Biomechanics pp 242-320 | Cite as

Bioviscoelastic Solids

  • Yuan-Cheng Fung


This chapter is focused on soft tissues. We shall first consider some of the most elastic materials in the animal kingdom: abductin, resilin, elastin, and collagen. Collagen will be discussed in greater detail because of its extreme importance to human physiology. Then we shall consider the thermodynamics of elastic deformation, and make clear that there are two sources of elasticity: one associated wit change of internal energy, and another associated with change of entropy. Following this, we shall consider the constitutive equations of soft tissues. Results of uniaxial tension experiments will be considered first, leading to the concept of quasilinear viscoelasticity. Then we will discuss biaxial loading experiments on soft tissues, methods for describing three-dimensional stresses and strains in large deformation, and the meaning of the pseudo-strain energy function.


Relaxation Function Strain Energy Function Stretch Ratio Ground Substance Elastin Fiber 
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  1. Abramowitz, M. and Stegun, A. (1964) Handbook of Mathematical Functions, Ser. 55. U.S. Government Printing Office, Washington, D.C.Google Scholar
  2. Alexander, R. M. (1968) Animal Mechanics. University of Washington Press, Seattle.Google Scholar
  3. Banga, G. (1966) Structure and function of elastin and collagen. Asso. Pry. 1st Inst. of Pathological Anatomy and Exp. Cancer Res., Med. University, Budapest.Google Scholar
  4. Bauer, R. D. and Pasch, T. H. (1971) The quasistatic and dynamic circumferential elastic modulus of the rat tail artery. Pflügers Arch. 330, 335–345.PubMedGoogle Scholar
  5. Becker, E. and Föppl. O. (1928) Dauerversuche zur Bestimmung der Festigkeitseigenschaften, Beziehungen zwischen Baustoffdämpfung und Verformungs geschuwindigkeit. Forschung Gebiete Ingenieurwesens. V.D.I., No. 304.Google Scholar
  6. Becker, R. and Döring, W. (1939) Ferronmagnetismus. Springer, Berlin, Chapter 19.Google Scholar
  7. Bergel, D. H. (1961) The dynamic elastic properties of the arterial wall. J. Physiol. 156, 458–469.PubMedGoogle Scholar
  8. Bergel, D. H. (1961) The static elastic properties of the arterial wall. J. Physiol. 156, 445–457.PubMedGoogle Scholar
  9. Biot, M. A. (1965) Mechanics of Incremental Deformations. Wiley, New York.Google Scholar
  10. Blatz, P. J., Chu, B. M., and Wayland, H. (1969) On the mechanical behavior of elastic animal tissue. Trans. Soc. Rheol. 13, 83–102.Google Scholar
  11. Bodner, S. R. (1968) In Mechanical Behavior of Materials under Dynamic Loads, U. S. Lindhom (ed.) Springer, New York, pp. 176–190.Google Scholar
  12. Bressan, G. M., Argos, P., and Stanley, K. K. (1987) Repeating structures of Chick tropoelastin revealed by complementary DNA cloning. Biochem. 26, 1497–1503.Google Scholar
  13. Buchtal, F. and Kaiser, E. (1951) The Rheology of the Cross Striated Muscle Fibre with Particular Reference to Isotonic Conditions. Det Kongelige Danske Videnskabernes Selskab, Copenhagen, Dan. Biol. Medd. 21, No. 7, p. 328.Google Scholar
  14. Chen, H. Y. L. and Fung, Y. C. (1973) In Biomechanics Symposium, ASME Publ. No. AMD-2, American Society of Mechanical Engineers, New York, pp. 9–10.Google Scholar
  15. Chu, B. M. and Blatz, R. J. (1972) Cumulative microdamage model to describe the hysteresis of living tissues. Annu. Biomed. Eng. 1, 204–211.Google Scholar
  16. Ciferri, A. (1963) The a ß transformation in keratin. Trans. Faraday Soc. 59, 562–569.Google Scholar
  17. Collins, R. and Hu, W. C. (1972) Dynamic constitutive relations for fresh aortic tissue. J. Biomech. 5, 333–337.PubMedGoogle Scholar
  18. Cowan, P. M., North, A. C. T., and Randall J. T. (1955) X-ray diffraction studies of collagen fibers. Symp. Soc. Exp. Biol. 9, 115–126.Google Scholar
  19. Dai, F., Rajagopal, K. R., and Wineman, A. S. (1992) Nonuniform extension of a nonlinear viscoelastic slab. Int. J. Solids Struct. 29, 911–930.Google Scholar
  20. Dale, W. C., Baer, E., Keller, A., and Kohn R. R. (1972) On the ultrastructure of mammalian tendon. Experientia 28, 1293–1295.PubMedGoogle Scholar
  21. Dale, W. C. and Baer, E. (1974) Fiber-buckling in composite systems: a model for the ultrastructure of uncalcified collagen tissues. J. Mater. Sci. 9, 369–382.Google Scholar
  22. Deak, S. B., Pierce, R. A., Belsky, S. A., Riley, D. J., and Boyd, C. D. (1988) Rat tropoelastin is synthesized from a 3.5 kilobase mRNA. J. Biol. Chem. 263, 13504–13507.Google Scholar
  23. Debes, J. (1992) The mechanical properties of pulmonary parenchyma and arteries. Ph. D. thesis, University of California, San Diego.Google Scholar
  24. Debes, J. and Fung, Y. C. (1992) The effect of temperture on the biaxial mechanics of excised lung parenchyma of the dog. J. Appl. Physiol. 73, 1171–1180.PubMedGoogle Scholar
  25. Diamant, J., Keller, A., Baer, E., Litt, M., and Arridge, R. G. C. (1972) Collagen; ultrastructure and its relation to mechanical properties as a function of ageing Proc. Roy. Soc. London B 180, 293–315.Google Scholar
  26. Dortmans, L. J. M. G., Ven, A. A. F. van de, and Sauren, A. A. H. J. (1987) A note on the reduced creep function corresponding to the quasi—linear visco-elastic model proposed by Fung. Private Communication.Google Scholar
  27. Dunn, F., Edmonds, P. D., and Fry, W. J. (1969) Ultrasound. In Biological Engineering, H. P. Schwan (ed.) McGraw-Hill, New York, p. 205.Google Scholar
  28. Emery, A. H. and White, M. L. (1969) A single-integral constitutive equation. Trans. Soc. Rheolo. 13, 103–110.Google Scholar
  29. Feughelman, M. (1963) Free-energy difference between the alpha and beta states in keratin. Nature 200, 127–129.Google Scholar
  30. Flory, P. J. and Garrett, R. R. (1958) Phase transitions in collagen and gelatin systems. J. Am. Chem. Soc. 80, 4836–4845.Google Scholar
  31. Fronek, K., Schmid-Schönbein, G., and Fung, Y. C. (1975) A noncontact method for three-dimensional analysis of vascular elasticity in vivo and in vitro. J. Appl. Physiol. 40, 634–637.Google Scholar
  32. Fung, Y. C. (1965) Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  33. Fung, Y. C. (1967) Elasticity of soft tissues in simple elongation. Am. J. Physiol. 213, 1532–1544.PubMedGoogle Scholar
  34. Fung, Y. C. (1968) Biomechanics: Its scope, history, and some problems of continuum mechanics is physiology. Appl. Mech. Rev. 21, 1–20.Google Scholar
  35. Fung, Y. C. (1972) Stress—strain-history relations of soft tissues in simple elongation. In Biomechanics: Its Foundations and Objectives, Y. C. Fung, N. Perrone, and M. Anliker (eds.) Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  36. Fung, Y. C. (1973) “Biorheology of soft tissues.” Presented on September 5, 1972 to the International Congress of Biorheology, Lyon, France. (Biorheology 10, 139–155.)Google Scholar
  37. Fung, Y. C. (1975) Stress, deformation, and atelectasis of the lung. Circulation Res. 37, 481–496.PubMedGoogle Scholar
  38. Fung, Y. C. (1977) A First Course in Continuum Mechanics. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  39. Fung, Y. C., Tong, P., and Patitucci, P. (1978) Stress and strain in the lung. J. Eng. Mech. Div. Am. Soc. Civil Eng. 104(EMI), 201–224.Google Scholar
  40. Fung, Y. C. (1979) Inversion of a class of nonlinear stress—strain relationships of biological soft tissues. J. Biomech. Eng. 101, 23–27.Google Scholar
  41. Fung, Y. C. and Sobin, S. S. (1981) The retained elasticity of elastin under fixation agents. J. Biomech. Eng. 103, 121–122.PubMedGoogle Scholar
  42. Fung, Y. C. (1990) Biomechanics: Motion, Flow, Stress, and Growth. Springer-Verlag, New York.Google Scholar
  43. Gathercole, L. J., Keller, A., and Shah, J. S. (1974) The periodic wave pattern in native tendon collagen: Correlation of polarizing with scanning electron microscopy. J. Microscopy 102, 95–105.Google Scholar
  44. Gizdulich, P. and Wesseling K. H. (1988) Forearm arterial pressure-volume relationships in man. Clin. Phys. Physiol. Meas. 9, 123–132.PubMedGoogle Scholar
  45. Gordon, M. K., Gerecke, D. R., and Olsen, B. R. (1987) Type XII collagen: Distinct extracellular matrix component discovered by cDNA cloning. Proc. Nat. Acad. Sci. U. S. A. 84, 6040–6044.Google Scholar
  46. Gosline, J. M. (1978) Hydrophobic interaction and a model for the elasticity of elastin. Biopolymers, 17, 677–695.PubMedGoogle Scholar
  47. Gray, W. R. (1970) Some kinetic aspects of crosslink biosynthesis. Adv. Exp. Med. Biol. 79, 285–290.Google Scholar
  48. Green, A. E. and Adkins, J. E. (1960) Large Elastic Deformations. Oxford University Press, New York.Google Scholar
  49. Guth, E., Wack, P. E., and Anthony, R. L. (1946) Significance of the equation of state for rubber. J. Appl. Physiol. 17, 347–351.Google Scholar
  50. Hardung, V. (1952) Ueber eine methode zur messung der dynamischen elastizität und viskosität kautschukähnlicher körper, insbesondere von Blutgefäszen und anderen elastischen geweheteilen. Heiv. Physiol. Pharm. Acta 10, 482–498.Google Scholar
  51. Harkness, M. C. R., Harkness, R. D., and McDonald, D. A. (1957) The collagen and elastin content of the arterial wall in the dog. Proc. Roy. Soc. London B 146, 541–551.Google Scholar
  52. Harkness, M. L. R. and Harkness, R. D. (1959a) Changes in the physical properties of the uterine cervix of the rat during pregnancy. J. Physiol. 148, 524–547.PubMedGoogle Scholar
  53. Harkness, M. L. R. and Harkness, R. D. (1959b) Effect of enzymes on mechanical properties of tissues. Nature 183, 821–822.Google Scholar
  54. Harkness, R. D. (1966) Collagen, Sci. Progr. 54, 257–274.Google Scholar
  55. Hart-Smith, L. J. and Crisp, J. D. C. (1967) Large elastic deformations of thin rubber membranes. Int. J. Eng. Sci. 5, 1–24.Google Scholar
  56. Hearle, J. W. S. (1963) Fiber structure. J. Appl. Polym. Sci. 7, 172–192, 207–223.Google Scholar
  57. Hoeltzel, D. A., Altman, P., Buzard, K., and Choe, K.-I. (1992) Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J. Biomech. Eng. 114, 202–215.PubMedGoogle Scholar
  58. Hoeve, C. A. J. and Flory, P. J. (1958). The elastic properties of elastin. J. Am. Chem. Soc. 80, 6523–6526.Google Scholar
  59. Hoppin, F. G., Lee, J. C., and Dawson, S. V. (1975) Properties of lung parenchyma in distortion. J. Appl. Physiol. 39, 742–751.PubMedGoogle Scholar
  60. Humphrey, J. D., Vawter, D. L., and Vito, R. P. (1987) Pseudoelasticity of excised visceral pleura. J. Biomech. Eng. 109, 115–120.PubMedGoogle Scholar
  61. Johnson, G. A., Rajagopal, K. R., and Woo, S. L.-Y. (1992) A single integral finite strain viscoelastic model of ligaments and tendons. To be published.Google Scholar
  62. Kastelic, J., Galeski, A., and Baer, E. (1978) The multicomposite structure of tendon. J. Connective Tissue Res. 6, 11–23.Google Scholar
  63. Kenedi, R. M., Gibson, T., and Daly, C. H. (1964) Bioengineering studies of the human skin; the effects of unidirectional tension. In Structure and Function of Connective and Skeletal Tissue, S. F. Jackson, S. M. Harkness, and G. R. Tristram (eds.) Scientific Committee, St. Andrews, Scotland, pp. 388–395.Google Scholar
  64. Kenedi, R. M., Gibson, T., Evans, J. H., and Barbenel, J.G. (1975) Tissue mechanics. Phys. Med. Biol. 20, 699–717.PubMedGoogle Scholar
  65. Kishino, A. and Yanagida, T. (1988) Force measurements by micromanipulation of a single actin filament by glass needles. Nature, 334, 74–76.PubMedGoogle Scholar
  66. Knopoff, L. (1965) Attenuation of elastic waves in the Earth. In Physical Acoustics, W. P. Mason (ed.) Academic Press, New York, Vol. IIIB, Chapter 7, pp. 287324.Google Scholar
  67. Kwan, M. K. and Woo, S. L.-Y. (1989) A structural model to describe the nonlinear stress—strain behavior for parallel-fibered collagenous tissues. J. Biomech. Eng. 111, 361–363.PubMedGoogle Scholar
  68. Lai-Fook, S. J. (1977) Lung parenchyma described as a prestressed compressible material. J. Biomech. 10, 357–365.PubMedGoogle Scholar
  69. Lai-Fook, S. J., Wilson, T. A., Hyatt, R. E., and Rodarte, J. R. (1976) Elastic constants of inflated lobes of dog lungs. J. Appl. Physiol. 40, 508–513.PubMedGoogle Scholar
  70. Lanczos, C. (1956) Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  71. Langewouters, G. J., Wesseling, K. H., and Goedhard, W. J. A. (1984) The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J. Biomech. 17, 425–435.PubMedGoogle Scholar
  72. Langewouters, G. J., Wesseling, K. H., and Goedhard, W. J. A. (1985) The pressure dependent dynamic elasticity for 35 thoracic and 16 abdominal human aortas in vitro described by a five component model. J. Biomech. 18, 613–620.PubMedGoogle Scholar
  73. Langewouters, G. J., Zwart, A., Busse, R., and Wesseling, K. H. (1986) Pressure-diameter relationships of segments of human finger arteries. Clin. Phys. Physiol. Meas. 7, 43–55.PubMedGoogle Scholar
  74. Lanir, Y. (1979a) A structural theory for the homogeneous biaxial stress—strain relationship in flat collagenous tissues. J. Biomech. 12, 423–436.PubMedGoogle Scholar
  75. Lanir, Y. (1979b) The rheological behavior of the skin: Experimental results and a structural model. Biorheology 16, 191–202.PubMedGoogle Scholar
  76. Lanir, Y. and Fung, Y. C. (1974) Two-dimensional mechanical properties of rabbit skin. I. Experimental system. J. Biomech. 7, 29–34. II. Experimental results. ibid., 7, 171–182.Google Scholar
  77. Lee, J. S., Frasher, W. G., and Fung, Y. C. (1967) Two-Dimensional Finite-Deformation on Experiments on Dog’s Arteries and Veins. Tech. Rept. No. AFOSR 67–1980, University of California, San Diego, California.Google Scholar
  78. Lee, J. S., Frasher, W. G., and Fung, Y. C. (1968) Comparison of the elasticity of an artery in vivo and in excision. J. Appl. Physiol. 25, 799–801.PubMedGoogle Scholar
  79. Lee, M. C., LeWinter, M. M., Freeman, G., Shabetai, R., and Fung, Y. C. (1985) Biaxial mechanical properties of the pericardium in normal and volume overloaded dogs. Am. J. Physiol. 249, H222 — H230.Google Scholar
  80. Majack, R. H. and Bornstein, P. (1985) Heparin regulates the collagen phenotype of vascular smooth muscle cells: Induced synthesis of an MPVrPV 60,000 collagen. J. Cell Biol. 100, 613–619.Google Scholar
  81. McElhaney, J. H. (1966) Dynamic response of bone and muscle tissue. J. Appl. Physiol. 21, 1231–1236.PubMedGoogle Scholar
  82. Mecham, R. P. and Heuser, J. E. (1991). In Cell biology and extracellular matrix. 2nd ed. (ed. by E. D. Hay), Chapter 3. Plenum Press, New York.Google Scholar
  83. Miller, E. J. (1988) Collagen types: Structure, distribution, and functions. Collagen 1, 139–154.Google Scholar
  84. Mooney, M. (1940) A theory of large elastic deformation. J. Appl. Phys. 11, 582–592.Google Scholar
  85. Morgan, F. R. (1960) The mechanical properties of collagen fibres: Stress—strain curves. J. Soc. Leather Trades Chem. 44, 171–182.Google Scholar
  86. Nemetschek, T., Riedl, H., Jonak, R., Nemetschek-Gansler, H., Bordas, J., Koch, M. H. J., and Schilling, V. (1980) Die viskoelastizität parallelsträngigen bindegewebes and ihre bedeutung für die function. Virchows Arch. A Path. Anat. Histol. 386, 125–151.Google Scholar
  87. Neubert, H. K. P. (1963) A simple model representing internal damping in solid materials. Aeronaut. Q. 14, 187–197.Google Scholar
  88. Nimni, M. E. (1988) Collagen. 4 Vols: 1. Biochemistry; 2. Biochemistry and Biomechanics; 3. Biotechnology; 4. Molecular Biology, B. R. Olsen (co-ed.) CRC Press, Boca Raton, FL.Google Scholar
  89. Olsen, B. R., Gerecke, D., Gordon, M., Green, G., Kimura, T., Konomi, H., Muragaki, Y., Ninomiya, Y., Nishimura, I., and Sugrue, S. (1988). A new dimension in the extracellular matrix. In Collagen, M. Nimni (ed.) CRC Press, Boca Raton, FL, Vol. 4.Google Scholar
  90. Patel, D. J., Carew, T. E., and Vaishnav, R. N. (1968) Compressibility of the arterial wall. Circulation Res. 23, 61–68.PubMedGoogle Scholar
  91. Patel, D. J., Tucker, W. K., and Janicki, J. S. (1970) Dynamic elastic properties of the aorta in radial direction. J. Appl. Physiol. 28, 578–582.PubMedGoogle Scholar
  92. Patel, D. J. and Vaishnav, R. N. (1972) The rheology of large blood vessels. In Cardiovascular Fluid Dynamics, D. H. Bergel (ed.) Academic, New York, Vol. 2, pp. 1–64.Google Scholar
  93. Pereira, J. M., Mansur, J. M., and Davis, B. R. (1991) The effects of layer properties on shear disturbance propagation in skin. J Biomech. Eng. 113, 30–35.PubMedGoogle Scholar
  94. Pinto, J. and Fung, Y. C. (1973) Mechanical properties of the heart muscle in the passive state, and stimulated papillary muscle in quick-release experiments. J. Biomech. 6, 597–616, 617–630.Google Scholar
  95. Pipkin, A. C. and Rogers, T. G. (1968) A nonlinear integral representation for viscoelastic behavior. J. Mech. Phys. Solids 16, 59–74.Google Scholar
  96. Raju, K. and Anwar, R. A. (1987) Primary structures of the bovine elastin a, b, and c deduced from the sequences of cDNA clones. J. Biol. Chem. 262, 5755–5762.PubMedGoogle Scholar
  97. Ramachandran, G. N. (ed.) (1967) Treatise on collagen. Vol. 1. Chemistry of Collagen. Vol. 2. Biology of Collagen. Vol. 3. Chemical Pathology of Collagen. Univ. Madra, India. Academic Press, New York.Google Scholar
  98. Ridge, M. D. and Wright, V. (1964) The description of skin stiffness. Biorheology 2, 67–74.Google Scholar
  99. Ridge, M. D. and Wright, V. (1966) Mechanical properties of skin: A bioengineering study of skin texture. J. Appl. Physiol. 21, 1602–1606.PubMedGoogle Scholar
  100. Riedl, H., Nemetschek, T., and Jonak, R. (1980) A mathematical model for the changes of the long-period structure of collagen. In Biology of Collagen, A. Viidik and J. Vuust (eds.) Academic Press, San Diego, pp. 289–296.Google Scholar
  101. Rivlin, R. S. (1947) Torsion of a rubber cylinder. J. Appl. Phys. 18, 444–449.Google Scholar
  102. Rivlin, R. S. and Saunders, D. W. (1951) Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber. Philos. Trans. Soc. London A 243, 251–288.Google Scholar
  103. Routbart, J. L. and Sack, H. S. (1966) Background internal friction of some pure metals at low frequencies. J. Appl. Phys. 37, 4803–4805.Google Scholar
  104. Schneider, D. (1982) Viscoelasticity and tearing strength of the human skin. Ph. D. Dissertation. Department of AMES/Bioengineering. University of California, San Diego.Google Scholar
  105. Shoemaker, P. A. (1984) Irreversible thermodynamics, the constitutive law, and a constitutive model for two-dimensional soft tissues. Ph. D. Dissertation, University of California, San Diego.Google Scholar
  106. Shoemaker, P. A., Schneider, D., Lee, M. C., and Fung, Y. C. (1986) A constitutive model for two-dimensional soft tissues an its application to experimental data. J. Biomech. 19, 695–702.PubMedGoogle Scholar
  107. Sidrick, N. (1976) Constitutive equation of rabbit skin subjected to shear stress. The torsion test. M. S. Thesis, AMES Bioengineering Department. University of California, San Diego.Google Scholar
  108. Snyder, R. W. (1972) Large deformation of isotropic biological tissue. J. Biomech. 5, 601–606.PubMedGoogle Scholar
  109. Sobin, S. S., Fung, Y. C., and Tremer, H. M. (1988) Collagen and elastin fibers in human pulmonary alveolar walls. J. Appl. Physiol. 64: 1659–1675.PubMedGoogle Scholar
  110. Theodorsen, T. and Garrick, E. (1940) Mechanism of Flutter. Rept. 685, U. S. Nat. Adv. Comm. Aeronaut.Google Scholar
  111. Tong, P. and Fung, Y. C. (1976) The stress—strain relationship for the skin. J. Biomech. 9, 649–657.PubMedGoogle Scholar
  112. Tong, P. and Fung, Y. C. (1976) The stress—strain relationship for the skin. J. Biomech. 9, 649–657.PubMedGoogle Scholar
  113. Torp, S., Arridge, R. G. C., Armeniades, C. D., and Baer, E. (1974) Structure-property relationships in tendon as a function of age. In Proc. 1974 Colston Conference, Dept. of Physics, University of Bristol, U. K., pp. 197–222. See also, pp. 223–250.Google Scholar
  114. Treloar, L. R. G. (1967) The Physics of Rubber Elasticity, 2nd edition. Oxford University Press, New York.Google Scholar
  115. Urry, D. W. (1985) Protein elasticity based on conformations of sequential polypeptides: the biological elastic fiber. J. Protein Chem. 3, 403–436.Google Scholar
  116. Urry, D. W., Haynes, B., and Harris, R. D. (1986) Temperature dependence of length of elastin and its polypentapeptide. Biochem. and Biophys. Res. Commun. 141, 749–755.Google Scholar
  117. Urry, D. W. (1991) Thermally driven self-assembly, molecular structuring, and entropic mechanisms in elastomeric polypeptides. In Molecular Conformation and Biological Interaction (G. N. Ramachandran Festschrift), P. Balaram and S. Ramaseshan (eds.) Indian Academy of Science, Bangalore, India, pp. 555–583.Google Scholar
  118. Urry, D. W. (1992) Free energy transduction in polypeptides and proteins based on inverse temperature transitions. Progr. Biophys. Mol. Biol. 57, 23–57.Google Scholar
  119. Valanis, K. C. and Landel, R. I. (1967) The strain-energy function of hyperelastic material in terms of the extension ratios. J. Appl. Phys. 38, 2997–3002.Google Scholar
  120. Van Brocklin, J. D. and Ellis, D. (1965) A study of the mechanical behavior of toe extensor tendons under applied stress. Arch. Phys. Med. Rehab. 46, 369–375.Google Scholar
  121. Vawter, D., Fung, Y. C., and West, J. B. (1978) Elasticity of excised dog lung parenchyma. J. Appl. Physiol. 45, 261–269.PubMedGoogle Scholar
  122. Vawter, D., Fung, Y. C., and West, J. B. (1979) Constitutive equaton of lung tissue elasticity. J. Biomech. Eng. Trans. ASME 101, 38–45.Google Scholar
  123. Veronda, D. R. and Westmann, R. A. (1970) Mechanical characterizations of ski-finite deformations. J. Biomech. 3, 111–124.PubMedGoogle Scholar
  124. Viidik, A. (1966) Biomechanics and functional adaptation of tendons and joint ligaments. In Studies on the Anatomy and Function of Bone and Joints, F. G. Evans (ed.) Springer-Verlag, New York, pp. 17–39.Google Scholar
  125. Viidik, A. (1968) A rheological model for uncalcified parallel-fibered collagenous tissue. J. Biomech. 1, 3–11.PubMedGoogle Scholar
  126. Viidik, A. (1978) On the correlation between structure and mechanical function of soft connective tissues. Verh. Anat. Ges. 72, 75–89.PubMedGoogle Scholar
  127. Viidik, A. and Vuust, J. (eds.) (1980) Biology of Collagen Academic Press, New York. Chapter 17, by Viidik, Mechanical Properties of Parallel-fibered Collagenous Tissues, pp. 237–255; Chapter 18, by Viidik, Interdependence between Structure and Function in Collagenous Tissues, pp. 257–280.Google Scholar
  128. Viidik, A. (1990) Structure and function of normal and healing tendons and ligaments. In Biomechanics of Diarthrodial Joints, Mow, Ratcliffe, and Woo (eds.) Springer-Verlag, New York, pp. 3–38.Google Scholar
  129. Wagner, K. W. (1913) Zur theorie der unvoll Kommener dielektrika. Ann. Phys. 40, 817–855.Google Scholar
  130. Wertheim, M. G. (1847) Memoire sur l’elasticite et la coheison des principaux tissus du corps humain. Ann. Chimie Phys. Paris (Ser. 3 ), 21, 385–414.Google Scholar
  131. Westerhof, N. and Noodergraaf, A. (1970) Arterial viscoelasticity: A generalized model. J. Biomech. 3, 357–379.PubMedGoogle Scholar
  132. Wilson, T. A. (1972) A continuum analysis of a two-dimensional mechanical model for the lung parenchyma. J. Appl. Physiol. 33, 472–478.PubMedGoogle Scholar
  133. Wineman, A. S. (1972) Large axially symmetric stretching of a nonlinear viscoelastic membrane. Int. J. Solids Struct. 8, 775–790.Google Scholar
  134. Wineman, A., Wilson, D., and Melvin, J. W. (1979) Material identification of soft tissue using membrane inflation. J. Biomech. 12, 841–850.PubMedGoogle Scholar
  135. Wineman, A. S. and Rajagopal, K. R. (1990) On a constitutive theory for materials undergoing microstructural changes. Arch. Mech. 42, 53–75, Warszawa.Google Scholar
  136. Woodhead-Galloway, J. (1980) Collagen: The anatomy of a protein. Arnold, London.Google Scholar
  137. Yager, D., Feldman, H., and Fung, Y. C. (1992) Microscopic vs. macroscopic deformation of the pulmonary alveolar duct. J. Appl. Physiol. 72, 1348–1354.PubMedGoogle Scholar
  138. Zeng, Y. J., Yager, D., and Fung, Y. C. (1987) Measurement of the mechanical properties of the human lung tissue. J. Biomech. Eng. 109, 169–174.PubMedGoogle Scholar
  139. Young, J. T., Vaishnav, R. N., and Patel, D. J. (1977) Nonlinear anisotropic viscoelastic properties of canine arterial segments. J. Biomech. 10, 549–559.PubMedGoogle Scholar

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© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Yuan-Cheng Fung
    • 1
  1. 1.Department of BioengineeringUniversity of California, San DiegoLa JollaUSA

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