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Experimental Characterization and Application of Thermodynamically Consistent Viscoelastic Models to Describe the Behavior of Collagen Dermal Grafts

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Experimental Characterization and Application of Thermodynamically Consistent Viscoelastic Models to Describe the Behavior of Collagen Dermal Grafts EXPERIMENTAL CHARACTERIZATION AND APPLICATION OF THERMODYNAMICALLY CONSISTENT VISCOELASTIC MODELS TO DESCRIBE THE BEHAVIOR OF COLLAGEN DERMAL GRAFTS By MULUGETA A HAILE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 1 © 2010 Mulugeta A Haile 2 To the memory of Abiyee 3 ACKNOWLEDGMENTS My deepest gratitude is due to my advisor and mentor Dr. Peter G. Ifju for his support, patience, and encouragement. I am always indebted for the research, teaching and other countless professional opportunities I was given while working with him. I would also like to thank Dr. Bhavani Sankar, Dr. Ghatu Subhash, and Dr. Jack Mecholsky for serving on my PhD committee and for their very useful feedback on the contents of this thesis. Finally, I would like to acknowledge the love and support I have received from my family and friends throughout my doctoral studies. I am so blessed to have them in my life. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................. 4 LIST OF FIGURES .......................................................................................................... 9 LIST OF ABBREVIATIONS ........................................................................................... 15 ABSTRACT ................................................................................................................... 18 CHAPTER 1 INTRODUCTION .................................................................................................... 21 Background ............................................................................................................. 24 Dissertation Outline ................................................................................................ 32 Main Contribution of the Thesis .............................................................................. 34 2 LITERATURE REVIEW .......................................................................................... 36 Introduction to Time-Dependent Material ................................................................ 36 Phenomenological Models - Differential Forms ...................................................... 37 Prony Series ........................................................................................................... 39 Integral Forms ......................................................................................................... 43 Hyperelasticity and Pseudoelasticity ....................................................................... 45 Time Dependent Elasticity: Viscoelasticity .............................................................. 48 Linear and Quasilinear Theories of Viscoelasticity ................................................. 50 Nonlinear Viscoelasticity ......................................................................................... 52 Strong and Weak Principles of Fading Memory ............................................... 54 Recent Studies ................................................................................................. 55 3 EXPERIMENTAL CHARACTERIZATION ............................................................... 58 Introduction ............................................................................................................. 58 Uniaxial Creep and Relaxation Tests ...................................................................... 58 Dynamic Test .......................................................................................................... 60 Experimental Procedures ........................................................................................ 60 Forming Speckle Pattern .................................................................................. 61 Hydration of Samples ....................................................................................... 63 Force Measurement ......................................................................................... 64 Strain Measurement using DIC ........................................................................ 66 Mechanical Testing ................................................................................................. 69 Response to Step Strain................................................................................... 69 Elastic response to step stretch ................................................................. 71 Relaxation response to step strain ............................................................. 73 Elastic Response and Isochronous Stress-Strain Curves ....................................... 76 5 Response to Ramp Strain ................................................................................ 76 Isochronous Stress-Strain ................................................................................ 79 Stress Relaxation at Multiple Strain Levels ...................................................... 79 Concluding Remarks............................................................................................... 82 4 ELASTIC IMAGE REGISTRATION AND REFRACTION CORRECTION FOR STRAIN MEASUREMENTS IN FLUID MEDIUM .................................................... 84 Background ............................................................................................................. 84 Introduction ............................................................................................................. 86 Refraction Induced Image Distortion ....................................................................... 87 Registration of Point Sets ....................................................................................... 90 Local Weighted Mean Transform ..................................................................... 90 Experimental Procedures ........................................................................................ 93 The Digital Image Correlation (DIC) Test Setup ............................................... 95 Acquiring DIC images of the template .............................................................. 95 Acquiring DIC Images of the Test Specimen .................................................... 96 Results and discussions ......................................................................................... 97 Recovering the Transformation ........................................................................ 98 Transforming images of the test specimen ..................................................... 100 Concluding Remarks............................................................................................. 106 5 APPLICATION OF THERMODYNAMICALLY CONSISTENT MODELS .............. 108 Introduction ........................................................................................................... 108 Analysis ................................................................................................................ 109 The Quasilinear Model (QLV) ............................................................................... 110 Implementation of the Quasilinear Viscoelastic Theory .................................. 111 The Elastic Response Function, e( ) ............................................................ 112 The Reduced Relaxation Function, G(t) ......................................................... 117 Non-Equilibrium Thermodynamic Model ............................................................... 122 Thermoviscoelastic Relaxation ....................................................................... 124 Thermoviscoelastic Creep .............................................................................. 125 Schapery’s Nonlinear Theory ................................................................................ 127 Introduction ..................................................................................................... 127 Application of Schapery's Theory ................................................................... 130 Concluding Remarks............................................................................................. 131 6 EQUIBIAXIAL CHARACTERIZATION USING BUBBLE INFLATION TEST ......... 133 Introduction ........................................................................................................... 133 Literature Survey on Equibiaxial Testing............................................................... 136 Bubble Inflation Test of Dermal Grafts .................................................................. 137 Materials and Methods.......................................................................................... 139 Sample Preparation ........................................................................................ 143 Dealing with Membrane Porosity .................................................................... 144 Curvature Modeling - Geometrical Formulation .............................................. 146 6 Biaxial Stress-Strain Relations .............................................................................. 147 Planar verses Bubble Inflation Equivalence .......................................................... 149 DIC Based Detection of Anisotropy ...................................................................... 151 Concluding Remarks............................................................................................
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