Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 10-8-2010 Characterization and sensitivity analysis of hyperelastic materials in biaxial tension Lowell Smoger Follow this and additional works at: http://scholarworks.rit.edu/theses Recommended Citation Smoger, Lowell, "Characterization and sensitivity analysis of hyperelastic materials in biaxial tension" (2010). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. CHARACTERIZATION AND SENSITIVITY ANALYSIS OF HYPERELASTIC MATERIALS IN BIAXIAL TENSION By Lowell M. Smoger Submitted in partial fulfillment of the requirement for the Master of Science In Mechanical Engineering Dr. Elizabeth DeBartolo _______________________ Department of Mechanical Engineering (Thesis Advisor) Dr. Risa J. Robinson _______________________ Department of Mechanical Engineering (Committee Member) Dr. Kathleen Lamkin-Kennard _______________________ Department of Mechanical Engineering (Committee Member) Dr. Mario Gomes _______________________ Department of Mechanical Engineering (Committee Member) Dr. Wayne Walter _______________________ Department of Mechanical Engineering (Department Representative) KATE GLEASON COLLEGE OF ENGINEERING ROCHESTER INSTITUTE OF TECHNOLOGY October 8th 2010 Permission to Duplicate Permission Granted Title: CHARACTERIZATION AND SENSITIVITY ANALYSIS OF HYPERELASTIC MATERIALS IN BIAXIAL TENSION I, Lowell M. Smoger, hereby grant permission to the Wallace Library of the Rochester Institute of Technology to reproduce my thesis in whole or in part. Any reproduction will not be for commercial use or profit. Date: _________________ Signature: ___________________________ ii Copyright by Lowell M. Smoger 2010 iii Acknowledgements There is something to be said for the support we get from others when they give it simply because they believe in us. To them, the only thing that matters is our success in accomplishing our goals, whatever they may be. My family has given me this support. I would like to thank you for giving this support simply because you believed in me. Specifically, I would like to thank my father, Barry, for his genuine interest in helping me solve the current issue. Your endless knowledge is what I strive to someday possess. My mother, Marci, made sure every choice I made was based on my happiness, not my laziness. Because of that I am very happy with the choices I’ve made, but still a little lazy. My brother, Julian, deserves thanks for putting my work into perspective when I felt that it would never end. His final acknowledgement of having a smart brother (pending college graduation) is truly appreciated more than he knows. Although not family by definition, the guidance and support from my adviser, Dr. Elizabeth DeBartolo, makes any less of an acknowledgement insulting. Like family, she seemed to take me under her wing because of my enthusiasm for the work, not my research credentials. Never did she make it seem like I was bothering her, even when I would pay her a third visit of the day and keep her from picking up her children on time. I cannot say how difficult, if not impossible, this work would have been without her guidance and support. To my committee members, Dr. Robinson, Dr. Lamkin-Kennard, and Dr. Gomes, I think I speak for Dr. DeBartolo and I when I say thank you for your guidance and support. You all have helped in different ways and we owe the success of this work to that input more than you likely know. For all of my experimental testing that required the use of sensors, motors and cameras, I owe a great deal of thanks to Professor John Wellin. Without him, the machine operation analysis and data collection process would have required an additional several months. Complete credit is also owed to him for the creation of the newest Labview VI. To the members of the machine shop, Dave Hathaway, Rob Kraynik, Steve Kosciol, and the Brinkman Lab, John Bonzo, thank you. The test fixture operates like it never has before because of your assistance and advice. For the molds and parts donated, my budget thanks you too. iv To Dr. Hensel, Diane Selleck and Barry Robinson, you have supported me all five years of my time here at RIT, for which I cannot express my gratitude here in full. Please know that because of you, my college experience has been everything I hoped it would and more. Finally, to my fellow graduate students, although we worked separately on our respective projects thanks for reminding me that I’m not alone and that we all experience very similar problems. Your perseverance served to strengthen my own. Again, thank you all. v Abstract The focus of this study was to improve characterization of hyperelastic materials in biaxial tension through improved design and validation of an existing test fixture and specimen geometry. Additionally, a sensitivity analysis of the material properties to variations in selected test parameters was conducted to better understand material response. Misalignment and binding in the original tensile test fixture resulted in non-equibiaxial loading and inaccurate stress-strain data. Analysis and modification were required to improve accuracy and repeatability. Vector analysis of the link system and the Minimum Constraint Design method were used to achieve this aim. Based on a proposed set of criteria, a FE analysis was conducted on several biaxial specimen geometries to determine the best shape and scale for obtaining stress and strain data. A stress decay factor (SDF) is proposed to predict internal stresses from measurable data. A test method has been designed around the use of the SDF and was ultimately applied to a cruciform specimen geometry. In addition to the ideal equibiaxial case, numerical simulations have been perturbed in two ways. The first variation involved a specimen gripped clamps offset by up to half the width of the clamp. The second variation involved non-equibiaxial load ratios ranging from 0.85 to 1.15. The goal was to quantify the change in stress-strain response to slight deviations from ideal loading conditions. Binding has been eliminated from the test fixture and a 1:1 load ratio has been achieved. The new specimen experiences less stress decay while achieving greater experimental strain. A high sensitivity to non-equibiaxial load ratios and low sensitivity to clamp offset are seen in the test parameter analysis. Finally, results from the SDF correction material characterization method is compared with results from an inflated boiling flask geometry. vi Table of Contents Permission to Duplicate .................................................................................................................. ii Acknowledgements ........................................................................................................................ iv Abstract .......................................................................................................................................... vi Table of Contents .......................................................................................................................... vii List of Figures ................................................................................................................................. x List of Tables ................................................................................................................................ xii 1. Background .............................................................................................................................. 1 1.1 Motivation ........................................................................................................................ 1 1.2 Existing Research ............................................................................................................. 1 1.3 Original Goals & Challenges ........................................................................................... 2 1.4 Revised Goals ................................................................................................................... 3 2. Preliminary Research & Experimentation ............................................................................... 4 2.1 Index of Equation Terms .................................................................................................. 4 2.2 Literature Review ............................................................................................................. 5 2.2.1 Fitting of the Pressure-Volume Curve ...................................................................... 5 2.2.2 Specimen Design & Test Methods ......................................................................... 13 2.2.3 Existing Criteria for Specimen Design ................................................................... 16 2.2.4 Gaps in the Literature.............................................................................................. 18 2.3 Analysis of Existing PV Data ........................................................................................ 19 2.3.1 Nominal PV Curves ................................................................................................ 19 2.3.2 Material Candidate Search .....................................................................................