
3.3.3. 3D Monodomain LCE with thermotropic response 118
3.4. Numerical Results 125
3.4.1. Soft Elastic Behavior in 3D Monodomain LCE 126
3.4.2. Texture modulation with microstructure stripe domains 131
3.4.3. Thermal Actuation in 3D Monodomain LCE 134
3.5. Conclusion 139
Chapter 4. Conclusions 142
Bibliography 148
국문 요약 157
Table 2.1. Center position of strain pattern in S = 0.5 60
Table 2.2. Error estimation in height 63
Table 2.3. Material properties used in contact simulation 86
Table 2.4. Contact properties used in the simulation 87
Table 2.5. Simulation conditions and properties in jumping simulation 87
Table 2.6. Simulation conditions and properties in crawling simulation 92
Table 2.7. Simulation conditions and properties in rolling simulation 99
Table 3.1. Material properties used in ABAQUS UMAT simulation 126
Figure 1.1. Nematic-isotropic phase transition of LCE in temperature change 17
Figure 1.2. Scalar order parameter as a function of temperature. 21
Figure 1.3. Photo-isomerization and corresponding molecular structure change in azobenzene. 22
Figure 1.4. Various alignment techniques of nematic LCEs categorized by mechanical, magnetic/electric, and surface treatments. 24
Figure 1.5. Layer-by-layer 3D printing system with magnetic field alignment. 25
Figure 1.6. Soft elastic behavior of LCE. A stress plateau emerges during the elongation. 28
Figure 2.1. (a) Configuration of the corotational formulation. (b) High-order plate and shell elements. 42
Figure 2.2. Schematic of optimization problem of (a) position control and (b) tip displacement maximization. Target position of (a) is definied by the ratio of... 45
Figure 2.3. (a) Convergence for iteration number and (b) intermediate patt ern shapes. The black area indicates no induced strain, the white area undergoes... 52
Figure 2.4. Configuration of design domain for topology-optimization simulation where the left edge is fully clamped. 53
Figure 2.5. (a) Bending behavior and (b) strain distribution with different S Constraints. Intensity graph wherein relative strain intensity is plotted. The blue... 55
Figure 2.6. (a) Bending behavior and (b) strain distribution with different S constraints. Intensity graph wherein relative strain intensity is plotted. Blue lines... 56
Figure 2.7. (a) Bending behavior of various pinch points for 0.6D, 0.8D, and 1.0D (from left to right), and strain pattern for: (b) S = 0.5 and (c) S = 0.8. In (b) and (c),... 59
Figure 2.8. Optimization result and calculated center position 60
Figure 2.9. Fitted quadratic function of center position. Coefficients of 2nd, 1st order and constant is -29.37, 27.02 and 31.47, respectively[이미지참조] 61
Figure 2.10. Position control with inverse design pattern in intermediate target positions. Blue dots denote the desired target point in each D value. 62
Figure 2.11. Desired target z-displacements and results from inversely-designed patterns. 62
Figure 2.12. (a) Path-tracing mechanism and bending behavior for (b) S = 0.8 and (c) S = 0.5. Strain patterns and their deformation are arranged from bottom to top,... 64
Figure 2.13. (a) A tracing path of the x-z plane and (b) strain-distribution profile. In (b), the strain patterns are arranged from top to bottom and follow the path sequence. 65
Figure 2.14. Maximum edge displacement for various aspect ratios and shell thickness. Upper-row shells have h = 1, d = 0.1. Lower row shells have h = 5, d =... 67
Figure 2.15. Maximum displacement result for different penetration depths. Penetration depth is 0.1, 0.25, and 0.5 from the front column 68
Figure 2.16. Schematic of the master element, slave node, and closest point. 80
Figure 2.17. Schematic of LCE jumping device 88
Figure 2.18. Overlapped snapshot of jumping simulation of bending LCE for 200ms loading time. Jumping did not occur. 88
Figure 2.19. Jumping simulation of 50ms loading time. 10mm of jumping height is achieved. 89
Figure 2.20. Vertical position of LCE shell in jumping simulation. Loading time is varied from 100ms to 40ms. 90
Figure 2.21. Jumping height with 5ms and 10ms loading time. BL denotes the length of jumping device in length direction. 91
Figure 2.22. Schematic of LCE crawling thin film. Friction difference at tip and center contacted area occurs the crawling motion. 92
Figure 2.23. Load ratio in loading and unloading. Unloding procedure is 8 times faster than loading. 93
Figure 2.24. Contacted position of tip and center in x direction. A denotes the starting point of relative slippage. B denotes the maximum deformation and C is... 93
Figure 2.25. (a) Contact forces in tip and center points. All the forces in each area are summed. (b) Friction force applied in crawling device. 94
Figure 2.26. Crawling on the frictionless surface. No forward movement occurred. 95
Figure 2.27. Crawling on the frictional surface. Horizontal displacement occurred. 95
Figure 2.28. Crawling motion when the bending moment is insufficient. 95
Figure 2.29. Crawling of LCE specimen with selective light-induced bending. 97
Figure 2.30. Crawling displacement and accumulated frictional work with different friction coefficients. 98
Figure 2.31. Schematic of LCE rolling band. Light illuminated area is controlled by angle θ. 99
Figure 2.32. Rolling band on the frictional floor with light irradiation from the upper-left direction. The snapshot shows the rolling speed is increasing. 100
Figure 2.33. Rolling with insufficient light illumination. Induced bending deformation does not produce enough driving force to rolling motion. 101
Figure 2.34. Rolling LCE band moves away from the light illuminating direction. 102
Figure 2.35. Rolling distance of LCE band with various illumination area 102
Figure 3.1. Order parameter change in experimental reference. Abrupt order collapse appears near TNI.[이미지참조] 119
Figure 3.2. Schematic of stretching simulation in align-perpendicular direction. Stress in the stretching direction and strain in the remainder direction is verified. 127
Figure 3.3. Soft elasticity dependence upon initial order parameter. Large initial order leads to a longer softened stress region 128
Figure 3.4. Shrinkage strain in an initially aligned direction. The magnitude of the contraction is larger in the high initial Q value. 129
Figure 3.5. Shrinkage strain in the third direction (not stretched, not aligned). The magnitude of the contraction is smaller than in the aligned direction. 129
Figure 3.6. Stress evolution of stretching in parallel and perpendicular directions. The soft elastic mode mainly occurs in a perpendicular direction. 130
Figure 3.7. Perpendicular stretch in aligned monodomain LCE and stripe domain formation. IM value reduces from initial value 1 - r-1/2[이미지참조] 132
Figure 3.8. Texture modulation at 60% stretch for Q=0.3, 0.5 and 0.7. 132
Figure 3.9. Evolution of microstructure index during 100% strain. Initial order parameter affects the transition to pure stretching phase. 133
Figure 3.10. Order-temperature relation for first and second-order phase transition 134
Figure 3.11. Actuating strain in heating LCE for 1st and 2nd order phase transition.[이미지참조] 135
Figure 3.12. Actuation strain in varied initial order parameters. 1st order phase transition is assumed.[이미지참조] 136
Figure 3.13. Heating rate-dependent effect of thermal actuation in LCE. 137
Figure 3.14. Bending of LCE cantilever with anticlastic curvature 138
Figure 3.15. Hole-opening deformation in LCE kirigami structure. 139