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"1 ““ ‘1“ "1‘1" "““ “‘1‘ 1.1112 111 1‘1 1~'1111 111“1‘11 1““1 111111 1“»11 1.1‘111‘1111'11‘511‘1..1‘~1£41111 ' 11111111111111.1111111111111111 "" T H ESlS ’4’Ih.;;-flh‘ .74; 1" —~k-“AH“‘MM \ l ‘I‘h‘ A-.. \, F .. ”.1 Li" .9 T C"? * ,_ ,tafl ,. r «LL... 5L 4;, 73533 g Ua4..&"'£ri;:;b g .V w \s , j _ W,— This is to certify that the thesis entitled Stability of Response of Canine Tendons to Repeated Elongations. presented by Michael Steven Sacks has been accepted towards fulfillment of the requirements for Nhsters degree in Mechanlcs / Major professor Robert P. Hubbard Date 7/31/83 0.7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU LlBRARlES .—;_. RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. .t. f}? 9" SEABILITY OF RESPONSE OF CANINE TENDONS TO REPEHTED EBONGNTIONS By Michael Steven Sacks A THESIS Suhnitted to Michigan State University in partial fulfillment of the requiranents for the degree of MASTER OF SCIENCE anartment of Metallurgy, Mechanics, and Laterial Science 1983 WT STABILITY OF RESPONSE OF CENINE ‘ENIIJNS ‘IOREPEATED WTIONS By Michael Steven Sacks The mechanical raponse of collagenous tissues to long term repeated elongation is not well understood, and hence requires further investigation. In this study, canine tendons were continuously cycled at a constant strain rate to. various strain levels for 2} hours. Characterization of the nechanical response included behavior of : the peak load, the naximum loading and unloading tangent moduli, the hysteresis, a power fit of the stress-strain curve, and the stability of the above parameters over the length of the test. The peak load and the uaximun tangent moduli attained equilibrium values later in the test at higher strain levels . The tendon slack length increased proportionally the same at all strain levels. Power fit coefficients indicated continuous change at all strain levels throughout the test, with greater changes at the lower strain levels . In general , the results indicated that the preconditioning assunption cbes not hold for long term repeated elongation . WIS There were neny special people involved in helping in the production and writing of my buster Thesis. I would like here to extend my deep gratitude to then, they are: Dorothy Ranetche, Janet Pram, Todd Segula, Glenn Beavis, Diane Pietryga, and Richard Geist; undergraduates who relieved me of much burdensane work and made the tisme mechanics lab a very enjoyable place to mrk. Robert E. Sdiaeffer, who's seeningly eidless patience and skill kept the sanetimes cranky test nachinery smoothly working. Jane Walsh, for thing the fine histological work, and for her warm frie'idship. Therese 'Ihelen and Laura Hayes, for doing such a fine job on the seeningly endless chore of typing the manuscript . ‘Ihe American Osteopathic Association for their geierous funding of this project. Dr. Robert Vin. Soutas-Little, for serving on my caunittee, for the many favors over my four years in the Bianechanics Department, and for helping to nuke it a fascinating and eijoyable place to work. Drs. mvid Sikarskie and Gary Cloud, for serving on my cannittee. My family, for their support in my academic pursuits. lastly, but met important; Dr. Robert P. Hubbard, for four years of friendship, guidance, and for establishing a very unique learning experience. ii List of WWW F igma O O O O O 0 Materials andMethods . . . A. B. C. D. E. Results A. B. C. D. E. F. G. H. Sample Preparation Testing Equipnent. Test Protocol . . . and Discussion. . . . . mta Aquisition, Storage, and Analysis. HistolOgY: Cross-Sectional Area Calculation, and SlippageMeasurenents..................20 Page 0 O O O O O O O Viii O O I O O O O O 10 O O O C O O O O 12 O O O O O O O 0 l3 PeakStress ..... .22 LadingandUnloadingMaxiJmm'Iangeitlbduli......36 Hysteresis ............ . SlackStrain....... Power Fit Coefficients . . Histology......... PhotographicMeasurenents. mlmion O I O O O O O O O O O O I Appendicesw ....... . Biblimmy0 O O O O O O O ....... 0 iii 0 O O ..... 44 O O O O O O O O 51 Figure 1. The four regions of a typical stress-strain curve for W O O O I O O O O O O O O O O O O O O O O O O O O O O 2. Typical stress-strain curves for tendon, and collagenous and.e1astic ligaments. . . . . . . . . . . . . . . . . . . 3. The effect of varying strain rate on tendon. . . . . . . . 4 . A typical stabilization time plot for the peak stress, loading and unloading.Maximum.Tangent.MOduli, showing the t-teSt' 2% and 5% difference Criteria. 0 o o o o o o o 5. Definition of the slack.strain for a typical stress- Strain me O O O O O O O O O O O O O O O O I O O O O O O 6. Typical behavior of the peak stress-vs.-time for a 2% am 6% Strain lwel mSt O O O O O O O O O O O I O O O O O 7. Typical behavior of the peak stress-vs.-log time for a 2% and 6% strain level test. . . . . . . . . . . . . . . 8. Means for the peak stress for the first and fifth cycles at the strain levels tested. . . . . . . . . . . . . . . . 9. The peak stresses-vs.-offset strain at the fifth cycle . . 10. Stabilization times for the peak stress. . . . . . . . . . 11. A typical loading and unloading MaximumlTangent Moduli (M.T.M. )-vs.-tjm plot 0 O O O O O O O O O O O O O I O O O 12. A.typical loading and.unloading Maximum.Tangent.Moduli (NLThM.)-vs.-log time pLot . . . . . . . . . . . . . . . . 13. The loading Maximim Tangent Moduli (M.T.M. )-vs.-strain level for the first and fifth cycles . . . . . . . . . . . 14. The unloading Maxim Tangent Moduli (M.T.M. )-vs.-strain level for the first and.fifth cycles . . . . . . . . . . . 15. Loading Maxiuun Tangent Moduli (M.T.M. )-vs.-offset strain LIST OF FIGURES atthefifthcycle.................... iv Page 17 18 24 26 28 31 34 37 37 38 40 42 Figure Page 16. Unloading Maxim Tangent Moduli (M.T.M. )-vs.-offset strainatthefifthcycle.. ..... ...........42 17 . Stabilization times for the loading and unloading MaatirmmTangeitModulim.T.M.)...............43 18. The initial response of the hysteresis at the 2% strain lwI I I I I _I I I I I I I I I I I I I I I I I I I I I I I 46 19. The initial response of the hysteresis at the 3% strain ladI I I I I I I I I I I I I I I I I I I I I I I I I I I I 46 20. The initial response of the hysteresis at the 4% strain lad-I I I I I I I I I I I I I I I I I I I I I I I I I I I I 47 21. The initial response of the hysteresis at the 6% strain lwaI I I I I I I I I I I I I I I I I I I I I I I I I I I I 47 22. The long term response of the hysteresis at the 2% strain 1“. I I I 0000000000 I I I I I I I I I I I I I I 49 23. The long term response of the hysteresis at the 3% strain lad-I I I I I I I I I I I I I I I I I I I I I I I I I I I I 49 24. The long term response of the hysteresis at the 4% strain ImelI I I I I I I I I I I I I I I ‘ I I I I I I I I I I I I I 50 25. The long term response of the hysteresis at the 6% strain lwelI I I I I I 0000000000 I I I I I I I I I I I I so 26. The initial response of the slack strain at the 2% strain 1“. I I I I I ......... I I I I I I I I I I I I I 53 27. The initial response of the slack strain at the 3% strain ImelI I I I I I I I I I I I I I I I I I I I I I I I I I I I 53 28. The initial response of the slack strain at the 6% strain 1“. I I I I I I I I I I I I I I I I I I I I I I I I I I I 54 29. The initial response of the slack strain at the 4% strain 1evel...... .......... ...... S4 30. Thelongtermresponseoftheslackstrainatthe2% Strain I“ I I I I I I I I I I I I I I I I I I I I I I I I 55 31. Thelongtermresponse oftheslack strain at the 3% strainlevel.......... ...... ........55 32. The long term response of the slack strain at the 4% Strain Imel I I I I I I I I I I I I I I I I I I I I I I I I 56 Figure Page 33. The long term response of the slack strain at the 6% Strain lwel I I I I I I I I I I I I I I I I I I I I I I I I 56 34. The long term response of the slack strain for all strain levels (standard errors have been relieved for clarity) . . . 58 35. A typical plot of a stress-strain curve plotted on log- -logaxes,withthefittedcurve. .............64 36. A typical plot of a stress-strain curve plotted on linear axes,withthefittedcurve.................64 37. The initial response of the power coefficieit A for the 2% Strain lmlI I I I I I I I I I I I I I I I I I I I I I I 60 38. The initial response of the power coefficient A for the 3% Strain lag-I I I I I I I I I I I I I I I I I I I I I I I 66 39. The initial response of the power coefficient A for the 4%strainleve1......... .......... ....67 40. The initial response of the power coefficient A for the 6% Strain IMII I I I I I I I I I I I I I I I I I I I I I I 67 41. The long term response of the power coefficient A for the 2% Strain ImelI I I I I I I I I I I I I I I I I I I I I I I 68 42. The long term response of the power coefficient A for the 3% Strain lwele I I I I I I I I I I I I I I I I I I I I I I 68 43. The long term response of the power coefficient A for the 4% Strain IMI I I I I I I I I I I I I I I I I I I I I I I 69 44. The long term response of the power coefficient A for the 6%strainlevel... ......... . ........ ..69 45. The initial response of the power coefficient B for the 2% strain ImelI I I I I I I I I I I I I I I I I I I I I I I 74 46. The initial response of the power coefficient B for the 3%strain1evel........ ....... . ....... 74 47. The initial reSponse of the power coefficient B for the 4% Strain lmlI I I I I I I I I I I I I I I I I I I I I I I 75 48. The initial response of the power coefficient B for the 6% Strain lmlI I I I I I I I I I I I I I I I I I I I I I I 75 49. The long term response of the power coefficient B for the 2% Strain ImelI I I I I I I I I I I I I I I I I I I I I I I 76 vi Figure . Page 50. The long term response of the power coefficient B for the 3% Strain IMI I I I I I I I I I I I I I I I I I I I I I I 76 51. The long term response of the power coefficient B for the 4% Strain 1%. I I I I I I I I I I I I I I I I I I I I I I 77 52. The long term response of the power coefficient B for the 6% Strait! lWeII I 'I I I I I I I I I I I I I I I I I I I I I 77 53. The long term response of the loading power coefficient B for all Strain 1mg. I I I I I I I I I I I I I I I I I I I 78 54. The long term response of the unloading coefficient B for all Strain lwelsI I I I I I I I I I I I I I I I I I I I I I 78 vii LISTOF TAKES Table 1. 12. 13. 14 . Names of Tendons, Initial Lamgths, and Cross-Sectional Page AreasfortheSuccessfulTests...............23 Results for the Peak Stress , Loading and Unloading Maximun Tangent Moduli (L-M.T.M. and UL-M.T.M., respectively) at the First and Fifth Cycles; and the loading Offset Strain at we Fiftkl CYCIe O O O O O O O O O O O O O O O O O O O O O Significantdifferences Between Strain Levels for the Peak Stress means, and the loading and Unloading Maxim Tangent Moduli (M.T.M.) neans for the First and Fifth Cycles . . . . Rqaeated Measures results for the Peak Stress, Loading and Unloading Maximum Tangent Moduli between the First and Fifm CYCIeS I O O O O O O O O O O O O O O O O O O 0 Stabilization Times (sec.) for the Peak Stress, and the loadingandlmloadingMaxinanangentmduli . . . . . . Statistical differences of the Stabilization Times Between Strain Levels of the Peak Stress, and the loading and UnloadingMaxinanangentModuli............ HfiteISis mta (%) O I O O O O C O O O O O O O O O O O 0 Repeated Measures for the Hysteresis . . ........ Significant differences Between Strain Levels for the Hwtera is O O O O I O O ..... O O O O O ........ mults for me Sth Strain ( % ) O O O O O O O O O O O 0 Significant differences Between Strain Levels for the for me Sth strain 0 O O I O O O O O O O O O O O ..... RepeatedMeasuresfortheSlackStrain. . . . . . . . . Mean Proportional Ranges of the Slack Strain (%) . . . . Awuts -mval‘m (in MPaX10-5). o s o o o o o 0 viii 27 29 30 33 35 45 48 51 50 59 60 62 65 Table 15. 16. 17. 18. 19. 20. Significant differences Between Strain Levels for A. . queatedMeasuresforA. . .............. ResultsforB(imitless)............... MeanProportiaanangesinB(%)....... . .. Significant differences Between Strain Levels for "B. . RqaeatedMeasuresforB................ Pmma¢ ic Raults O O O O O O O O O O O O O O O O 0 xi Page . 70 I. IN'JRODLKH'IQJ meledge of the mechanical response of connective tissue is necessary to may areas of medical science. Workers in sports medicine, orthopedics, prosthetic develognent, and related fields all require a thorough understanding of how mnnective tissues respond under physiological and injurious conditions. Beginning in the 1960's, the mechanical behavior of soft connective tissues, such as tendons and ligaments, have been studied using the experimental and analytical techniques of materials science and continuun mechanics. Works by thg [1], Viidik [2,3], Crisp [4], Rant and Little [5], Butler, et a1. [6], and Harmless [7] all have reported non-linear, viscoelastic responses for collagenous tissues, nanifested in a sensitivity for deformation rate and previous deformation history. A smmary of the known nechanical response of collagenous tissues follows. Cmnective tissues, such as tendons and ligaments, consist of extracellular constituents including: collagen and elastin fibers, and a natrix or ground substance. A definite relationship has been found between the structure of these constituents and their function [Viidik-3 ] . Experimental evidence is not conclusive on the mechanical role of the ground substance [Yannas—S, Parington and Wood—9]. However, a recent study by Rant [10] indicates that the ground substance in tendon may contribute significantly to its energy absorbtion. In the literature, it is generally agreed that the major stress-bearing canponent of connective tissues are the collagen fibers, and that the function of the elastin fibers are to bring the tissue back to its original shape when the load is renoved. In 2 tendon, collagen fibers are essentially parallel to the long axis of the tendon, and are wavy or helical when not transmitting load. Collagen makes up approximtely 75% of the dry weight of a tendon, while elastin only 5% [Elliot-ll]. The stress-strain curve for a tendon is ccmnonly divided into four regions, shown in Figure 1 ”raider—61. As the tendon is first loaded, the lax collagen fibers are not yet straightened, so the mechanical response is due to the elastin fibers (Region I). The degree of strain for which the individual collagen fibers becane straight and begin to bear load varies fran fiber to fiber [Dianant, et al.912, Viidik-13]. Thus, as the tendon is extended further, the tissue beam successively stiffer (Region II). II'nis region will continue until all fibers are straightened, and then a region of apparent constant stiffness begins (Region III). Further extension beyond this region will cause successive fiber rupture and tendon failure (Region IV). 'lhe mechanical response of tendons is iupressive: they have an ultimte tensile strength of about 50-100 MPa, and an elongation to failure of 15%-30% [Viidik-2]. These figures can be canpared to an alnminiuln alloy, for which these parameters are 210 MPa and 12%, respectively. The exposition of ligaments varies fran predominently collagenous (e.g. cruciate ligaments of the knee) to predaninently elastic liganent (e.g. ligamentun flavun of the spinal column). Figure 2 shows typical stress-strain curves for tendon, and collagenous and elastic ligaments . 'Ihe lower stiffness and greater REGION 4 DECREASINC STIFFNESS. FAILURE REGION 3 HIGHER. CONSTANY STIFFNESS (D U) Lu e p_. U) REGION 2 INCREASING STIFFNESS REGION I LOW. CONSTANT STIFFNESS I STRAIN Figure l - 'lhe four regions of a typical stress-strain curve for tendon. / / TENOON COLLAGENOUS LIGANENT , , I ,’ / U) (I) Lu CZ ,— m ELASTIC LIGAMENT STRAIN Figure 2 - Typical stress-strain curves for tendon , and collagenous and elastic ligaments. 4 elongation of tissues which contain more elastin are due to a much lower stiffness of the elastin fibers. The viscoelastic character of tendons and ligaments is evident in their strain rate, relaxation, and creep behaviors. The general effect of strain rate is an increase in stiffness with an increase in strain rate, as seen for tendon in Figure 3. ln relaxation, there is an initial rapid decrease in load, then the decrease in load becanes successively slower as tine increases. Several authors [Haut and Little-5 , Fung-l4 , Jenkins and Little-15] have reported an increase in relaxation (initial peak minus an apparent equilibrium load) with an increase in the peak load achieved in the relaxation test. A linear relation has been found between the normalized load (normalized load equals the current load divided by the initial load) and the logarithim of time [Rant and Little-S, Hubbard, et al.-16, Little, et al.-17], in which the slope is a measurement of the degree of relaxation. In creep, tendons and ligaments show a time behavior similar to relaxation, with the strain rapidly increasing initially, 100% PER SECOND 1% PER SECOND STRESS 0.01% PER SECOND STRAIN _ Figure 3 - The effect of varying strain rate on tendon. 5 than increasing less with time. Cohen [18] has reported an increase in the degree and rate in creep with an increase ofrlcad for the human _f_l;e_x_or__ digitorum tendon. . ‘Ihe mechanical properties of tendons arnd ligaments, like all collageneous tissue, are dependent on their previous mechanical history. This dependence becames apparent in recovery and preconditioning stability. Recovery is a tendency for the tissues, after a defamation history, to revert to their previous response after a waiting period. 'Ihe precise cause and character of recovery is not Innown, however Woo, et al. [19] stated that one hour was appropriate for recovery of the canine Leia]; collaterial ligament at low strains and strain rates (less than 2.5% and l%/s, respectively). Preconditioning is a property of collagenous tissues that, after a small number of repeated ectensions, the tissue's response is stable (i.e. repeatable) from cycle to cycle. This concept is consistent with the thought that when people perform sale activity pattern, after a (arm-up period, they experience an apparently stable performance of their connective tissues. ‘lhe mnost rapid changes in mechanical response occur during initial preconditioning [Viidik—2 I . There is a drop in the peak load and hysteresis, as well as an increase in the maxinmm stiffnas. It has been conjectured [Viidik-2, Hubbard, et a1.-16] that these changes could be attributed to the upgrading of the parallel alignment of the fibers, as well as a partial redistribution of the ground substance, including vater. However , experimental verification for these explanations are lacking. 6 The stability of the mechanical response following preconditioning is not completely supported by the literature. Fung [1] has stated the need to keep the preconditioning chta (e.g. the initial 20 cycles) because of the insufficent understanding of the phenomenon. In a primate spinal ligament study‘conducted by Little, et a1. [20], a test protocol was used that included preconditioning for 10 cycles at l%/s, with preconditioning stability check cycles throughout the test. Their protocol also included single and cyclic extensions and relaxation tests. A consistent decrease in the peak stress and tangent modulus occured throughout the test sequence (the peakstressdecayedoftencbwntosoitofthepeakvalueinthe preconditioning cycles). The ligamentum flavum, tested along with other more highly collagenous ligaments , showed smaller decreases in the tangent modulus and peak stress, probably due to the predominance of elastin in the tissue. Hubbard, et a1. [16], in their study of tendons from hnnans of various ages, showed similar results. Their test protocol vas very similar to the spinal ligament protocol, with strains not exceeding 7%. Results showed statistically significant (p=0.05) decreases in the peak stress, with the final value (at 9600s) of approximately 65% of the peak stress at the end of preconditioning. The maximum tangent modulus also decreasedtoafinalvalueofabout85%of itsvalueat the end of preconditioning. Clearly, stable responses d) not appear to be reached in the testing protocol used in the above two studies [16, 20]. Several authors have mathematically modeled the mechanical properties of tendons and ligaments, led by Fung [1] who proposed the 7 use? of quasi-linear viscoelastic theory to model tissue responses. This approach was based on an earlier modeling of the time dependent elasticity of rubber [Guth, et al.-21]. Haut and Little [5] used Fung's approach to model rat tail tendons, an almost pure source of collagen. The theory ‘68 adequate to describe strain rate dependent properties, but in the case of sinusoidal cyclic extensions (run for 15 cycles), it did not agree well with the experimental data. It predicted a much lower peak-load and rate of. decay of the peak-loads with time when compared to the experimental chta. Similar conclusions were made by Jenkins and Little [15] in the study of the ligamentum mirage, a predominently elastic ligament. Woo, et a1. [19] utilized Fung's theory to model the medial collateral ligament. The test protocol began with preconditioning the sample by cycling it 20 times at a constant strain rate of 0.1%/s, then waiting a one hour recovery period. The sample was then tested at 3 strain rates (.Ol%/sec, .1%/sec, and l.0%/sec), with a final check loop at .01%/sec, with one hour periods between each test. Although agreement between theory and experimental data was generally good, in cyclic tests (run for 10 cycles) the theory predicted higher peak and valley stresses than experimental data as time increases. If the cyclic tests had been run longer, the theoretical predictions of Woo, et al., [19] would probably have continued to deviate more from the experimental (hta. Recent models for parallel-fibered tissue have taken a micro— structural rather than a phenomenological approach. Lanir [22] assumed that the non-linear response of the tissue is due to the varying lengths of the collagen fibers. He developed a model which utilized a function of the distribution of fiber lengths, and assnmled 8 the wavy collagen fibers were linear viscoelastic and are arranged in a planar configuration, with the linear elastic elastin fibers being the sole recrimping agent. A similar model was used by Little, et al. [17] to model spinal ligaments from primates where good agreement was found :hn the (exunzuu: strain JEHIB tests. Iknewer, Iiuar dud xxx: attempt to model the relaxation or cyclic creep tests also done.in the project. The above models do not adequately predict the response to cyclic elongation. Yet, the responses of tendons and ligaments to cyclic elongation are central to» their biological function. Duringr the course of cannon activities, people subject their connective tissues to numenous cycles of load and. ékfikmmation. Playing musical instruments, repetitive work tasks, and sporting activities result in several thousand cycles of mechanical demand on connective tissue. The experimental eta for cyclic loading is ectrenely limited. Most of the existing chta is only for short time periods, and only one study by Rigby [23] dealt with long term cyclic extension (greater than 1600s) . However, Rigby' s reults for rat tail tendons indicate an initial drop in the peak stress, than a continued rise to the end of the tet (38hrs), conflicting with other studie. The generally poor agreelent between available models and existing cyclic data further indicate that the mechanisms involved in cyclic loading are poorly understood. This inconplete understanding of both cyclic response (short and long team) and.preconditioning stability, has lead to the present study. In this study, basic information about the stability of the reponse of collagenous tissue to long term cyclic extensions was 9 sought. Three specific quetions were addresed: 1) Do connective tissue repond in a consistent or stable manner to repeated extensions? 2) Does stability occur at same levels of cyclic extension and not at others? I 3) Are response after many cycle qnnlitatively different from the first few cycle? 10 II. MATERIALS AND ME'IHOIB A. Sample Preparation Tendon sample were obtained from the hindlimbs of dogs sacrified after veterinary school surgery classe. All hindlimbs were either dissected within a few hours, or refrigerated whole (at 4°C) and dissected within 3 days. The tendons were carefully rembved to avoid damage by excessive pulling or by nicking with a scalpel. They were usually can: near time bone insertion point and at the muscledbemkxn interface. If the tendon passed over a joint it usually was flared and such a tendon was cut approximately midway in the flared region. The following tendons were used: fibularis longus, flexors digitorum superficialis and profundus, and extensors digitorum l_on_g§, lateralis, 95.115”: and camnunis. These were chosen for their regular geometry, with at least 40 mm of apparently constant cross-sectional area. Thick tendons with diameters greater than 5 mm were avoided, since it was thought that large cross-sections would not insure unifonm.gripping of the interior fibers during testing. Upon nxmrnmflq, each Izemkxn was numnxxei in an paper txnxfl. soaked with Ringers lactate solution (see Appendix A) and sealed in a small plastic bag. Groups of tendons from each cbg were put in a larger bag, and these larger bags were put in air-tight containers and stored at —70°C. This method of packing was used to prevent sample dehydration and decay while frozen. B. Tasting Equipment Tets were performed utilizing an lnstron* servohydraulic materials teting machine, which could be computer controlled. The *Model 1331, lnstron Corp, Canton Mass. ll actuator was mounted in the upper crosshead and the load cell was mounted within the immersion bath, between the lower grips and the lower crosshead. By having the load cell not mounted between the upper grips and the actuator, noise in the load signal from actuator motion and vibration was greatly reduced. The actuator has a maximum travel. rate of 1 m/sec, more than ample for these tets. The load cell used was a fully subtersible Interface SST-100.}48 N (100 pound) cell. An immersion bath was used to facilitate a physiological environment, and eliminate any chance of tissue drying, which would drastically affect the mechanical reponse. Gripping, often a difficult problem in soft tissue teting, was done by cenenting waterproof 100 grit silicon sandpaper to the grip's inner surfaces. The grips were a simple clamp type, with a gripping surface dimension of 15 mm x 20 mm. This provided ample friction without damaging the sample. Histology dnne on preliminary tets showed the fibers within the grips to be continuous and carpresed together , but neither torn nor fractured. The omputer used for tet control and data acquisition and analysis has a Digital Equipnent Corp. PDP 11/23; coupled to the computer were 2 R101 hard disk drive, and 2 RXOZ floppy disk drive. An lnstron bechine Inteface unit enabled camand and data cmnmmnioation between the computer and the teting machine. Data has displayed using a Tektronix 4010-1 graphics terminal and a Printronix P-300 high speed line printer. The graphics routine utilized was MLLPLT [29], a powerful data-file based program. [eta vas also monitored and stored on a Nicolet digital oscilloscope, which had a mini-floppy disk for data storage. 12 c. Test protocol Throughout the preparation and testing, the sample were kept either fully moistened or immersed in Ringers lactate solution at room temperature (22°C). Tet preparation began by first removing a sample from the freezer, then placing it still wrapped in the towel into a container filled with Ringers lactate solution at room temperature. The sample was allowed to sit in the container for a minimum of 15 minute for canplete thawing and any osmotic procese to stabilize. The paper towel was retoved and the sample placed on a plastic dissection tablet. Next, the tendon sheath was removed with great care to insure no fibers were damaged. 'me sample was marked with Nigrosin dye approximately every 5 mm, so that deformation and any grip slippage that may have occured could be measured photographically. The tendon sheath was removed because it is not rigidly connected to the tendon fibers and hence may not closely follow fiber movelent. Teting began by mounting the prepared sample into the upper grip, then lowering it into the lower grip and securing it. The front cover plate of the immersion bath was monmted and the bath filled. With the sample slack, the load reading was electronically zeroed by adjusting offset controls on the lnstron load controller. Carefully monitoring the load signal on the Nicolet, the sample was slowly extended until a load of 0.004 N (typically a stress of 2 KPa) was achieved, the smallet load measuresble by the equipment. The length of the sample at this point was taken to be its initial length, and a photograph was taken. The values for the initial length, strain level 13 required for teting, and the carputer file names were entered into the teting progam for computer control. The teting involved cyclic extensions at a constant rate, with the maximum extension held constant. Maximum strains of 2%, 3%, 4%, and 6% were chosen to study strain level sensitivity. Strain rate sensitivity was not investigated in this study, and a censtant rate of 5%/s was chosen as an intermediate value between rapid and slow physiological movenent. A constant strain rate was chosen to eliminate strain rate effects, and to allow a constant number of data sample per percent strain so all strain levels could be analyzed identically. However, by fixing the strain rate, the frequency and total number of ectensions varied between strain levels. For the total tet time of 90003, this method reulted in frequencie and total number of extensions of: a) 1.250 Hz and 11,250 cycle at 2% strain b) 0.825 Hz and 7,500 cycle at 3% strain c) 0.625 Hz and 5,625 cycle at 4% strain d) 0.417 Hz and 3,750 cycle at 6% strain Upon test completion, the sample was then extended until a load of 0.004 N was achieved. This was considered to be the final length, and a photograph taken. The sample was then removed and placed into a sealed container filled with Ringers lactate and refrigerated at 4°C. D. we Aquisition, Storage, and Analysis Groups of raw data were taken throughout each tet approximately every 70 seconds. Each raw data group consisted of an array of 2,080 data pairs of load and deflection values taken every 6 milliseconds for a total of 12.48 seconds. In order to have continuous l4 load—deflection data for later analysis, the first raw eta group and one group every half-hour were written to a raw data file on a hard disk. A subroutine analyzed each raw data group and generated the following values for each complete cycle within the group: 1. time, deflection, and load value at the load peak 2 . loading and unloading energie 3. maximum loading and unloading stiffnese These values from each data group were written to a summarized data file on a hard disk. The peak deflection value were not recorded because these values are virtually identical to the deflection at [the load peak, except for a short time lag due to the viscoelastic propertie of the tendon . The energies were calculated from the areas under the load-etension curve, utilizing a simple rectangular-rule area approximation algorithm. This method was chosen as the most direct, and elimanated the need to preuppose an analytic behavior of the load-ertension curve. The maximum stiffnese were calculated with a linear regresion on the last 19 data pairs before the load peak and on the first 19 pairs after the load peak. The 19 data pairs correponded to the final .57% strain of extension for all tets. A 19 data point ”window“ was used because it was large enough to filter out the noise in the load-ectension curve, yet small enough to obtain an accurate etimate of the maximum stiffnes. Both the sumary and raw data files were constructed for plotting by MULPLT [24], a data file based ounputer plotting routine. The load peak-versus-time (hta were plotted on linear, semilog and log-log axe to see if the load peak-versus-time behavior followed a simple analytic function. 15 The stres peaks and the maximum tangent moduli (M.T.M.) were converted from the peak load and maximum stiffnes, repectively. The peak stres was calculated by dividing the peak load by the cross-sectional area. The maximum tangent moduli were calculated by the following equation : __ LO .MsTsMo - (m. Stfs) X law where Lo is the initial length, and A is the cross-sectional area. This yields a maximum tangent moduli expresed in MPa per percent strain. The stability of the stres peaks and the maximum tangent moduli were analyzed by a computer program. This program worked by acessing the summarized data file frcm a particular tet (which contains the above mechanical parameters), and calculating for each data group the mean value, mean time, standard error, and the number of sample for the mechanical parameter considered. It then-cmpared the mean value by checking to see if any two mean values considered were different, doing so in the following manner. Starting at the beginning of the sumary file (i.e. the beginning of the test), a particular data group was successively culpared to each following data group in order to detect the last data group that was not different from the particular data group. Several different criteria were need to tet for a difference between the two means: a t-test at p=0.05 [25], which assumed the means had the same population distribution and used a pooled etimate for the standard error, and the difference between the 16 two means being within either 1%, 2%, or 5% of the initial value of the mechanical parameter considered. The latter method vas chosen so the time of stabilization could be related to the total change of a mechanical parameter cccuring in each test. The objective of the canparison was to find the last data grow whose mean value was not different from the mean value of the data grow considered, for each of the above criteria. The program created a file of the mean times for each data grow within the summary file, and the last data group not different for each data grow, for each criterion. The stabilization program allowed canparisons of the time for stability of a mechanical parameter between both different strain levels and the different criteria within each strain level. For a given criterion in a particular test, the more stable a mechanical parameter was, the sooner in the test the data grows would have the time of the last not different data grow equal to 90008 (2.5 hrs, the total time of the test). For ease of analysis, the time of the last data grow not different vs. the time of the data grow considered were plotted by MULPLT‘, an example shown in Figure 4. The ectrenes of the curves can range front a diagonal line to a horizontal line at 90008. The first ectrene curve would indicate a canpletely unstable parameter, since each data grow would be different from all succesive grows. The second would indicate a completely stable parameter , since all éta grows would not be different frcm each other. Indicated on the plot are the times where the chta grows were no longer different from the last 5400 - - 5400 a . . 9 1 3' :3 3600 J L 3600 F0 . 1 " A - m - - m . » 9 ' o - r TEST CRIT. : J A - 2% GRIT. _ -' V - 5i CRIT. 0 l I I I I 0 2 3 4 5 6 PERCENT STRAIN Figure 10 - Stabilization times for the peak stress. 35 TAKE 6 - Statistical differences of the Stabilization Times Between Strain Levels of the Peak Stress, and the Loading and Unloading Maximum Tangent Moduli* Strain Level Interval Tested” 6%-4% 6%—3% 6%-2% 4%-3% 4%-2% 3%-2% Peak Stress t-test Criterion N- N N N N N 2% Criterion Y Y Y N N N 5% Criterion Y N Y N N N L-M. T.M. t-test Criterion Y Y Y N N N U-M.T.M. t-tafit Criterion Y Y Y N Y Y *Behrens-Fisher test (p-0.05) using Coclnran and Cox estimates for the critical values [27]. **N indicates no significant difference, Y (hes. 36 the large scatter in the data makes conclusive trends from the statis— tical results difficult to obtain, there is an overall rise in stabi— lization time with an increase in strain level for the peak stress. C. Loading and Unloading Faximum Tangent Moduli Figure 11 shows a typical loading and unloading Maximum Tangent h Moduli (M.T.M.)~vs.-time plot. In the loading M.T.M., an initial increase occurs, then agradual decrease continues to the end of the test, similar to the behavior reported for human tendon [Hubbard-16 ] . The unloading M.T.M. decays rapidly at first, then continues to more slowly. Figure 12 shows these curves plotted on semi-log axes. Similar to the peak stress behavior, a linear behavior (hes not occur, although the latter part of the data appears to becane somewhat linear. Because of this non-linearity, no curve fitting was done on the M.T.M. data. The results for the M.T.M. data are listed in Table 2. These results are canparable to hman tencbn [Hubbard-l6], which have value of 6 MPa/% at 7%: strain and for primate [Selke, et. al.-28], which has a value of about 7.7 MPa/% at 5% strain. Figure 13 shows the loading M.T.M. means plotted against strain level for the lst and 5th cycle. A sharp rise occurs at the 4%-3% interval, with the 6%-4% and 2%-3% intervals retaining relatively constant. The means at the fifth cycle are greater than the lst cycle for all strain levels, with larger increases at higher strain levels . Statistical differences for the loading M.T.M. , listed in Table 3, occur only at the 4%-3% and 4%—2% intervals. An explanation for this could be that the 4 and 6 percent strain levels lie within 37 TIME (SEC) 0 1800 .3600 5400 7200 ' 9000 1.m 'J J I l I I '4' l lLLLl I l | [4114' l l I l ' 1.00 U - LOAD | N G _ I - UNLOADING E S L: 2 U A E a: CL 3 0: w R 0- :0 PE :2. 2 :3 V R z z T— 0.60 T I r I l—I I I l I I I I I l I I i I I ' T‘Ii' T I l I 4 0-60 0 1800 3600 ‘ 5400 7200 9000 TIME (SEC) Figure 11 - A typical loading and Imloading Maxiimm Tangent Moduli (M.T.M. )-vs.-time plot. LOG (TIME) 0 I 2 3 4 1.10 ' g I l I l l l 1 1o /LOADING r C 1.00 - 1.00 2 II 0 A :3 0 ' 3': ‘2’ R E 0.90 - — 030 O v z . / 5 h UNLOAOING ' E 2 A a 0.80 - - 0.80 E N _. E is ‘ ~ 3 o l 2 0.70 - - 0.70 v 0.60 e l 1 l T I r 0.60 0 I 2 3 4 LOG (TIME) Figure 12 - A typical loading and unloading Maximum Tangent Moduli (M.T.M. )-vs._lw tine plOt. 38 PERCENT STRAIN .3 4 5 - 6 12 I l I I I 12 'I I' 11. O - FIRST CYCLE I- 11 10- o - FIFTH CYCLE -10 A 4 I. z E 9‘ '9 -—I 1.11 'I ' 8 I O 8 - A a T - 5 CL 7-I I-7 > J .- OP 1: a ‘ . 27 a. I- ; 5. . b 5 a v +_ _4 (t3 2 4 - u C 3- -3 3 £ 4 b w 21 L2 1- —1 J . 0 0 q .- u- - .- PERCENT STRAIN Figure 13 - The loading Maximum Tangent Moduli (M.T.M.)-vs.-strain level for the first and fifth cycles. 39 Region III, where a constant stiffness occurs. However, the occurance and precise definition of this region for these tests are beyond the present study. The lack of a statistical significant difference at the 3%—2% interval could be due to a lower signal-to-noise ratio for the load-deflection signals for 2% strain than those at 3% strain. The M.T.M. data are mlculated from these signals, and a larger proportional error in the signals for 2% strain would induce a larger error in the M.T.M. data. Repeated measures for the loading M.T.M. listed in Table 4, show significant increases between the lst and 5th cycle for all strain levels. These results indicate substantial stiffening of the sample within the first five cycles at all strain levels tested. Means for the unloading M.T.M. for both the lst and 5th cycles are plotted in Figure 14. Again, a large increase in the mean value occurs at the 4%-3% interval at both cycles. Also a decrease in the means can be seen at all strain levels frcm the first to the fifth cycles. Statistical results, taken from Table 3, indicate significant differences occur only at the 4%-3% and 4%-2% intervals. The significant differences cccuring only at these intervals could be explained by a lower signal-to-noise ratio at 2% strain as proposed for the loading M.T.M. Repeated measures results for the unloading M.T.M. , listed in Table 4, indicate significant differences between the lst and 5th cycles cccuring at the 2%, 3%, and 4% strain levels. Precisely why the 6% unloading M.T.M. (hes not change significantly from the first to the fifth cycle is not known. It is possible that the same mechanisms previously mentioned that caused a lower peak stress also 40 PERCENT STRAIN 12 --12 11- -11 10- -10 A 1 ’ 8- -a E « . 2‘ CL 7- '7 g m " - é 5' '5 a v 4" P4 (1% 2 I . r3 5 3d -3 :I < 0- FIRST CYCLE . V 2‘ b2 ‘ .- FIFTH CYCLE " o I I l. I l 0 2 3 ' 4 5 6 PERCENT STRAIN Figure 14 - The unloading Maximum Tangent Moduli (M.T.M.)-vs.-strain level for the first and fifth cycles. . ‘ 41 muse the unloading M.T.M. to remain relatively constant between 4% and 6% strain. In Figures 15 and 16 the loading and unloading M.T.M., respectively, are plotted against the offset strain at 5th cycle taken fram Table 2. The overall trend is very similar to the peak stress response; a decrease in the range of the offset strain occurs with a decrease in strain level. The similarity is mostly due to the fact that the offset strain values are identiml in all the offset plots. A linear regression on both the lmding and unloading M. T.M. indimtes that the slopes are statistimlly different from zero, showing a definite increase in both loading and unloading M.T.M. with an increase in strain level. Similar to the peak stress data, plotting against the offset strain does not reduce the smtter, implying that variations in pretest conditions does not fully account for the smtter in the M.T.M. data. Stabilization times for the M.T.M. are listed in Table 5, and are shown in Figure 17. The results for the 1%, 2%, and 5% difference criteria were eliminated bemuse of noise in the M.T.M.-versus-time curves: generally a difference of about 5% was needed for a statistiml significance. The t-tests results indimte a rise in stabilization time with an increase in strain level. Also, the unloading M.T.M. appears to take longer to stabilize than the loading M.T.M. Statistiml results, listed in Table 6, indimte that only at the 6% strain level are loading M.T.M. results signifimntly different from the other strain levels . The unloading data indimte that both the 6% and 2% tests are different from the other strain levels. The large data smtter in the M. T.M. mta probably masks the more subtle MTM (MPA PER PERCENT) 42 OFFSET STRAIN (PERCENT) 0 ,1 2 3 4 s 8 ,2 I I I I I 11- .2. 10" D )- 9-1 A. I. 8‘ 9. h . A C] . 7- o 0 D .. ‘ r 6- O - . ' A _ 5.. 9 .. 4- ' '_. - CI . 3- - ‘ . A D I- 2" o - 6x STRAIN )- ‘ 4-41:STRAIN~ 1" {AA A-SSSTRAIN— ‘ O-ZXSTRAIN- 0 r I . I r I 0 1 2 3 4 5 6 OFFSET STRAIN (PERCENT) —a I... a” MUQAUIOONJNIOE; d O (lNBO‘dBd 838 WIN) mm Figure 15 - Lmding Maximum Tangent Moduli (M.T.M.)-vs.-offset strain Figure 16 - Unloading Maximum Tangent Moduli '\ MTM (MPA PER PERCENT) at the fifth cycle. OFFSET STRAIN (PERCENT) 0 1 2 3 4 5 6 13 I I I I I 12 - D L 1 A I. 11- __ . O 0 _ 1° 1 A 4 9 [:1 CJ " 9- _ a -‘ 9 L 7- . A 4 '_ 0 - T '_ 5 - L . ' c1 . 4- _ n A I- 3 - . CI .. 2 - I: - ax sTRAIN '_ -- . 0 - 4: STRAIN P 1- Q4 A - 3: STRAIN _ 4 o - 21: STRAIN . 0 I I I I I 0 1 2 3 4 5 6 OFFSET STRAIN (PERCENT) strain at the fifth cycle. 10 nuauonxnmu) 0.... (11130838 838 mm) mm (M.T.M. )-vs.—offset 43 PERCENT STRAIN 2 3 4 5 6 I _ J 1 J I 9000 - ‘ 9000 j 0 - T TEST: L0A0INc NTN : - 4 - T TEST: UNLOADING IIITII __ A 7200 J ' - :- 7200 o « I . g m . - 3» U) C - 9 V q - C LAJ q P ‘ N 2 5‘00 " T 'P - 5400 3 '— 1 . . (5 s - I .. e E .36 ‘ r“\ - 2;: E 00 t '1 _- 3600 F11. a _ :- f; g Ni '- (lg V’ 1800 - - 1800 V o ‘1 I 1. -_ o - - - - _ PERCENT STRAIN Figure 17 - Stabilization times for the loading and Tangent Moduli (M.T.M. ). I E T E 44 trends in the data. However, the above results imply a signifimnt rise in stabilization time at 6% strain for the loading M.T.M. , and an overall signifimnt rise in stabilization time with an increase in strain level for the unloading M.T.M. D. Hysteresis Results for the hysteresis data are listed in Table 7. Figures- 18-21 shows these values plotted for the initial response (the first data grow, corresponding to the initial 12 seconds of the test) for the 2%, 3%, 4%, and 6% strain levels, respectively. These results are comparable to human values of 15% - 45% [Hubbard—16], and to primate 19% - 38% [Selke, et. al.-27]. For all strain levels, a rapid initial decrease occurs, with slower changes at the end of the data grow. The initial hystersis ranged at 40%-47%, then drcped to about 17%-22% after 12 seconds for all strain levels. Repeated measures for the hysteresis data, listed in Table 8, indimte signifimnt decreases occur throughout all strain levels during the initial 12 seconds of testing. Figures 22-25 are plots of the long term response for the hysteresis for the 2%, 3%, 4%, and 6% tests, repectively. The first and last cycles in the first data grow are shown on these plots as coinciding. All strain levels show a sharp decrease between the last cycle in the first data grow and the cycle at 18008, and apprmch a value of about 17% by 90008. Repeated measures for the hysteresis, listed in Table 8, reveal that signifimnt changes occur between 128 and 18008, but almost no signifimnt changes after 18008. It appears that signifimnt changes in the hysteresis occur only in the initial 18008. A future investigation of the initial 18008 would be necessary 45 H5.N co.ma mm.m mo.c~ mm.ha mecca mH.N ob.me m~.m ma.¢e mm.o co.cm mm.o mm.be .ncewa he.me mm.~ mm.va Nh.m mm.mH om.m mH.mH moovm mm.~ Hp.¢~ mm.N ~m.mH mm.m ma.o~ mv.m 05.5H mcoma mo.m He.sa m~.o oh.mm oe.m mm.- mNH eh.m we.ma m¢.m mo.ma mm.h Ho.mm mo.m ma.m~ ma cacao me macho lav nuns nenuuunmm I 5 money Hm.m mN.H~ NH.v mm.m~ mo.m mo.Hm mm.m «H.h~ «a macho hm.m mm.mm Nh.h hN.N¢ H<.m mm.h¢ ~¢.m mo.~¢ an macho .nme en nnsooo pecan reuse use .nennu ensue sateen we use upe+ .m.m aw .m.m we .m.m am .m.m mm Figure 18 — The initial response of the hysteresis at the 2% strain Figure 19 - PERCENT HYSTERESIS level. CYCLE NUMBER 1 2 3 4 5 8 7 8 10 60 l I I l l l l l I I 50 - .. e .Z '_ (J) Lu 1 . E.) 40 -I P - U) - | . >— I ..I ‘ .- 5 . - “J 30 _ _ U . . 0: U _ - O. 20 - _ no ..ll'l'll'. The initial response of the hysteresis at the 3% strain level 46 CYCLE NUMBER 87'89101112131415 12345 I Lllllllllll l I I IIIII'V'IIIIIIIIV IIII'lIIIIIllIlIlll'lllI'll!IIIIIIIIIIIIIIII'TIIIIIIIIIIIII O 1 2 J 4 5 6 7 8 9 IO )1 TIME (SEC) 12 0 1 2 3 4 5 6 7 8 9 TIME (SEC) 10 H 12 20 8938315114 1N3083d SIsaaalSAH 1N3083d 47 CYCLE NUMBER I 2 3 4 5 8 7 8 80 J. 11 l l I L 60 A — J . 50 -' b 50 m I b a - - .8 Lu . :0 o: ’ 0 on . z >- P ‘1 I ‘I w— I '2 * I 3 In 30 -I - 30 m 0 . :0 a: ’ "T m U) (L j ’ L7) 20 - I.- 20 - b '0 UUT'UVIIUTVIU'UV'ThIIIYIUIIIIIIUFUV'IIIU'YIIIFIIU'IIUT ‘0 0123456709101112 TIME(SEC) Figure 20 - The initial response of the hysteresis at the 4% strain level. CYCLE NUMBER 1 2 3 4_ 5 60 I If I I l 60 4 I- - h- 1 . 50 d -'50 -I I- n - - r8 3 . t 17 °‘ 91 t; 40 - 4O 2: d I- .9 E - :r .< e ‘ I- a w 30 - — 30 m o 23 a: ‘ ' "1 nu .. _ ‘2 Q. U) 4 I- 20 - — 20 4 b d - . I- ‘0 'U'Ul'W'U'ITIIIUUITIIUVI'U'IIIVU'I'IUVUII'88'6'18'186'18818 '0 0 1 2 J 4 5 6 7 8 9 10 11 12 TIME (SEC) Figure 21 - The initial response of the hysteresis at the 6% strain evel. 48 moooml mNH z z N z z z z z mecca! moooml mcoma mocmh .mma um musuoo macho :umam may .mummu Hw>wa cflmuum we ms» ypm+ .88 x .88838 “333.53 8 8....865 z .221“ Jamaica... 2 z z z z z z z moomhl mcowml moovm mcomm «mwmoumummm may uOm mausmmmz_uoum®mmm I z w 2 z mcomml mccma w .M w M. mccmHI mNH u w w a a w w » mma n mam m maomu mwapzo m mdm¢9 mum and mmaomu mmanmo mo mv wm «N 49 CYCLE NUMBER 2250 4500 0750 9000 11250 60 l . l k L . I 1 l 4 .1 60 so - " b so 9 .3 b r? m - E .0 “’ ' § q "' ‘0 :3 L - ‘3" E - — 5 ’i ‘ ’ 2’. m m m _. 1 1. ‘fi ‘0 fifiI ' I I I I I ‘rT I l I Irr I r1 I 'I’ I I IWT '0 0 1&0 3000 5400 7200 9000 we (see) Figure 22 - 'lhe long term response of the hysteresis at the 2% strain level. CYCLE NUMBER 0 1500 3000 +500 6000 7500 60 i L l l L L L L L 80 50 -' .— 50 q " I a - - a U 4 1. 23 ea 4o 8 w - - g, ..L _ 5 I - 0 - 3 E d b a m 30 -' _ '- 30 I"'I o J 1 . .33, 95 _ 4 I _ <9 a 1’ _ m 20 J L - 20 J " .. . r 1 1- ‘0 rTTrT I II I l I r. I I I I I rI I ' I I rI—I I r! I '0 0 1000 30m 5‘00 7200 9000 TIME (see) Figure 23 - J'Ihe long term response of the hysteresis at the 3% strain 50 CYCLE NUMBER 0 1125 2250 3375 4500 5625 J .- w - ll - w <2 L L r3 8 < ‘} '- g or. LA.) 40 -I v— 40 m p— Z 9 L .- -1 I -I .. .— g r— 4 - _‘ E 30 - — 30 m o . - 2 85 .. .. e ‘L .. _ m 20 - 1 ' - 20 . 1 I 1 1 1 ‘0 ' I I rr I I I TI I I rl' I l’ I I l’ I I 'T I l’ I I I I I l ‘0 O 1000 3600 5400 7200 9000 mac (SEC) Figure 24 — The long term response of the hysteresis at the 4% strain level. CYCLE NUMBER 0 750 1500 i250 3000 3750 m l_._ l l L A; . A L l + 4 ' l l L w < r- 50 - T - 50 a - - 3 Lu - . . 70 :7. . - 5 E - . .. 5 E ' Jab . g: m 30 — 30 m 0 23 c: ‘ .. a E d - Us 20 -] — 20 - .N I I Ij—I ' 0 I . l I I ~ 10 I I I I—rI ' r Ij' I I rI I TI 0 l I I rrl ' T—Ij I I ' ‘0 0 1 500 3500 5400- 7200 9000 TIME (SEC) Figure 25 - 'Ihe long term response of the hysteresis at the 6% strain level. 51 to determine more precisely when the hystersis stabilizes within the initial 18008. Statistical results for differences between strain levels for the hysteresis, listed in We 9, indicate almost no significant difference between strain levels. Scatter my be masking out very small differences in hysteresis between strain levels, but present results imply the hysteresis behavior is essentially insensitive to strain level. TAEE 9 - Significant differences Between Strain Levels for the Hysteresis* Strain Level Interval Tested“ 6%-4% 6%-3% 6%-2% 4%—3% 4%-2% 3%-2% lst Cycle N N N N N N Last Cycle N N N N N N 18008 N Y N Y N N 3600s N Y N Y N N 90003 N N N N N N *Behren-Fisher test (p=0.05) using Cochran and Cox estiuates for the critical values [27]. **N indicates no significant difference, Y does. E. Slack Strain Table 10 lists the loading and unloading slack strain results for all strain levels. The initial loading slack strains are zero by definition; the sauple being at its initial length at the beginning of the test. Figures 26-29 show the initial responses (first 12 sec. of the test) of the slack strain at the 2%, 3%, 4%, and 6% strain levels, respectively. A general trend at all strain levels is that the differences between the loading and unloading (hta diminish with time. Also, succesive increases in the slack strain decrease with time. Figures 30-33 show the long term responses of the slack strain at the 3.3. Mean 3.3. 60 Loading Mean 5.3. unloading Mean 8.3. 52 11113112: 10 - Results for the Slack Strain (%) 0.7562 0.1767 0.0000 0.0000 1.1765 0.4056 0.0000 1.5270 0.3027 6 §§ ON so 3' N UI cycle 02 0.7375 0.0541 0.7559 0.1347 0.9424 0.3155 1.2670 0.3979 1.2299 0.1017 1.5604 0.2450 1.7045 1.4644 2.2009 0.6007 Cycle 03 0.6779 0.0571 0.7723 0.1976 1.0313 0.2500 1.3070 0.3634 1.3204 0.2050 1.6246 0.1709 1.0004 0.6113 2.3606 0.6702 Cycle 15 0.6787 0.0770 0.7703 0.1026 1.1130 0.3375 1.4400 0.3571 1.4234 0.2470 1.6017 0.2710 2.0526 0.5260 2.4605 0.5057 123 0.7759 0.1235 0.9941 0.3276 1.2030 0.3251 1.4700 0.3543 1.5210 .03193 1.7270 0.2777 18003 0.9060 0.1602 1.0650 0.2257 1.4025 0.2620 1.7600 0.3179 2.0390 0.3613 2.1044 0.3962 2.9236 0.6142 +Fbr the 6! strain level tests, the fifth cycle occurs at 12:. 36003 1.0100 0.1270 1.0070 0.1656 1.6450 0.2609 1.0060 0.3640 2.0900 0.4019 2.2437 0.3775 3.0119 0.6756 3.2409 0.6754 5400: 1.012 0.2022 1.1600 0.1514 1.7304 0.2403 1.0740 0.3370 2.1107 0.3456 2.3306 0.3794 2.9797 0.6302 3.3060 0.6520 7200: 1.0650 0.1905 1.1320 0.1402 1.7350 0.2555 1.0540 0.2011 2.1332 0.3924 2.3420 0.4060 3.1061 0.6172 3.4045 0.6031 90003 1.0530 0.1793 1.1090 0.1030 1.7150 0.2620 1.0310 0.3143 2.2320 0.3142 2.3660 0.3090 3.2400 0.6942 3.4231 0.6126 53 CYCLE NUMBER 3 4 5 6 7 a 9 10 11 12 13 14 1s 1 1 1 1 1 1 1 1 1 1 1 1 c1 - LOADING I - UNLOAOING § 11 111 U SLACK STRAIN (PERCENT) d N I II'II II'II II'III I'IIII'I III'III I'II II' N (lNBOHBd) mvals NOV/“IS IITTIIIIIII'TIII'IIIIIIIII'IIII'IIII'IIII'IIII'IIII'IIII 0 1 2 J 4 5 6 7 0 9 10 11 12 mar (SEC) Figure 26 - l‘lhe initial response of the slack strain at the 2% strain CYCLE NUMBER 1 2 3 4 5 0 7 0 9 10 1 1 1 1 1 1 1 1 1 1 1’ j 0 - LOADING 4 3 - - UNLOAUING U I u SLACK STRAIN (PERCENT) N M (maaaad) NIVULS xows IILALAIALLIIAALLILILAIIIll l o | AL 'rrII'IIII'IIII'TIII'IIII'IIII'IIII'IIIII' O 0123450709101112 TIME(SEC) Figure 27 -— l‘l‘he initial response of the slack strain at the 3% strain 54 CYCLE NUMBER 1 2 3 4» 5 6 7 l L I I I I L E] - LOADING I - UNLOAOING O AAJlALAAl‘lAA I. ALI IAALIIL SLACK STRAIN (PERCENT) N d ALLEALLA 'IIII'IIII'IITI'IIII'IIII'IIII'IIII'TIII' N (1N3383d) vams MOV'IS 0 1 2 3 4 5 0 7 0 9 10 11 12 TIME (SEC) Figure 28- The initial response of the slack strain at the 4% strain level. ' CYCLE NUMBER 1 2 3 4 5 L I I A I 4.0 y c: - LOADING :- 4'0 j I - UNLOADING :' .1: T. A I I m '2 3.0 - - 3.0 g 111 1 I g 1 . 93 1.1.1 ‘ L a -: _ . E: V I I § 3 1° ‘3 .I—. :- 2 1— 1 . :1 I A m J ' ’— a x j : 0 o . , m S " D Z m 1.0 1 1..— 1,0 3 J I. 3 E 0.0 - : -- 0.0 O 2 3 4-5 6 7 0 9 1011 12 TIME (SEC) Figure 29 - 'me initial response of the slack strain at the 6% strain level. 55 CYCLE NUMBER 0 2250 4500 6750 . 9000 1 1 250 I . I a I . I . I ‘ C] — LOADING L' “ I I - UNLOAOING : 1— _‘ - 3 EJ 3 1 I o a ‘ : x e, : - 2o < ' 2 -§ ‘ '- 2 z < 2 . : A m ‘ I- v 1— . _ m x ‘ : n 0 j _ r2 ’ S 1 _‘ -I :1 1 (D ‘ : oY—IVUIYUIIV'IIIT—I’"F'UI'IIIIT'II' o 0 1300 3600 5400 7200 9000 11m; (SEC) Figure 30 - The long term response of the slack strain at the 2% strain level. CYCLE NUMBER 0 1500 3000 4500 6000 7500 J . I L L . . I . I . I ‘ j C] - LOADING 1" 4 . I - UNLOADING ; l 2 A '1 : m E 3 J .. 3 t; w I : n 3 1 ’ X LU cu L 0. < r- E11 V d p m z 1 : 2 c2:- 2 1 L- 2 Z r— 1 I ’13 (I) 1 I- m x . _ (2g 0 g : m :5 . . z m 1 "j 1" 1 C 1 D J 2. o l I I TV T I.‘rT—rtfifi'—r U l r ‘I If U l I I rTjTI I F o 0 1800 3600 5400 7200 9000 TIME (SEC) Figure 31 - The long term response of the slack strain at the 3% strain level. 56 CYCLE NUMBER 0 1 125 2250 3375 4500 5625 L . L L I . L . L . I D -’ LOADING I - UNLOAOIN'G SLACK STRAIN (PERCENT) TTI'IIIIIIUIIIIIIU'TIIIIIIIUIIIII'IIII' N (lNaaaad) vaals xzms TU'IT'IFIUT'YIIIU'IUIIj'IIII1" o 0 1000‘ 3000 5400 7200 9000 me (SEC) Figure 32 - The .long term response of the slack strain at the 4% strain level. . CYCLE NUMBER 0 750 1500 2250 3000 3750 _L l l 1 l L l 1L4 l L l I L i 4 4 I l A | .— ’1' m a 331‘... g i: 3 g 0 a | I I x m . g, ‘2 2 3‘3 2 2 ' 2 2 E 1 ,3 ES 3 n S : '3 m 1': 1 3 3 D - LOADING ‘ I - UNLOAOING o 'jrl" V" fl'l I [Tl II 1 rr' Iri II T" Ir! 0 o 1000 3000 3400 7200 . 9000 TIME (SEC) Figure 33 - 'Ihe long term response of the slack strain at the 6% strain level. S7 2%, 3%, 4%, and 6% strain levels, respectively. In these plots, the first data points are the values for the last cycle in the first data group at 123. the differences between the long term loading and unloading data appear to ranain relatively constant. The largest increases occur between 123 and 18003. Differences between strain levels can be more easily perceived in Figure 34, where the long term responses have been plotted for all strain levels together (standard errors have been rancved for clarity). 'Ihe greater increase in the loading and unloading slack strain between 123 and 18003 with an increase in strain level can be clearly seen. Also, there is an apparent greater rise in the slack strain past 18003 with an increase in strain level. Statistics on the slack strain results are listed in Table 11. Generally, significant differences in the slack strain occur at all intervals, with a few inconsistent exceptions. These exceptions nay be primarily due to data scatter, rather then indicating trends in the data. Repeated measures for the slack strain, listed in Table 12, indicate that statistical changes for the loading slack strain occur from 123 to 1800s for all strain levels; with the exception of the 2% tests, which occurs fran 18003-36003. All unloading slack strain data show significant changes from 123 to 18003. Generally, long term increases in the slack strain (both loading and unloading) are small enough that subsequent intervals past 18003 show no significant changes. However, all strain levels show significant changes both fran 18003 to 90003 and fran 123 to 90003 indicating significant increases cccuring over these time periods. Interestingly, the 6% strain level shows several significantly different intervals past 58 TIME (SEC) 0 1800 3600 5400 7200 9000 3.5 l l l l 14 l i 1 l i l 1 l I L I I l l l IJLL 1 LL 1 l_LJ_Lr 3.5 3.0 L. 3.0 A " U) 1— . 5 2.5 :- 2.5 (9) Q . X E ' m a b v 2.0 :" 2-0 g z D _ E : 2 1.5 - 1.5 A 1;) g r?! 70 a : 0 S 1.0 1.- 1 0 '2 m . d a - ll LOADINC A — J: o " 0-5 o - II unsoaomc a - as 1:110:30: '_"' 0-5 0 - 0: Loam-c o - 13 “name ; O - Cs UILOAOIIO o — as unonouo 0.0 IT? I l I I r! I’ l I I I I T l’ r I [fr' rj ' fir' l I l 000 O 1800 .3600 5400 7200 9000 TIME (SEC) Figure 34 - The long term response of the slack strain for all strain levels (standard errors have been renoved for clarity). 59 .88 s .850006 280230 on 80865 2: .aummmwuoccs me cofimsaocfi 8 cu mama. fl 326 00m. 9.680 .22 833 09.330 05 Com mmumsaumm goo can enhance magma .mc.cuac ammo umnmfimucmucmma » a s w w » mcccc w a w w w » mcccm » a a w s » mccca a w w w a z Cacao smug m a z a a z Cacao 00H mcecmoauc » a w u u a mcccc » a a w a a mcccm » u a a w » mccca » w z a w z Cacao smug MCBMOA mmncm cmucc cmucc cause cmucc ”clam «acmumma Hm>000cH Hmcmcnccmuum «aficuum xomam may uOm mamamq cfimuum cmmsumm mmocmumuwwo ucMOMMMcmam I AH flames 60 >4>I>4>1 >1>4>4>4 moocml MNH Z>4>IZ >4>4>1>| mocoml mooma 2222 2222' moooml mcomh .mfi um 088 326 ficfl mfi .308 032 5.5m cc 05 08+ mc.cua .3338... z z z N + z z z wm z a N N z z z 2 av z w z N z z z N mm 2 z z w z z z 2 am mMMGMOch z z z N + z z N aw z z z N z w z w av z z z N z Z z N wm z z N z z z z N «N . mmflnmon mccmhl moovml mcomml mccmHI mNH mlm MIN NIH mocfim moomm mooma mNH m wHDmU mmaphu mmdomu mwdoho acfimnum xomHm can now mousmmmz_c0umoaum I «H mumcy 61 18003, implying that changes at this level are larger than at the lower strain levels. In Table 13 the mean proportional ranges of the slack strain are listed, and were calculated as the total increase in a mean value for a parameter over a specified interval divided by the strain level, 'then multiplied by 100 to express it in percent. This was cbne to see if the slack strain behavior was proportionally equal at all strain levels . 'Ihe total mean proportional ranges for the loading slack strain are all close to 55%, and for the unloading data close to 22%. The increase from the first cycle to 123 is always about 38% for the loading data, but rises with strain level for the unloading data. Both the loading and unloading mean proportional ranges increase with an increase in strain level from 123 to 18003. Fran 18003 to 90003 the loading and unloading slack strain mean proportional range appears to generally decrease with an increase in strain level. larger increases occur for both the loading and unloading data frcm 123 to 18003 at higher strain levels. The initial responses (lst cycle to 123) 'are approximately equal at all strain levels for the loading @ta, but generally increase with strain level for the unloading data. Finally, the decrease in the mean proportional range with an increase in strain level fran 18003 to 90003 appears to "offset" the increase in the mean proportional range within an increase in strain level fran 123 to 18003 (particularly in the loading data), which appears to help nake the total range equal between strain levels. Generally, the total changes of the loading and unloading slack strain frcm the lst cycle to 90003 are proportionally equal at the strain levels tested, 62 IAELE 13 - Mean Proportional Ranges of the Slack Strain (%) Loading Strain lst Cycle- lst cycle- _ Level 90003 123, 123-18003 18003-90003 2% 53.25 34.21 6.55 7.31 3% 57.17 38.03 9.32 7.75 4% 55.82 40.10 12.94 4.83 6% 54.08 38.80 14.52 5.35 unloading Strain lst cycle- lst cycle- Level 90003 .125 123-18003 18003-90003 2% 21.64 5.80 3.55 6.20 3% 21.82 5.02 7.25 1.58 4% 21.00 10.05 11.42 4.56 6% 21.82 11.90 10.96 5.07 63 with the uajor increases in slack strain occuring in the initial 18003. F. Power Fit Coefficients The power fits showed a high correlation to the data, with the correlation coefficient, r2, attaining value of 0.95 or greater. Figure 35 shows a typical plot of the actual data plotted on log-log axis, with the fitted curve superimposed over it. Clearly, the data showed a narked linearity when plotted this way. In Figure 36, the identical data is shown plotted on nornal linear axis, again showing the closeness of that fit. Results for the power fit coefficient A are listed in Table 14. Figures 37—40 show the coefficient A plotted for the 2%, 3%, 4%, and 6% strain levels, respectively, for the first 123 of the test. large scatter can be seen at all strain levels. The coefficient Aacts as a scale factor in the regression fitting; and it appears to absorb mast of the scatter in the data, as seen in the peak stress-vs.-offset strain plot (Figure 9). Overall (A) remains relatively constant in the initial part of the test. Figures 41—44 show the long term response of A for 2%, 3%, 4%, and 6% strain levels, respectively. Similar behavior is seen, with the A's remaining relatively constant throughout the test. Statistics for A, listed in Table 15 show no significiant differences occur at any interval, with only one exception, at the 6%-4% interval at 90003. Repeated measures for A listed in Table 16, also yield identical results. The statistical results indicate that values for A are not different both within any strain level and between strain levels. 64 + U) (n Lin (r )— 21 o 3.0 - O ..I 2.0 - 1 1.0 - 4 0.0 ' j ' I ' 1 ' I j l ' I ' I ‘ l 0.00 0.10 0.20 0.30 0.40 0:50 0.60 0.70 0.60 LOG(STRA1N — SLACK STRAIN + 1) Figure 35 - A typical plot of a stress-strain curve plotted on log - log axes, with the fitted curve. FITTED CURVE 20- 15- STRESS (MFA) Io- ACTUAL DATA 'I'VTT'r—rlr'r‘rrrivrvrl'Irff1 STRAIN (PERCENT) Figure 36 - A typical plot of a stress-strain curve plotted on linear axes, with the fitted curve. 28 5.3. Unloading 8.3. 34 Loading SOB. unloading 8.2. 4‘ Loading Mean 5.8. Unloading Mean 3.3. 64 Loading Mean 8.3. unloading Mean 5.8. 65 MEM-AResultséMeanValues cycle 01 0.3137 0.1882 0.5292 0.5096 0.4920 0.3360 0.3951 0.1462 0.4744 0.2418 0.6349 0.4939 0.3310 0.3214 0.3702 0.2588 cycle 12 1.4293 1.2483 0.4827 0.4253 0.6533 0.4081 0.4418 0.1953 0.4311 0.1826 0.4479 0.2236 0.3586 0.2106 0.3608 0.1517 Olcle I3 0.8253 0.6331 0.4083 0.1974 0.5742 0.2393 0.5369 0.1953 0.5877 0.3183 0.4942 0.3249 0.3077 0.1660 0.3533 0.1636 cycle 15 0.8129 0.8306 0.3802 0.2575 0.6669 0.4627 0.5369 0.1958 0.5748 0.2642 0.4768 0.1760 0.4052 0.2566 0.4253 0.3085 123 0.6839 0.5729 0.4271 0.0939 0.5401 0.2494 0.5803 0.2732 0.6219 0.1457 0.5001 0.3342 18003 0.3658 0.3411 0.4607 0.3393 0.4066 0.4181 0.4623 0.2796 0.6085 0.2261 0.5498 0.2003 0.3732 0.2202 0.3100 0.1391 +Pbr the 6% strain level tests, the fifth cycle occurs at 123. (inMPax10-) 36003 0.4653 0.3101 0.3299 0.1879 0.4374 0.2241 0.4085 0.1527 0.5737 0.1555 0.5707 0.2229 0.3743 0.1621 0.3521 0.1797 54003 0.4131 0.3309 0.2629 0.1512 0.6900 0.5558 0.4651 0.1344 0.5308 0.2209 0.7520 0.3198 0.2547 0.1507 0.3224 0.1854 5 72003 0.4943 0.3183 0.4512 0.3325 0.5309 0.2551 0.4256 0.2657 0.7555 0.6799 0.6217 0.3116 0.3465 0.1983 0.3501 0.2198 90003 0.4033 0.2021 0.5758 0.3977 0.5186 0.4558 0.4723 0.4971 0.6248 0.2897 0.5343 0.1739 0.2963 0.1721 0.2532 0.1247 Figure 37 - The 66 CYCLE NUMBER 3 4 5 8 7 - 8 9 IO 11 12 13 14 15 3.0 I I I I L L I I I I I L I I 3.0 4 0 - LOADING : " . I UNLOAOING _ 2.5 - W - 2.5 15 2.0 - - 2.0 > I ‘ " A 4 " z 9 . » '0 . . > X 1.5 d '- 1.5 x < ‘ I ‘5 - I c) < 1.0 - I- 1.0 3 ‘ F 0.5 - - 0.5 1 r 0.0 6Wfr'li'nrw‘liiir'8111'lIIV'ITTI'UIfi'IUfiVYIU'U‘II 0.0 0 I 2 3 4 5 6 7 8 TIME (SEC) strain level . CYCLE NUMBER 9 IO 11 12 initial response of the power coefficient A for the 2% 1 2 ' 3 4 5 s 7 a 9 10 30 I I 1 I 1 l 1 I 1 I 3.0 ' c1 - LOADING : ‘ I - UNLOAOING _ 2.5 ; -— 2.5 A ‘ L 2.0 > ‘0 2.0 "' .. A I j . g e -I : > X ‘5 .:. I- 1.5 x 3:“ ‘ I 5 2 ‘ ._ ('1‘ V -‘ - 1.0 v < 1.0 -.. .. 3 : os -: - 0.5 - III IUIU 0.0 0.0 ‘II'IU'U'IIIUIVIIIII‘UI'IIUU'IIUU'IIUU'UITI'II'I'I ' O 1 2 J 4 5 6 7 8 9 10 I1 12 TIME (SEC) Figure 38 - The initial response of the power coefficient A for the 3% strain level. 67 CYCLE NUMBER 1 2 3 4 5 6 7 8 30 I I ' I I I ' I I 30 Cl - LOADING - j I - UNLOADING: d I- 2.5 -‘ - 2.5 1 I ’6 2.0 .. - 2.0 > | d F 2 9 1 : E X 1.5 ‘l' '— 1.5 x < . . a; I I o v .. . I < 1.0 -' I- 1.0 3 I I 0.5 d - 0.5 000 VIIIIUIT'IIII'UUII'III‘lUTUIIYVIU'UUII'IIUVIIIUI'IIUIIIIU' 0'0 O 1 2 5 .4 5 6 7 8 9 1O 11 12 TIME (SEC) Figure 39 - The initial response of the power coefficient A for the 4% strain level. CYCLE NUMBER 1 2 3 4 5 3.0 I I I I I 3.0 D - LOADING _ . a - umoaomc . 2.5 - - 2.5 8 2.0 - - 2.0 > | ' " A o i h i .— < - g x 1.5 -I - 1.5 x < . . Q ‘ ’ _a 3 ‘ - 9 4 10 - 10 3 0.5 - ' l ‘E ii I l — 0.5 0.0 IIIW81'I‘IYIUT‘TIUIU'IIIU‘I'I'U;IIII;—UIIV;IIII1IOUTIU'I'UI' 0-0 o 11 12 TIME (see) Figure 40 - The initial response of the power coefficient A for the 6% stram level. 68 CYCLE NUMBER 0 2250 4500 0750 9000 1 1250 3.0 L . I I I . I . I I I 3.0 CI - L 0 A 0 I N c - . I - u N L o A 0 IN 0 : 2.5 - - 2.5 G? 2.0 - :- 2.0 > I 1 . A o - z ,. . 11 x ‘ - 3’ 1.5 - '- 1.: x < . . . a p ..A e » C.) < 1.0 I— 1 .0 3 r- 0.5 0.5 0.0 0.0 0 1000 3000 5400 7200 9000 TIME (SEC) Figure 41 - Toe long term response of the power coefficient A for the 2% strain level. CYCLE NUMBER 0 1500 3000 +500 5000 7500 30 1 I L I l L L l I l ' 3.0 - -‘ c1 - LOADING . . I - UNLOADING : 2.5 - -'2.5 I; 2.0 .. - 2.0 > I 1 . A . z 9 - ‘0 . . > x 1.5 - — 1.5 x g 1 I _. E .- O v .. I < 1.0 I- 1.0 8', 0.5 0.5 0'0 I l I I I I I‘I' I 1 IT I ‘ I I I-r I '3 I I I I I I I I’ I r r! 0.0 o 1000 3500 5400 7200 9000 TIME (SEC) Figure 42 - The long term response of the power coefficient A for the 3% strain level. 69 CYCLE NUMBER 0 1 125 2250 3375 4500 5625 3.0 l I l L l l l 1 | l l 3.0 J 0 - LOADING : I - u NLOADING _ 2.5 - — 2.5 :3 2.0 - — 2.0 > I 1 : ’2 9 . . '0 . L > X 1.5 - '- 1.5 x g : 3 2 - CI! < 1.0 - — 1.0 3 0.5 — 0.5 0.0 I r I I I I l I l I l I I I I T ' I I l I I I I I " I IT! I r 0.0 o 1000 3500 5400 7200 9000 TIME (SEC) Figure 43 - The long term response of the power coefficient A for the 4% strain level. CYCLE NUMBER 0 750 1500 2250 3000 3750 3.0 L l l I; L L l L I l g l L 3 o 3 D - L o A DIN 0 ; ‘ I - u N L o A 0 IN G - -' I- 2.5 1 r 2.5 1 I ’6 2.0 -. L 2.0 > I 1 . A o -1 - .7. r— d " g x 1 I 1.5 - I- 1.5 < 1 ' x (L 4 . _. 2 -1 . O V p .. I < 1.0 1 - 1 D 8 J I 4 I- -I II 0.5 -1 - 0.5 I. 0.0 I—rI I r I I r I' r l I I I I I rI I I r r I r r ' I I rl I r 0-0 O 1800 5600 5 400 7200 9000 TIME (SEC) Figure 44 - ‘Ihe long term response of the power coefficient A for 6% strain level. 70 22222 22222 wmlmm .008 M 605.83% 383230 0: 800365 2!. 452 mosag H8330 05 you mmumsaumm goo.o:m cmuguoo magma Amc.cuae 0mm» umnmamucmngmm. 22222 22222 22222 22222 22222 22222 amuse amuse wwumm .uoumme assumucH H0504 cnmuum 22222 22222 «le0 2222:» 22222 wwlmo mooom mooom mooma manao.ummq macho and manomoaco mooom moomm wooed maoso ummq macho uma mmfiomoq «d uOm magma 505m 5058 8053mm? €033.58 I ma a 71 .m3 um 288 326 50: 05 .380 H92 38% we 05 08+ Bang .38 and... w z z Z z z z + z z z we w z z z z z z z z z z aw » z z z z z z z z z 2 mm N z z Z Z z z z Z z 2 mm a z z z z z z + z z 2 mm M z z 2 z z z z z z z wv w z z z. z z z z z z 2 an N z z z z z z z z z w wN “GENOA moooml moooal mcooml moeNhI moovml moooMI mccmal mNH mIm MIN NIH mNH mecca moomh moovm moomm mooma mNH m mHoaU mmaohu mwauhu mmaoxo .& now 8033.. 80.80% I 3 a 72 Table 17 lists the results for the power coefficient B for all strain levels. Figures 45-48 show the initial response for B at 2%, 3%, 4%, and 6% strain levels, respectively. Scatter in the B results is substantially snaller than for A. In general, the data behavior is similar to the slack strain data; with differences between the loading and unloading data diminishing with time. Greater increases occur in the loading curves. Figures ”-52 depict the long term B results for the 2%, 3%, 4%, and 6% strain levels, respectively. Here, as in the slack strain , a large increase in both the loading and unloading data occurs from 123 to 1800s. However, greater increases occur at lower strain levels here. 'Ihe overall values for B increase with a decrease in strain level. This increase can be easily seen for the loading data in Figure 53, and for unloading data in Figure 54. Larger increases occur at both the lst cycle-90005 and 1800-90003 intervals for the loading and unloading chta data at lower strain levels . In Table 18, the mean proportional ranges for all B data are listed. For the loading data, all mean proportional ranges increase with a decrease in strain level. ‘Ihe unloading data behaves similarly, with the exception fran 18003 to 90003, which behaves oppositely. This result indicates that greater changes in the unloading B occur past 18003 at higher strain levels. Overall, it appears that not only does the B decrease with an increase in strain level, but greater changes occur during testing at the lower strain levels. Statistical results for B are listed in Table 19. Significant differences occur for the loading data at all strain level intervals for most cycles, with the exception of the 4%—3% and 6%—3% intervals. 2! Loading 3.3. MM Cycle Cycle 41 42 4.1320 4.0210 0.5388 0.3728 5.3810 5.2280 1.3120 0.5410 3.1780 3.8350 0.5795 0.7209 4.2850 4.2880 0.7988 0.7444 3.4803 4.0280 0.4983 0.4813 4.3398 4.5950 0.5138 0.8048 2.9949 3.3715 0.1749 0.3830 3.5280 3.8870 0.3481 0.3998 73 - Rmults for B (unitless) cycle I3 4.5140 0.4209 5.4010 0.6848 3.7420 0.8040 4.2150 0.8191 4.1757 0.4469 4.6010 0.6869 3.5311 0.3647 3.6097 0.4760 cycle 45 4.6140 0.4191 5.4710 0.4143 3.7970 0.8710 4.1880 0.7809 4.2360 0.4412 4.5992 0.5564 3.4414 0.3111 3.5780 0.3318 12: 4.8290 0.6023 5.5306 0.8209 3.9597 0.8889 4.2930 0.7071 4.5970 0.7926 4.6880 0.5690 18003 6.1070 0.4224 6.2870 0.4673 4.8090 1.1150 5.0580 0.8692 4.8570 0.6788 5.1220 0.5611 3.8740 0.5042 4.0870 0.5221 49hr the GI strain level tests, the fifth cycle occurs at 125. 36003 5.9470 0.6424 6.5970 0.8779 4.7240 1.0860 5.1906 0.9170 4.9510 0.5041 5.1904 0.7308 3.8596 0.3274 4.0567 0.2620 54003 6.1070 0.8727 6.7570 1.6670 4.5740 0.8771 5.1750 0.9125 5.0830 0.8048 5.0740 0.6657 4.1030 0.4242 4.1536 0.5234 72003 5.9875 0.9545 6.4800 0.6362 4.6820 0.8645 5.3810 0.9727 4.9510 0.8614 5.2387 0.6635 3.9880 0.5984 4.1126 0.4326 90008 6.2070 0.7626 6.2850 0.5117 4.8180 1.1023 5.1980 0.8834 5.0060 0.5482 5.3410 0.6178 3.9163 0.6989 4.1400 0.3691 74 CYCLE NUMBER 1 2 3 4 5 8 7 8 9 10 11 12 I3 14 15 _., l 1 1 L 1 l 1 l L I l l 1 l . 7 « c3 - LOADING : ‘1 I - UNLOADING :- 8 -§ 5- 8 3 a 5 J; :- 5 a) - E- a) 1 Z 4 1 :- 4 : : ‘1 a- 3 -j :- 3 ‘4 :. 2 : 2 IIIIIII—‘IIIIlIIII'I—III'IITI'I‘IITIIII'TIII'IITT‘IIIT'IIII 0 1 2 3 4 5 8 7 8 9 10 11 12 TIME (SEC) Figure 45 - 'lhe initial response of the power coefficient 8 for the 2% strain level. CYCLE NUMBER 1 2 3 I 4 5 8 7 8 8 10 7 l 1 L I L l l g I 1 7 CI - LOADING : _ I - UNLOAOING ;_ 1 : 8 -‘ E- 6 E- 5 o: :— w E- 4 I- I- :— 3 ~ 2. 2 ITIIIII'ITIT'IIII'IIIT'IIII'TIUT'TIIIIIII'TIIII'IIII'IIII 2 0 1 2 J 4 5 6 7 8 9 10 11 12 TIME (SEC) Figure 46 - The initial response of the coef ' ' strain 1 . power f1c1ent B for the 3% 75 CYCLE NUMBER 1 2 3 4 5 6 7 7 L l L l I l l U - LOADING 3 _: I — UNLOADING [— 6 -" 7— 5 .; :- 5 ‘1' 75 1 I m -; '." m ‘ “i E- 4 L' :— lAlAALA AAA IIIIIIIII'IIIUIUIIT'IIYII'IIIT'IVII'YIIVIIITI'III I'TUI‘IUIII 2 0 1 2 3 4 5 6 7 8 9 10 11 12 TIME (SEC) Figure 47 - The initial response of the power coefficient B for the 4% strain level. CYCLE NUMBER 1 2 3 4 5 7 l I I I l 7 D 1 D - LOADING : _‘ I - UNLOADING -_ I I d I- 1 I- 6 1 - 6 . 1 1- < I d h - F a v- 4 P D b - d P 4 I- m 1 :- (I) 1 D I I 4 -; I- 4 D a I- 4 TI .- 4 D - - fl - 4 P 1 I- d D 3 '1 .- 3 4 D d P 1 n - — ‘ F 4 b a i 2 Y'II'UIIU'IIIU'Ur60'I'UI'U‘II'IIIIIIIrr'TrT—T‘O'UHITUWI4".0' 2 0123458789101112 11ME(SEC) Figure 48 - The initial response of the power. coefficient B for the 6% strain level. 76 CYCLE NUMBER 0 2250 4500 6750 9000 11250 I I ' l l I ‘ l ' :—-7 E—s CD I 11) 5-5 L4 0 - LOADING '_ I - UNLOADING ' I rI tr 3 anleI'IT'II'II'II'IIII' I I 0 1 800 .3600 5400 7200 9000 TIME (SEC) Figure 49 - The long term response of the power coefficient B for the 2% strain level . CYCLE NUMBER 3000 4500 8000 7500 l . L . 1 . I . 3 .L 1 0 - LOADINO E 7; I - UNLOADING E'7 E. :-6 m E :—5 t :—4 : 3 T—rrr'rI'TI'II'II'II'rr‘rI'II'II" J O 1 800 3600 5400 7200 TIME (SEC) Figure 50 - The long term response of the power coefficient B for the 3% strain level. 9000 77 CYCLE NUMBER 0 1 125 2250 3375 4500 5825 1 . 1 3 1 . I . 1 1 c1 - LOADING E 7 1 I - UNLOADING _ 7 1 I 5 fl 7 5 1 b 4 I- A 7. co 1 : on 5 -: E- 5 1 t 4 I- ”: T 3 : 4? .— 4 1 L J [I T I I I 'fI l I I l I I i I rl I fl I I l I I I' I F 3 O 1800 3800 5400 7200 9000 TIME (SEC) Figure 51 - The long term response of the power coefficient B for the 4% strain level. CYCLE NUMBER o 750 1500 2250 3000 3750 L l l 1 . L 1 1‘ l 1 g E 1 . . L 3 0 - LOADING E 7 _ I - UNLOADING E” 7 j E- 8 - E- 6 < b .1 E. a: : I: m 5 -§ :- 5 -‘ e 4 J E- 4 1 a -l’ — . i 3 3 r0 4 rj I ' I III I I I I ' rrrflrrT I I IrI I I O 1800 .3600 5400 7200 9000 111.18 (sec) Figure 52 - The long term response of the power coefficient B for the 6% strain level. 78 TIME (SEC) 0 1800 3600 5‘00 7200 9000 7 l l l l I l l LLl 1 1 l 1 1 LL 1 l l l l I l l l L l l I l - 7 o - 2: snuuu o - 0: srauw I _‘ A — 3: suuuw c1 - 0: Stan» f_ s - - 6 m :- 5 :0 L 4 j . 3 rrI I I r] I fl I I I If I I I If I IT I | I I I I I I 3 O 1800 3500 5‘00 7200 9000 “ME (SEC) Figure 53 - The long term response of the loading power coefficient B for all strain levels. TIME (SEC) 0 1800 3600 5400 7200 9000 7 J l l l | L 1 L1 1 l l l l l 1 l L I l l l l LL l I 1 L] J l 7 3 O - zx STRAIN O - 0: Stan" : J A - 3: stun: I - ex smuu I 1 I j . _: C 1 E CD 5 j - 5 CO 4 C 1 W : d X...- - 1 b * 1 /a_——-———-*———~a :- 4 1 y : 1 :- ‘1 I 3 I I I I I I I I I I T I l I o I r I I I I I I I ' n I l o 7 I 3 O 1800 3600 5400 7200 9000 TIME (SEC) Figure 54 - The long term response of the unloading coefficient B for all strain levels. 79. BABEE 18 - Mean Proportional Changes in B (%) Loading B Strain lst Cycle- lst Cycle- Level 90005 lgg 123-18003 18008-90008 2% 1.0375 0.6390 0.6890 0.0500 3% 0.5473 0.2831 0.2861 0.0030 4% 0.3814 0.0650 0.1023 0.0373 6% 0.1536 0.0721 0.0792 0.0071 Unloading B Strain lst cycle- lst cycle- Lewel 90003 lgg 123-18003 18003-90003 2% 0.4620 0.0848 0.3772 0.0010 3% 0.3110 0.0093 0.3017 0.0467 4% 0.2503 0.0871 0.1633 0.0548 6% 0.1020 0.0083 0.0937 0.088 80 .88 s .888008 0:830:53 8 80865 2.... 5.2 839 H8300 05 now moumsaumm gno_o:m cmunopo mafia: .mc.onmc 0000 umnmflmucwunmm. » a z a a » mecca » w z w a » moomm » w z a w » mooma u w z u a a macho gang 2 z z a a a macaw 00H mmflomoauo » w z a z » mooom » u z a z » mooom » w z a a » mooma » z z a z a macho ammo » a z a z w macho 00H mcwomoq wmlmm wmlmc wmlwfi wmlmm mmlwo wvlww «tnmumma Hm>umuCH Hwamq Camuum «Q How maw>mn Camuum cmmsumm mmocmumwuflv HCMmewcmwm I ma mumgy 81 The unloading data behaves similarly, except that the ass-3% interval is significantly different. The lack of a significant difference at 4%—3% interval for all the B data could be due to either the values for B within this interval are nearly identical, or to excessive noise... The latter may be more probable since a significant difference also does not occur at the 6%-3% interval. Repeated measures for B, listed in Table 20, indicate significant differences occur only for the loading data between lst and 2nd cycle , and for both loading and unloading data between 125 and 18005. Although the 6% strain level tests show periodic significant differences past 18005, no significant difference occurs fran 1800 to 9000. Close inspection of the 6% strain level mean values, listed in Table 14, indicated a steady rise in B until 72005, where B tends to drop slighly for both the loading and unloading data. This slight drop in B would explain why periodic significant differences occur at 6% strain past 18005, but does not occmr between 18005 and 90005. 'Ihis drop could be due to fiber or fibril damage, or grip slippage cccuring past 54005 in the sanple at 6% strain, but proof of this conjecture is beyond the scope of this study. The retaining strain levels show no significant differences past 18005 and between 18005 and 90005, indicating no significant changes past 18005. All strain levels show significant differences between 125 and 90005, but none in the first data group past the first cycle. Evidently, changes in B are only large enough to show a significant difference between 125 and 18005 and between the lst and 20d cycle for the loading B. These results imply the greatest increases in B are in the first half-hour, and that a rapid change occurs initially for the loading curve. 82 >4>4>4>4 >4>4>i>4 moocal mNH 2222 2222 moooml moowa 2222 222% mecca! moans 2222 2222 mccmhl moovm .nma an nncooo cacao cameo men .nnnmu edema decenn no 0:0 005+ 8.ch J80 can... z z w + z z 2 cc 2 z a z z z 2 we 2 z a z z z 2 mm . z z w z z z 2 an mmwcooHcD » z u + z z e we 2 z w z z z u we z z w z z z s cm 2 z a a z a z 3 mmflcmoq ncccmu ncccmu mcccflu mma mum mum and moomm mooma mad m mHDmU mwapmo mmaomu mmaomo am now $05ch.. condoned u cm a 83 'Ihe higher values for B at lower strain levels could be due to the nature of the stress-strain curve. A higher strain level test would include more of Region III, where the local value for B would be one. Hence, the overall value for B for the entire curve would be reduced with an increase in strain level. A further investigation of the stress-strain curve would be necessary to confirm this. The lower values reported by Haut and Little [5] are most probably due to offsets of l to the stress-strain data used in the power fit for this study. These offsets cause the least squares regression equation to yield a larger value for the power coefficient B, and a maller A. It is possible that strain rate and strain level effects also influenced the power fit coefficients. Haut and Little [5] had a neximun strain of 1.8%, and a neximun strain rate of 0.68%/s, as opposed to 2% to 6% strain and a strain rate of S%/s used here. Hubbard, et. al. [16] indicated sane strain rate sensitivity for huuan tendon in the peak stress, loading M.T.M., and the hysteresis. However, no curve fitting was done, so a direct cauparison is not possible. A .future investigation of the strain rate sensitivity of tendon is necessary to earplore the power fit coefficient results further. Greater increases in B at lower strain levels could be explained by changes in the microstructure of the tendon. As stated in the introduction, changes in the microstructure of the tendon occur during the precmditioning cycles . Also , the stability of these changes past preconditioning has not been well cbcmented. An increase in alignment could continue throughout the test, causing changes in the stress-strain curve prinarily in- Region II. 'Ihis inproved alignment would cause a larger value for B in Region II. Since the lower strain 84 levels are mostly in this Region, they would experience larger changes in B. Also, the effect of this continually inproving alignment would be less prcminate at higher strain levels , since they contain proportionally less of Region II. Further support of this etplanation is beyond this study, but continued changes in the stress-strain curves at all strain levels indicate sane structural changes occur. G. Histology ' Histological results indicate continuous , unruptured fibers throughout the gripped and non-gripped sections . The griped sections were always very catpressed, but neither broken nor torn, as discussed for the preliminary tests in the materials and methods section. The only problem area in the sanples were in the grip-nongripped section interface. The fibers here appeared to be somewhat ruptured and flared, and not uniform. ‘Ihis could be due to the fact that the fibers rise out of the plane of the thinner gripped section to meet the thicker non-gripped section, hence appering to be broken. However, scmedauegetothe tendon nay have occured here. Further investigation of the condition of the fibers was not possible with the histological techniques used. In general, except for the canpressed fibers in the gripped ends, no fiber damage could be seen in the histological slides. H. Photographic Measurenents Photographic measurenents, listed in Table 21, are shown as percent increases from the initial length right before testing and the final length right after testing. Large scatter is seen throughout the results, but there appers to be greater elongations of the specimens near the gripped ends. In one case, the ends of the tencbn " “3.545.. 85 'IABLE 21 - Photograghic Results Percent Increase in tendon length section fron before just to after testing GriptoGrip Uppersriptouot LowerGriptoDot 2.22 -2.03 0.92 2.28 10.55 0.59 1.17 3.74 1.07 2.17 0.25 0.81 0.48 0.48 2.75 2.82 1.90 2.35 *15.25 0.74 *8.92 3.97 *14.91 1.31 0.61 *4.36 *5.08 1.15 *10.36 *Excess ive Elongation *5.97 1.77 3.11 *8.90 *7.55 1.25 1.19 *8.78 *10.99 0.98 *3.42 0.00 -2.06 0.45 *14.45 Dot to Dot 0.59 4.55 -0.41 -0.08 0.97 0.65 0.05 3.61 -1.09 1.76 0.02 0.78 0.25 0.22 0.63 87 elongated 10% nore than the middle section. Due to operational problans with the camera, the tests which corresponded to each photo was unknown, and several photo series were lost. However, the available results indicate that sane slippage or damage in or near the grips nay have occured. It is not possible to determine the'exact influence these larger elongations near the grip ends had on the results. It is possible that sane of the scatter seen in the data was caused by the mechanism which caused the greater elongation near the grips. 88 IV. (DMLBIOQ Although the gripping method used in this study appeared to be adequate initially, photographic neasurenent results indimte possible dauagetothetendoninornearthegrips. ‘Ihecanpressicnofthe tendon within the grips nay have mused sane damge to. the tendon, unobservable by the histologiml techniques used. Such éanege could muse excessive elongation near the grips, since breakage would decrease the number of fibers bearing load, inducing greater stresses on these loaded fibers. Further developnent of gripping, elongation measurenent and histologiml techniques are needed to better insure the validity of the results. The most rapid changes in the mechaniml response of the tendon took place in the initial part (first 123) of the test. Substantial decreases the peak stress, unloading M.T.M., hysteresis; as well as increases in the lmding um, slack strain, and the power fit coefficient B were greatest in this initial section. line changes in the above mechanical parameters indimte that the stress-strain curves have a nerked tendency to "close-np" (i.e. difference between the loading and unloading curves diminish) in the initial section of the test. This is particularly evident in the decreasing differences in the lmding and unloading M.T.M., B, slack strain, and the sharp initial decrease in the hystersis. his initial part corresponds to preconditioning, and the changes are virtually idential to the rapid changes discussed earlier for preconditioning. 'Ihese large changes imply that sane type of change in the tendon's structure must occur in the initial section of the test. 89 For the long-term response , the largest changes in the nnechaniml response occured between the initial 125 of the test and 1800s later. Continued increases in the power fit coefficient B and the slack strain occured, but to a less extent than in the initial part. The um, peak stress, and the hysteresis continued to decrease, also to a less extent. Past 18003, the changes diminished even further. The hysteresis essentially stabilized to about 16% for all strain levels past 1800s. Changes in the other mechaniml parameters reduced throughout the rest of the test. The tendency for the stress-strain curves to "close-up" further appears not to occur signifimntly past 18003, although continued changes in the power fit coefficient B indimtes continued changes in the stress-strain curves in both the loading and unloading parts of the stress-strain curve. Generally, results for the stabil ization time indimte a strain level sensitivity; higher strain levels induce a longer stabilization time. It must be enphasized that the precise time for stabilization depends on the exact criteria used. Although the t-test criterion indimted no significant sensitivity to strain level for stabilization of the peak stress, it did show an overall rise in the stabilization for tie M.T.M. data. The 2% and 5% difference criteria, usable only for a peak stress, also indimted an overall increase in stabilization time with an increase in strain level. Evidently, a higher strain level induces longer continued changm in the peak stress and the M.T.M. For the other mechaniml parameters, only the power fit coefficient B showed a strain level sensitivity. Total increases in 90 the slack strain appear to be proportionally the same throughout the strain levels tested, and the hysteresis showed no detectable change at different strain levels. The B showed a signifimnt rise in value with a decrease in strain level, as well as greater increases within a test at lower strain levels. The exact muse for this behavior is not known, but it is conjectured that it is due to a possible continued changes in the stress-strain curve in Region II during the test, which would effect the power fit coefficients more at lower strain levels. In conclusion, changes in the mechaniml response of the tendon continue throughout the test, and appear to take longer to stabilize with an increase in strain level. The most rapid changes occur at the beginning of the test, with continuing changes diminishing with time. Clearly, the preconditioning assuuption dnes not precisely hold for long term cyclic extensions . Although the overall response appeared to visually stabilize initially, the long term B, M.T.M., slack strain, and peak stress indimte that this does not happen. Recanmendations for future studies include: 1. Improve the gripping technique to better insure that no danage is done to the sanples. 2. A closer investigation of the initial 1800s of the test, especially for the hysteresis behavior. 3. Extend the strain level range to include lower strain levels (e.g. 0.5%, 1%). 4. Investigate cyclic creep at various stress levels, and canpare to the results in this study. 5. Optimlly nonitor sanple extensions at different intervals along the samples. It is hoped that this initial study will further the knowledge of the mechaniml response of connective tissues. APPENDICES 91 Appendix A Ringers Lactate Solution For a 20 liter container: 1. 2. 3. 4. NaCl 170 .36 9. K21: 7.95 9. CaCl (dehydrate): 4.73 g. Sodium Lactate: 58.67 g. 92. Appendix B Histology Method Fixation Tissue fixed three days in Mercuric dnloride—formalin _S__tgck_: NaCl 9 911 HgCl2 70 gm H20 1000 m1 Worm : 9 parts stock: 1 part neutral formalin On second day in fix tissue was trinmed and desired sanples returned to fix. Cleaning, infiltration and enbedding Tissues were processed through a graded series of alcohols to toluene followed by paraplast plus. This was dane overnight on an autotechnimn. Tissues were enbedding in paraplast plus (up 56°C) enbedding nediun (Lancer). Cuttling' : Blocks were cut at 7n on rotary microtcme and sections mounted on slides. These were allowed to dry overnight at 37° before staining. Staingg' : Sections were stained with Heretoxyl in-Ecsin following standard H & E procedures. Harris Heretoxylin and Lipp's Gern'an Eosin were used although any standard H 8 E solutions will give good results. BIBLIW 10. 11. 12. 93 Bibliography Fung, Y.C. , "Stress-Strain History Relations of Soft Tissues in Simple Elongation, " Bianechanics - Its Foundations and Objectives, eds. Fung, Perrone, and Anliker, Prentice Hall, New Jersey, 1972. Viidik, A. , "Mechaniml Properties of Parallel Fibered Collageneous Tissues,“ Biology of Collogen, eds. Viidik, Vuust, Amdenic Press, Landon, 1980. 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Haut, R.G., ”Correlation Between Strain-Rate-Sensitivity in Rat Tail Tendon and Tissue G1ycosaminoglymns,” 1983 Bianechanics Sm ASHE 1983. Elliot, P.M., "Structure and function of mammlian tendon,” Biol. Rev., Vol. 40, pp. 342-421, 1965. Diamant, J., Keller, A., Baer, E., Litt, M., and Arridge, R.G.C., 'Collogen; ultrastructure and its relation to mechaniml properties as a function of ageing," Proc. R. Soc. Lond., Vol. B180, pp. 293-315, 1972. Viidik, A., "A rheologiml mnodel for unmlcified parallel-fibered collageneous tissue,” J. Bianech, Vol. 1, pp. 3-11, 1968. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 94 Fung, Y.C., ”Elasticity in Soft Tissue," Am. J. Physiol., Vol. 213, pp. 1532-1544, 1967. Jenkins, R.B., Little, R.W. , ”A constitutive equation for parallel-fibered elastin tissue,” J. Bianech, Vol. 7, pp. 397-402 , 1974 . Hubbard, R.P., Soutas-Little, R.W., ”Mechaniml Properties of Human Tendon and Their Age Dependence,” Final Report to the Nat. 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Physics, Vol. 17, pp. 347-351, 1940. Lanir, Y., ”Structure-strength relations in mammilian tendon,“ Jo BiOQ'IYSiCS, V01. 24' me 541-554, 19740 Rigby, B.J . , “Effect of cyclic extension on the physiml properties of tencbn collogen and its possible relation to biologiml ageing of collogen. " Nature, Vol . 202 , pp. 1072-1074, 1964. l'Mulplt", a graphics computer routine written by: Dr. T.V. Atkinson, Dept. of Chenistry, Michigan State University, East Lansing, MI, 48824. Crow, E.I., Davis, F.A., Maxfield, M.A., "Statistics Fanual,” Dover, 1960. Morrison, D.F., "Multi-Variate Statistiml Methods," McGraw—Hill, 1976. 95 27. Winer, B.J., "Statistiml Principles in Experimental Design", McGraw-Hill, 1962. 28. Selke, B.J., Little, R.W., Hubbard, R.P., 'Mechaniml Properties of Lower Limb Tendons and Ligaments in Primates,” AFA FRL-TR-82-56, Air Force Aerospace Medial Research laboratory, Wright-Patterson Air Force Base, Ohio, 1982.