A micromechanics finite-strain constitutive model of fibrous tissue

Journal of the Mechanics and Physics of Solids

Volumn 59, Issue 9, 2011, Pages 1823-1837

  Chen, Huan ^a   Liu, Yi ^a   Zhao, Xuefeng ^a   Lanir, Yoram ^b   Kassab, Ghassan S ^a,c  

^a Indiana University Purdue University Indianapolis   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c INDIANA UNIVERSITY   (United States)

Author keywords

Collagen; Fibers; Microstructure; Tissue; Vessel

Indexed keywords

AFFINE DEFORMATION; BIOLOGICAL TISSUES; ENGINEERED TISSUES; FIBER DISTRIBUTION; FIBROUS TISSUE; FINITE-ELEMENT; HETEROGENEOUS INTERACTIONS; HOMOGENIZATION THEORY; LOW PRESSURES; MACROSCOPIC DEFORMATIONS; MATERIAL NON-LINEARITY; MICROSTRUCTURAL MODELS; SECOND ORDERS; STRESS STRAIN RELATION; TISSUE COMPONENTS; VESSEL;

BLOOD VESSELS; COLLAGEN; COMPUTER SIMULATION; CONSTITUTIVE MODELS; DEFORMATION; FIBERS; FINITE ELEMENT METHOD; FORECASTING; HISTOLOGY; MICROMECHANICS; MICROSTRUCTURE; STRAIN; TISSUE;

BIOMECHANICS;

EID: 80051792162     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2011.05.012     Document Type: Article

References (55)

1. L. Annovazzi, and F. Genna An engineering, multiscale constitutive model for fiber-forming collagen in tension J. Biomed. Mater. Res. Part A 92 1 2010 254 266
2. T. Azuma, and M. Hasegawa A rheological approach to the architecture of arterial walls Japan J. Physiol. 21 1971 37 47
3. T. Azuma, and S. Oka Mechanical equilibrium of blood vessel walls Am. J. Physiol. 221 1971 1310
4. I.A. Brown A scanning electron microscope study of the effect of uniaxial tension on human skin Br. J. Dermatol. 89 1973 383 393
5. C.J. Chuong, and Y.C. Fung Three-dimensional stress distribution in arteries ASME J. Biomech. Eng. 105 1983 268 274 (Pubitemid 14164182)
6. S.L. Dahl, M.E. Vaughn, J.J. Hu, N.J. Driessen, F.P. Baaijens, J.D. Humphrey, and L.E. Niklason A microstructurally motivated model of the mechanical behavior of tissue engineered blood vessels Ann. Biomed. Eng. 36 11 2008 1782 1792
7. W.F. Decraemer, M.A. Maes, and V.J. Vanhuyse An elastic stressstrain relation for soft biological tissues based on a structure model J. Biomech. 13 1980 463 468 (Pubitemid 10119798)
8. S.X. Deng, J. Tomioka, J.C. Debes, and Y.C. Fung New experiments on shear modulus of elasticity of arteries Am. J. Physiol. 266 1994 1 10
9. P. Fratzl, K. Misof, and I. Zizak Fibrillar structure and mechanical properties of collagen J. Struct. Biol. 122 1997 119 122
10. Y.C. Fung, K. Fronek, and P. Patitucci Pseudoelasticity of arteries and the choice of its mathematical expression Am. J. Physiol. 237 1979 620 631
11. E. Gentleman, A.N. Lay, D.A. Dickerson, E.A. Nauman, G.A. Livesay, and K.C. Dee Mechanical characterization of collagen fibers and scaffolds for tissue engineering Biomaterials 24 2003 3805 3813 (Pubitemid 36773614)
12. J. Gosline, M. Lillie, E. Carrington, P. Guerette, C. Ortlepp, and K. Savage Elastic protein: biological roles and mechanical properties Philos. Trans. R. Soc. Lond. B 357 2002 121 132 (Pubitemid 34276203)
13. N. Gundiah, M.B. Ratcliffe, and L.A. Pruitt Determination of strain energy function for arterial elastin: experiments using histology and mechanical tests J. Biomech. 40 2007 585 594
14. R. Hill On constitutive macro-variables for the heterogeneous solids at finite strain Proc. R. Soc. Lond. A 326 1972 131 147
15. R. Hill, and J. Rice Elastic potentials and the structure of in elastic constitutive laws SIAM J. Appl. Math. 25 1973 448 461
16. G.A. Holzapfel, and T.C. Gasser A new constitutive framework for arterial wall mechanics and a comparative study of material models J. Elasticity 61 2000 1 48 (Pubitemid 32732278)
17. G.A. Holzapfel, and H.W. Weizsacker Biomechanical behavior of the arterial wall and its numerical characterization Comput. Biol. Med. 28 1998 377 392 (Pubitemid 28481518)
18. J.D. Humphrey Mechanics of arterial wall: review and directions Crit. Rev. Biomed. Eng. 23 1995 1 162 (Pubitemid 26132679)
19. J.D. Humphrey, and F.C. Yin A new constitutive formulation for characterizing the mechanical behavior of soft tissue Biophys. J. 52 4 1987 563 570
20. M. Kailasam, P. Ponte Castaneda, and J.R. Willis The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites - I. Philos. Trans. R. Soc. Lond. A 355 1997 1835 1852
21. M. Kroon, and G.A. Holzapfel A new constitutive model for multi-layered collagenous tissues J. Biomech. 41 2008 2766 2771
22. Y. Lanir A structural theory for the homogeneous biaxial stressstrain relationship in flat collagenous tissues J. Biomech. 12 1979 423 436 (Pubitemid 9191484)
23. Y. Lanir Constitutive equations for fibrous connective tissues J. Biomech. 16 1983 1 12 (Pubitemid 13125809)
24. R. Lebensohn, Y. Liu, and P. Ponte Castaneda Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates Proc. R. Soc. Lond. Ser. A 460 2004 1381 1405 (Pubitemid 38608941)
25. D. Li, and A.M. Robertson A structural multi-mechanism constitutive equation for cerebral arterial tissue Int. J. Solids Struct. 46 2009 2920 2928
26. Liu, Y., 2003. Macroscopic behavior, field fluctuations and texture evolution in viscoplastic polycrystals. Ph.D. Thesis, University of Pennsylvania, U.S.A.
27. Y. Liu, P. Gilormini, and P. Ponte Castaneda Variational self-consistent estimates for texture evolution in viscoplastic polycrystals - application to titanium Acta Mater. 51 2003 5425 5437
28. Y. Liu, and P. Ponte Castaneda Second-order estimates for the effective behavior and field fluctuations in viscoplastic polycrystals J. Mech. Phys. Solids 52 2004 467 495
29. Y. Liu, and P. Ponte Castaneda Homogenization estimates for the effective behavior and field heterogeneity in cubic and HCP polycrystals J. Mech. Phys. Solids 52 2004 1175 1211
30. O. Lokshin, and Y. Lanir Micro and macro rheology of planar tissues Biomaterials 30 2009 3118 3127
31. O. Lopez-Pamies, and P. Ponte Castaneda Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations J. Elasticity 76 2004 247 287 (Pubitemid 40512156)
32. O. Lopez-Pamies, and P. Ponte Castaneda Second-order homogenization estimates incorporating field fluctuations in finite elasticity Math. Mech. Solids 9 2004 243 270
33. O. Lopez-Pamies, and P. Ponte Castaneda On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformation: I - Theory J. Mech. Phys. Solids 54 2006 807 830 (Pubitemid 43121439)
34. O. Lopez-Pamies, and P. Ponte Castaneda Homogenization-based constitutive models for porous elastomer and implications for macroscopic instabilities. I - Analysis J. Mech. Phys. Solids 55 2007 1677 1701 (Pubitemid 46977427)
35. X. Lu, A. Pandit, and G.S. Kassab Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model Am. J. Physiol. Heart Circ. Physiol. 287 2004 1663 1669
36. V. Mohanaradhakrishnan, N. Ramanathan, and Y. Nayudamma Strength of collagen fibers obtained from different sources Biorheology 7 1970 119 124
37. R. Ogden Extremun principles in nonlinear elasticity and their application to composites: Part I Int. J. Solids Struct. 14 1978 265 282 (Pubitemid 8596869)
38. Oka, S., 1967. Theoretical studies on hemorheology. The 16th Rheology Symposium, Sapporo.
39. S. Oka Some theoretical studies on hemorheology M. Kotani, Advances in Biophysics 1972 University of Tokyo Press Tokyo 97
40. S. Oka, and T. Azuma Physical theory of tension in thick walled blood vessels in equilibrium Biorheology 7 1970 109 117
41. V. Ottani, M. Raspanti, and A. Ruggeri Collagen structure and functional implications Micron 32 2001 251 260
42. P. Ponte Castaneda Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory and II. Applications J. Mech. Phys. Solids 50 2002 737 782
43. P. Ponte Castaneda, and E. Tiberio A second-order homogenization procedure in finite elasticity and applications to black-filled elastomers J. Mech. Phys. Solids 48 2000 1389 1411 (Pubitemid 30594339)
44. P. Ponte Castaneda, and J.R. Willis The effect of spatial distribution on the effective behavior of composite materials and cracked media J. Mech. Phys. Solids 43 1995 1919 1951
45. J.A.G. Rhodin Architecture of the vessel wall R.M. Berne, Handbook of Physiology vol. 2 1979 American Physiology Society, Sect. 2 1 31
46. M.S. Sacks Incorporation of experimentally derived fiber orientation into a structural constitutive model for planar collagenous tissues J. Biomech. Eng. 125 2 2003 280 287 (Pubitemid 36506143)
47. A. Sverdlik, and Y. Lanir Time-dependent mechanical behavior of sheep digital tendons, including the effects of preconditioning J. Biomech. Eng. 124 1 2002 78 84 (Pubitemid 34165118)
48. K. Takamizawa, and K. Hayashi Strain energy density function and uniform strain hypothesis for arterial mechanics J. Biomech. 20 1987 7 17 (Pubitemid 17000562)
49. R.N. Vaishnav, J.T. Young, and D.J. Patel Distribution of stresses and of strain-energy density through the wall thickness in a canine aortic segment. Circ. Res. 32 1973 577 583
50. R.P. Vito, and S. Dixon Blood vessel constitutive models - 19952002 Ann. Rev. Biomed. Eng. 5 2003 413 439 (Pubitemid 40125318)
51. J.R. Willis Bounds and self-consistent estimates for the overall moduli of anisotropic composites J. Mech. Phys. Solids 25 1977 185 202 (Pubitemid 8551428)
52. H. Wolinsky, and S. Glagov A lamellar unit of aortic medial structure and function in mammals Circ. Res. 20 1967 99 111
53. F.L. Wuyts, V.J. Vanhuyse, G.J. Langewoutters, W.F. Decraemer, E.R. Raman, and S. Buyle Elastic properties of human aortas in relation to age and atherosclerosis: a structural model Phys. Med. Biol. 40 1995 1577 1597
54. A. Zoumi, X. Lu, G.S. Kassab, and B.J. Tromberg Imaging coronary artery microstructure using second-harmonic and two-photon fluorescence microscopy Biophys. J. 87 2004 2778 2786
55. M.A. Zulliger, F. Fridez, K. Hayashi, and N. Stergiopulos A strain energy function for arteries accounting for wall composition and structure J. Biomech. 37 2004 989 1000 (Pubitemid 38686323)