Characterization of Aorta and Diaphragm at High Strain Rate Loading

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CHARACTERIZATION OF AORTA AND

DIAPHRAGM AT HIGH STRAIN RATE LOADING

PIYUSH GAUR

DEPARTMENT OF MECHANICAL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY DELHI

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©Indian Institute of Technology Delhi (IITD), New Delhi, 2019

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CHARACTERIZATION OF AORTA AND

DIAPHRAGM AT HIGH STRAIN RATE LOADING

by

PIYUSH GAUR

Department of Mechanical Engineering

Submitted

in fulfilment of the requirements for the degree of Doctor of Philosophy

to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI

OCTOBER 2019

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DEDICATION

यत्करोषि यदश्नाषि यज्जुहोषि ददाषि यत् | यत्तपस्यषि कौन्तेय तत्कुरुष्व मदपपणम् || 27 ||

शुभाशुभफलैरेवं मोक्ष्यिे कमपबन्धनै: |

िंन्याियोगयुक्तात्मा षवमुक्तो मामुपैष्यषि || 28 ||

TRANSLATION

All that you do, all that you eat, all that you offer and give away, as well as all austerities that you may perform, should be done as an offering unto ME (THE ALMIGHTY LORD).

In this way you will be freed from all reactions to good and evil deeds, and by this principle of renunciation you will be liberated and come to ME (THE ALMIGHTY LORD).

Bhagvad-Gita: Chapter 9: Verse 27 & 28.

I am dedicating this work to the “Almighty Lord”. I am just a medium through whom he (God) aspires to bring salvation and peace to the world.

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AUTHORS DECELARATION

I hereby declare that I am the sole author of this thesis. This is a true copy of my thesis, including any required final revisions, as accepted by my examiners.

I understand that my thesis will be made electronically available to the public.

Piyush Gaur

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CERTIFICATE

This is to certify that the thesis entitled “Characterization of Aorta and Diaphragm at High Strain Rate Loading” being submitted by Mr. Piyush Gaur to the Indian Institute of Technology Delhi for the award of Doctor of Philosophy in Mechanical Engineering Department is a record of bonafide research work carried out by him. He has worked under our guidance and has fulfilled the requirements for the submission of thesis, which, in our opinion, has reached the requisite standard.

The results contained in this thesis have not been submitted in part or full, to any University or Institute for the award of degree or diploma.

Dr. Anoop Chawla Dr. Sudipto Mukherjee

Professor Professor

Department of Mechanical Engineering Department of Mechanical Engineering Indian Institute of Technology Delhi Indian Institute of Technology Delhi

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ACKNOWLEDGEMENTS

We all want to live our lives in our own ways but this is not possible of course without the help of others. The years – spent during this PhD research – have been incredible and magnificent. I have accomplished the biggest and the most earnest dream of my life. I would like to thank everyone who helped me directly or indirectly in the pursuit of higher learning and in achieving the highest accolade of higher education and scientific research.

This Ph.D. research thesis is a part of a research project entitled, “Thorax Model Abdomen Building and Validation” that is carried out by Mercedes Benz Research and Development and led by IIT Delhi under Dr Anoop Chawla as the academic partner. This project mainly aims in developing a material model to predict injuries to soft tissues of the thorax region.

Since I do want to risk forgetting to mention anyone, I would first of all like to express my thanks to all of those who know or feel that they in some way have contributed to my research work. Firstly, I would like to thank my supervisors – Dr. Anoop Chawla and Dr. Sudipto Mukherjee, many thanks for entrusting me with the responsibility and giving me your full support and confidence in performing my Ph.D. research work. I am privileged to learn the basics of Biomechanics and Soft tissue modelling under your tutelage. We discuss heartily in every possible topics. Thanks for allowing me to explore new ideas, but also pulled me back whenever I was veering away from my main focus. Andrew Blows & Tim Mumford, I learned a lot from your expertise in constitutive and FE modelling. Thanks for sparing me your valuable time for learning in LS Dyna modelling approaches. Thanks for your insightful comments.

Secondly, I would like to thank the members of my student research committee (SRC) – Dr.

Jayant Kumar Dutta, Dr. Naresh Verma Datla and Dr. Sanjeev Sanghi – for taking out

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v precious time to evaluate my research work. I express my gratitude for all your efforts and kindness. I appreciate your kind words and valuable suggestions.

Furthermore, I would like to thanks Dr. Sanjeev Lalwani from AIIMS Trauma Centre for availability of human samples required for testing on timely basis. I would also like to thank my colleagues from Impact lab. Special thanks to Khyati Verma, Karan Devane and Devendra Kumar, for your help and support in carrying out the testing work for this research. I learned a great deal and was honoured to work with them. My gratitude also goes forever to Sanyam Sharma, Neha Saxsena, Kuldeep Singh and Kamal Rana for their generosity, friendship and hospitality.

My wife Mradula Sharma for her smile, support, care and for being always there when I needed her. My infinite gratitude goes to all of my close friends who made me stay at IIT Delhi an unforgettable experience. Finally, I could not have completed this thesis without the support of my parents and elder sister. Above all, I wish to remember and pay my obeisance and reverence to the Almighty for his graciousness. Thanks for everything.

PIYUSH GAUR

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ABSTRACT

Motor vehicle crashes (MVC's) commonly result in life threating thoracic and abdominal injuries. Finite element models of the whole human body are being developed to understand the loading mechanisms and injury patterns of vehicle occupants during a vehicle crash event. In these crashes soft tissues are subjected to high strain rate loading, leading to severe and fatal injuries. The mechanical behavior of soft tissues differs with change in loading conditions; hence FE human body models need dynamic material data for accurate rendering. This thesis presents a methodology to characterize the impact response of the human aorta and diaphragm through physical testing and to identify a suitable material model to represent their behavior under impact conditions.

Development of two experimental setups, a quasi-static test setup and a drop tower based dynamic test set up for conducting uniaxial tensile tests on aorta and diaphragm specimens covering a range of strain rates from 0.001/s to 200/s, to obtain their stress-strain responses has been reported. The stress-strain responses of aorta and diaphragm under uniaxial tension show material non-linearity, large deformation (>20%) before failure and response that is dependent on strain rate. Constitutive model for representing aorta and diaphragm tissues have been developed and programmed in LS Dyna to include strain rate dependent effects and bilinear behaviour established through testing. An inverse FE characterization method was used to tune the material parameters using genetic algorithm (GA) as the optimization tool.

The aorta and diaphragm are in reality are subjected to combined loading due to the contact with the belt system or other vehicle interior parts, i.e., steering wheel for unbelted occupants during vehicular impacts. A biaxial device, capable of achieving strain rates up to 250/s was

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vii developed and used to test the porcine aorta both uniaxially and biaxially due to paucity of human samples. The porcine aortic tissue showed non-Hookean material response and strain rate dependency in both circumferential and longitudinal loading directions. Enhanced stiffness in the circumferential direction is indicated for the aorta as compared to the longitudinal direction indicating the need of anisotropic formulation. A strain rate dependent bilinear orthotropic constitutive model is proposed to characterize the behaviour of aorta under multiaxial loading conditions. The Poisson’s ratio of the linear region for both circumferential and longitudinal direction was evaluated using digital image correlation (DIC). The load-deformation relationship indicated in constrained biaxial tests were about 38% and 10% more stiffer in longitudinal and circumferential direction than that obtained from uniaxial tests for all strain rates.

Finally, the application of strain rate dependent bilinear constitutive model proposed in this thesis has been demonstrated through simulations of impact response of GHBMC human body models. The outcome of this work contributes to evolving bio-fidelic FE human body models, to study diaphragmatic and aortic injuries.

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सार

मोटर वाहन दुर्घटना (एमवीसी) में पर वक्ष और पेट की चोटों के कारण जीवन का खतरा

होता है। वाहन दुर्घटना की र्टना के दौरान वाहन में बैठे लोगो के लोड िंग तिंत्र और चोट के pattern को समझने के ललए पूरे मानव शरीर के FE मॉ ल ववकलसत ककए जा रहे हैं।

इन दुर्घटनाओिं में नरम ऊतकों पर उच्च तनाव दर पर loading आती है, जजससे गिंभीर और र्ातक चोटें आती हैं। नरम ऊतकों का यािंत्रत्रक व्यवहार लोड िंग जथिततयों में पररवतघन के साि लभन्न होता है; इसललए FE मानव मॉ ल को सटीक प्रततपादन के ललए गततशील मटेररयल प्रॉपटी की आवश्यकता होती है। यह िीलसस मैकेतनकल परीक्षण के माध्यम से

मानव महाधमनी और ायाफ्राम के प्रभाव की प्रततकिया को चचजननत करने के ललए और प्रभाव जथिततयों के तहत उनके व्यवहार का प्रतततनचधत्व करने के ललए एक उपयुक्त मॉ ल की पहचान करने के ललए एक कायघप्रणाली प्रथतुत करता है।

दो प्रायोचगक सेटअपों का ववकास, एक quasi-static परीक्षण सेटअप और महाधमनी पर uniaxial तन्यता परीक्षण करने के ललए एक ड्रॉप टॉवर आधाररत ायनेलमक टेथट थिावपत ककया गया है, जो उनके तनाव को प्राप्त करने के ललए 0.001 / s से 200 / s तक की

थरेन दरों की सीमा को कवर करता है। Uniaxial टेंशन के तहत महाधमनी और ायाफ्राम के तनाव-तनाव प्रततकियाएिं ववफलता और प्रततकिया से पहले गैर-रैखखकता, बडे ववरूपण थरेन (> 20%) ददखाती हैं जो तनाव दर पर तनभघर है। महाधमनी और ायाफ्राम ऊतकों

का दशाघने के ललए कम्प्यूटेशनल मॉ ल ववकलसत ककया गया है और परीक्षण के माध्यम से थिावपत थरेन दर तनभघर प्रभावों और bi-linear व्यवहार को शालमल करने के ललए एलएस ायना (LS-Dyna) में प्रोग्राम ककया गया है। अनुिमण उपकरण के रूप में

आनुविंलशक एल्गोररथ्म (GA) का उपयोग करके मटेररयल प्रॉपटीज को ट्यून करने के ललए

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ix एक व्युत्िम FE लक्षण वणघन ववचध का उपयोग ककया गया िा।

महाधमनी और ायाफ्राम पर वाथतव में बेल्ट लसथटम या अन्य आिंतररक वाहन भागों के

साि सिंपकघ के कारण सिंयुक्त लोड िंग आती हैं, जैसे एक द्ववअक्षीय उपकरण, जो 250 / s तक की थरेन दरों को प्राप्त करने में सक्षम िा और मानव नमूनों की लशचिलता के कारण uniaxial और biaxial दोनों तरह से पोलसघन महाधमनी का परीक्षण करने के ललए

इथतेमाल ककया गया िा। पोलसघन महाधमनी ऊतक ने पररधीय और अनुदैध्यघ लोड िंग

ददशाओिं में गैर-हुककयन प्रततकिया और तनाव दर तनभघरता ददखाई। पररचध ददशा में बढी हुई कठोरता महाधमनी के ललए सिंकेत के रूप में अनुदैध्यघ ददशा की तुलना में अतनसोरोवपक सूत्रीकरण की आवश्यकता को दशाघती है। एक तनाव दर पर तनभघर bilinear ऑिोरोवपक constitutive मॉ ल को मल्टीएजक्सअल लोड िंग पररजथिततयों में महाधमनी के व्यवहार को

चचजननत करने का प्रथताव है। पररचध और अनुदैध्यघ ददशा दोनों के ललए रेखीय क्षेत्र के

पोइसन अनुपात का मूल्यािंकन ड जजटल छवव सहसिंबिंध (DIC) का उपयोग करके ककया

गया िा। वववश biaxial परीक्षणों में सिंकेततत लो -ववकृतत सिंबिंध अनुदैध्यघ और पररधीय ददशा में लगभग 38% और 10% अचधक जथटफ़ िा, जो सभी तनाव दरों के ललए अतनतयजक्तक परीक्षण से प्राप्त हुआ िा।

अिंत में, इस िीलसस में प्रथताववत थरेन रेट ड पें ेंट bilinear constitutive मॉ ल के

आवेदन को GHBMC FE model के प्रभाव प्रततकिया के लसमुलेशन के माध्यम से

प्रदलशघत ककया गया है। इस काम का नतीजा ायाफ्रालमक और महाधमनी चोटों का

अध्ययन करने के ललए बायोकफ ेललक FE model को ववकलसत करने में योगदान देता है

।

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LIST OF FIGURES

Figure 1-1: The United Nations Decade of Action for Road Safety 2011-2020 (Collaboration, 2011). ... 2 Figure 1-2: Road traffic injuries in developed countries (Naci et al., 2009). ... 3 Figure 1-3: (a) Impact of a car representing primary impact, (b) Impact of dummy with vehicle steering wheel representing the secondary impact (Mu, 2001). ... 6 Figure 1-4: (a) Hybrid III Dummy Model ( LSTC), (b) MADYMO Q3 Multibody model (van Rooij et al., 2018). ... 8 Figure 1-5: GHBMC Human Body model, (b) THUMS model of the 50^th percentile of the male occupant. ... 12 Figure 2-1: Colonel John Paul Stapp strapped with accelerometers and load cells to measure his performance during the experiment (www.stapp.org). ... 20 Figure 2-2: Anatomy of the human aorta (Reproduced from Gray, 2000). ... 25

Figure 2-3: Cut section of the human thorax (Adopted from

http://www.anatomyatlases.org/). ... 25 Figure 2-4: (a) The wall structure of aorta, (b) Anatomical axis of the isolated aorta (Shah et al., 2006). ... 27 Figure 2-5: Pressure-volume apparatus for arterial inflation (Biewener, 1992). ... 32 Figure 2-6: Bubble inflation experiment on circular aorta specimen (Mohan & Melvin, 1983). ... 33 Figure 2-7: Uniaxial experiment on dumbbell shaped aortic tissue (Mohan & Melvin, 1982).

... 35 Figure 2-8: Schematic illustration of (a) Abdominal, (b) Thoracic parts of the diaphragm, along with (c) openings of the diaphragm, inferior to superior, and superior to inferior views

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respectively (Adopted from “http://antranik.org/muscles-of-the-thorax-for-breathing-and- the-pelvic-floor-the-diaphragm/”)... 42 Figure 2-9: Intra-operative photograph of a radial tear within the left hemi diaphragm (Bosanquet et al., 2009). ... 45 Figure 2-10: (a) Final meshed diaphragm model, (b) Integration of diaphragm model in the abdominal segment of HUMOS HBM (Behr et al., 2006). ... 49 Figure 3-1: Research methodology adopted to accomplish research objective for uniaxial tensile tests for the aorta and diaphragm... 60 Figure 3-2: GHBMC model showing initial conditions for, (a) Frontal Impact, (b) Side Impact for diaphragm and (c-d) set for aorta & Von Mises Strain rate vs. Time curve for (e) Diaphragm, (f) Aortic tissue. ... 63 Figure 4-1: Specimen location and fiber orientations of diaphragm tissue. ... 68 Figure 4-2: (a) Measurement of specimen length, (b) final sample for testing, (c) specimen mounted on tensile test set-up, (d) diaphragm specimen within cryogenic grippers (enlarged view). ... 70 Figure 4-3: Tensile testing setups, (a) Quasi-static tensile test set up and (b) Dynamic tensile test setup... 74 Figure 4-4: Preconditioning response of one of the diaphragm specimen in quasi-static testing. ... 77 Figure 4-5: Rupture pattern of diaphragm tissue in (a) Quasi-static tensile test, (b) Dynamic tensile test... 77 Figure 4-6: (a) Strain rate vs. Time curve for diaphragm specimens, (b) Representative stress- strain curve is showing the determination of mechanical properties. (b) Stress-strain curves computed using both engineering and true stress-strain definitions. ... 80 Figure 4-7: High-speed video stills of a typical uniaxial dynamic tensile test ... 82

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xvii Figure 4-8: Representative engineering stress-strain curve for diaphragm specimens: (a)

Quasi-static strain rate, (b) 65/s strain rate, (c) 130/s strain rate, (d) 190/s strain rate. ... 84

Figure 4-9: Characteristic average by strain rate. ... 85

Figure 4-10: Bilinear fits of diaphragm specimens... 88

Figure 4-11: Stress-strain plot of the quasi-static test (HD1-04). ... 90

Figure 4-12: (a) Failure stress variation, (b) Failure strain variation, (c) Elastic modulus variation wrt strain rate (Mean ± SD). ... 93

Figure 5-1: (a) Aortic tissue showing the longitudinal and circumferential orientation, (b) Measurement of specimen length, (c) Final sample for testing, (d) Specimen mounted on quasistatic tensile testing set-up, (e) Aorta specimen with cryogenic grippers mounted. ... 99

Figure 5-2: (a) Elongation vs time profile during preconditioning of the aorta specimen, (b) Ruptured aortic tissue after the test. ... 102

Figure 5-3: Load vs. Time curve for one of the aortic specimen test showing peak load point. ... 103

Figure 5-4: (a): Strain rate vs time curve showing steadiness of strain rate w.r.t time for human aortic specimens (b) Stress-strain curves computed using both engineering and true stress-strain definitions, (c) Representative stress-strain curve showing the determination of mechanical properties. ... 106

Figure 5-5: High-speed video stills of a typical uniaxial dynamic tensile test on the human aorta... 107

Figure 5-6: Representative engineering stress-strain curves for aortic specimens in longitudinal & circumferential direction: (a) Quasi-static strain rate (0.001/s), (b) 65/s strain rate, (c) 130/s strain rate, and (d) 190/s strain rate... 110

Figure 5-7: Representative stress-strain plot of human aortic tissue. ... 114

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Figure 5-8: Influence of elastic modulus, failure stress and failure strain with strain rate for longitudinal and circumferential aortic specimens. Values given include mean and standard deviation. ... 118 Figure 6-1: Flow of the data for the UMAT subroutine (Erhart, 2010). ... 122 Figure 6-2: (a) Typical stress-strain behaviour of soft tissues under loading, (b)Loading and unloading path of the specimen at different strain rates. ... 126 Figure 6-3: Flowchart of a subroutine in UMAT 41 for computation of stress. ... 126 Figure 6-4: Schematic diagram of material parameters estimation using a genetic algorithm.

... 131 Figure 6-5: (a) Finite element model of tensile test set-up, (b) Isometric view. ... 133 Figure 6-6: FE simulation output response with different material parameters for one of the diaphragm specimen (HD2-05) at impact velocity of 4.5 m/s. ... 139 Figure 6-7: Convergence plot observed for three human diaphragm specimens. ... 141 Figure 6-8: Comparisons of time histories of section force from FE simulations with optimized material parameters from UMAT vs experimental force time response for diaphragm tests at three grippers to gripper strain rates, i.e., at 65/s, 130/s, and 190/s strain rates. Note: All FE simulations were performed until the time of failure defined based on test data; no failure criteria was used in UMAT... 143 Figure 6-9: A depictions of the model showing (a) the initial FE model used for optimization and (b) the stages of deformation induced in diaphragm specimen during extension. The red contours show the area of maximum strain, i.e., initial tear region. ... 143 Figure 6-10: Variation of (a) Elastic modulus (b) Toe strain parameters w.r.t strain obtained from FE simulations (Mean ± SD). ... 144 Figure 6-11: Age effects of diaphragm tissue w.r.t strain rate (Mean ±SD). ... 146 Figure 6-12: Objective function vs iteration plot for longitudinal aortic specimens. ... 147

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xix Figure 6-13: Comparisons of time histories of section force from FE simulations with optimized material parameters from UMAT vs experimental force time response for aorta tests in a Longitudinal direction(a-c) and Circumferential direction(d-f) at three experimental gripper to gripper strain rates, i.e., at 65/s, 130/s and 190/s. Note: All FE simulation were performed until the time of failure defined based on test data; no failure criteria was used in

UMAT. ... 149

Figure 6-14: A depictions of the model showing (a) the initial FE model used for optimization and (b) the stages of deformation induced in the aortic specimen during extension. The red contours show the area of maximum stress, i.e., initial tear region. ... 150

Figure 6-15: Variation of (a) Elastic modulus and (b) toe strain of aortic tissue with strain rate in Longitudinal and Circumferential direction (Mean ±SD). ... 151

Figure 6-16: Transverse and lateral strain measured for longitudinal aorta using DIC, (b) Variation of Poisson's ratio. ... 152

Figure 7-1: (a) Intact Porcine Aorta, (b) Material orientations, (c) Rectangular specimen, (d) Specimen with markers in grippers of biaxial machine. ... 160

Figure 7-2:(a) Die used for cruciform samples, (b) Die on the surface of the aorta, (c) Specimen imprint on the surface of the aorta, (d) cruciform specimen (e) Specimen with markers in grippers. ... 163

Figure 7-3: (a) Schematic, (b) 3D sketch of biaxial setup, (c) Assembled biaxial test device. ... 167

Figure 7-4: Reference and consecutives images used in strain calculation using DIC from uniaxial tests... 170

Figure 7-5: FE model of biaxial setup with aorta specimen. ... 172

Figure 7-6: Material axis for the orthotropic model in FE simulation ... 174

Figure 7-7: Assumed elements for ROI in FE simulations ... 175

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Figure 7-8: Correction factor evaluation for orthotropic material at a velocity of 0.7 m/s in longitudinal direction keeping constrained the circumferential direction. ... 176 Figure 7-9: Video stills of a typical uniaxial tensile test of the porcine aorta at 2.8 m/s. . 177 Figure 7-10: Representative stress-strain curves for porcine aortic specimens in longitudinal and circumferential direction:(a) 0.01/s strain rate, (b) 70/s strain rate, (c) 150/s strain rate, and (d) 250/s strain rate. L- Longitudinal, C- Circumferential. ... 180 Figure 7-11: Influence of elastic modulus, failure stress and failure strain for longitudinal and circumferential porcine specimens (Mean ±SD). ... 185 Figure 7-12: Poisson’s ratio evaluation for aortic specimens in uniaxial tensile tests. ... 186 Figure 7-13: Poisson's ratio variation with strain rate for the longitudinal and circumferential aortic specimen. ... 188 Figure 7-14: Shear modulus values obtained for the longitudinal and circumferential aorta.

... 189 Figure 7-15: Typical stress distribution in cruciform specimens at (a) 0.7m/s and (b) 2.0 m/s velocity. ... 191 Figure 7-16: Failure progression for aortic specimen (PA20-02) loaded in the circumferential direction in constrained biaxial tests. ... 194 Figure 7-17: Representative stress-strain curves obtained for porcine aorta in constrained biaxial tests at (a) 0.01/s, (b) 70/s, (c) 150/s and (d) 250/s strain rates (Note - *L – Longitudinal direction, C- Circumferential Direction, LL – Loaded in longitudinal direction, CL – Loaded in circumferential direction). ... 197 Figure 7-18: Bilinear orthotropic model used is the estimation of mechanical properties of porcine aorta in constrained biaxial tests (Long – Longitudinal direction, Circ- Circumferential direction) ... 197

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xxi Figure 7-19: Comparisons and regression plots of (a) Elastic modulus, (b) Failure stress, (c) Failure strain with strain rate in uniaxial and constrained biaxial tests. ... 203 Figure 8-1: The GHBMC set up for frontal chest pendulum impact (Kroell et al. (1974)) ... 211 Figure 8-2: The GHBMC setup for side impact test setup (Shaw et al. (2006)). ... 212 Figure 8-3: Frontal impact (configuration of Kroell et al. (1971, 1974)) response comparison. (a) Force-time and (b) Force-deflection comparison. ... 213 Figure 8-4: Comparison of maximum green strain variation with time in frontal impact for (a) Diaphragm tissue, (b) Human Aorta defined in Cases A-D. ... 215 Figure 8-5: The impactor contact force vs time curve for side impact test in all four cases.

... 216 Figure 8-6: Comparison of maximum green strain variation with time in side-impact for (a) Diaphragm tissue, (b) Human Aorta in Cases A-D. ... 217

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LIST OF TABLES

Table 2-1: ATDs available and their field of applications (Schmitt et al., 2004). ... 22

Table 2-2: Summary of tests performed on aortic tissue ... 37

Table 2-3: Summary of constitutive model proposed for aorta in literature. ... 39

Table 2-4: Summary of mechanical properties used in Behr et al. (2006). ... 49

Table 4-1: Subject Information ... 67

Table 4-2: Test matrix for human diaphragm used in quasi-static and dynamic tensile tests. ... 70

Table 4-3: Averages and standard deviations by strain rate. ... 82

Table 4-4: Ultimate mechanical properties of the human diaphragm. ... 82

Table 4-5: Effective failure strain in the different tests for every strain rate. ... 94

Table 5-1: Subject Information ... 98

Table 5-2: Test matrix for human aorta used in quasi-static and dynamic tensile tests. ... 100

Table 5-3: Ultimate mechanical properties of human aorta in longitudinal and circumferential direction (L – Longitudinal aorta, C – Circumferential aorta). ... 110

Table 5-4: Effective failure strain for longitudinal and circumferential aortic tissue. ... 115

Table 6-1: Specimen size used in FE model ... 133

Table 6-2: Material properties of aortic and diaphragm in UMAT, load cell, upper and lower gripper used in FE model (* Long – the Longitudinal direction, Circ – circumferential direction). ... 135

Table 6-3: Variable bounds used for the diaphragm in the GA process ... 138

Table 6-4: Variable bounds used for aorta in GA ... 138

Table 6-5: Average optimized parameters for diaphragm tissue obtained from GA optimization. ... 142

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xxiii Table 6-6: Average optimized parameters for aortic tissue obtained from GA

optimization(Mean ±SD) ... 149

Table 6-7: Average Poisson's ratio evaluated through digital image correlation method. 152 Table 7-1: Specimen details for uniaxial tensile tests (*L - Longitudinal direction, C- Circumferential direction, F - Failed test)... 160

Table 7-2: Biaxial tissue testing sample details ... 163

Table 7-3: Biaxial device capacity ... 164

Table 7-4: Material models used to model aorta in FE simulation for evaluation of correction factor ... 173

Table 7-5: Properties obtained in longitudinal direction for porcine tissue. ... 180

Table 7-6: Mechanical properties obtained in circumferential direction for porcine aorta181 Table 7-7: Poisson's ratio for longitudinal and circumferential aortic specimens ... 186

Table 7-8: Shear modulus values obtained for the longitudinal and circumferential aorta. ... 188

Table 7-9: Constrained biaxial test results ... 198

Table 7-10: Comparison to published aorta properties. ... 204

Table 8-1- Aorta and diaphragm properties used in human body simulations ... 209

Table 8-2: Properties used in frontal and side impact simulations ... 209

Table 9-1: Mechanical properties obtained for diaphragm and aorta from experiments. .. 223

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LIST OF ACRONYMS

AGE Age of the test subject in years

AIIMS All India Institute of Medical Sciences AIS Abbreviated Injury Scale

CT Computer Tomography DI Diaphragmatic Injuries FE Finite Element

GA Genetic Algorithm

GHMBC Global Human Body Model Consortium HUMOS Human Body Model for Safety

DIC Digital Image Correlation

JPNATC Jai Prakash Nagar Apex Trauma Center MASS Mass of the test subject

MODTOE Modulus of toe region MODMID Modulus of linear region MODEND Modulus of post yield region PMHS Post-mortem Human Subject

PIPER Position and Personalize Advance Human Body Models RMS Root mean square

THUMS Total Human Body Model for Safety TRA Traumatic Rupture of Aorta

TRD Traumatic Rupture of Diaphragm

UMAT User material subroutine

WHMBS Wayne State Human Body Model for Safety

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xxv

LIST OF SYMBOLS

Ag1 Acceleration profile of gripper 1 A0 Initial Cross-sectional area Cijkl Material Matrix

Co Wave velocity of the material E Elastic modulus

Eij Elastic modulus components in i,j direction where i, j = 1, 2, 3.

E1 Toe modulus E2 Elastic modulus

E2_min Minimum modulus

E2_max Maximum modulus

E2_0.001/s Modulus at 0.001/s strain rate

E2_200/s Modulus at 200/s strain rate

f(X) Fitness function

Gij Shear modulus, where i, j = 1, 2.

K Bulk modulus Mg1 Mass of the gripper 1 ΔV Equivalent barrier speed /s Strain rate

𝜎_𝑓 Failure engineering stress

∈_𝐸 Failure engineering strain 𝜖_𝑇 True strain

Ft Load measured at load cell

F1c Inertially compensated force at gripper 1

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F4c Inertially compensated force at gripper 1 𝐹_𝑖^𝑒𝑥𝑝 Experimental force response

𝐹_𝑖^𝑠𝑖𝑚 Simulation force response Δl Change in gauge length L Gauge length

Lc Characteristic element length σT True stress

TPE Stress in passive element

TSE Stress in elastic element TCE Stress in contractile element Δt Time step

𝛆_{𝐭𝐨𝐭𝐚𝐥} Total effective strain 𝛆_𝐱 Strain in x direction 𝜺_𝒚 Strain in y direction 𝜺_𝒛 Strain in z direction 𝛆_𝐱𝐲 Strain in xy direction 𝛆_𝐲𝐳 Strain in yz direction 𝛆_𝒛𝒙 Strain in zx direction

ɛt_0.001/s Toe strain at 0.001/s strain rate ɛt_200/s Toe strain at 200/s strain rate ɛt_400/s Toe strain at 400/s strain rate ɛt_600/s Toe strain at 600/s strain rate Eij Modulus values in i and j direction σij (ekl) Stress tensor

𝜎_𝑖𝑗^𝐷 Stress tensor at previous time step ƛ & µ Lame’s constant

νij Poisson’s ratio I and j direction where i, j = 1, 2, 3.

Characterization of Aorta and Diaphragm at High Strain Rate Loading

CHARACTERIZATION OF AORTA AND

DIAPHRAGM AT HIGH STRAIN RATE LOADING

PIYUSH GAUR

DEPARTMENT OF MECHANICAL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY DELHI

CHARACTERIZATION OF AORTA AND

DIAPHRAGM AT HIGH STRAIN RATE LOADING

PIYUSH GAUR

Department of Mechanical Engineering

Submitted

in fulfilment of the requirements for the degree of Doctor of Philosophy

to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI

OCTOBER 2019

DEDICATION

यत्करोषि यदश्नाषि यज्जुहोषि ददाषि यत् | यत्तपस्यषि कौन्तेय तत्कुरुष्व मदपपणम् || 27 ||

शुभाशुभफलैरेवं मोक्ष्यिे कमपबन्धनै: |

िंन्याियोगयुक्तात्मा षवमुक्तो मामुपैष्यषि || 28 ||

AUTHORS DECELARATION

Piyush Gaur

CERTIFICATE

Dr. Anoop Chawla Dr. Sudipto Mukherjee

ACKNOWLEDGEMENTS

ABSTRACT

सार

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

LIST OF ACRONYMS

LIST OF SYMBOLS