Multiporoelasticity of hierarchically structured materials: Micromechanical foundations and application to bone

Journal of Engineering Mechanics

Volumn 135, Issue 5, 2009, Pages 382-394

  Hellmich, Christian ^a   Celundova, Dana ^a,b   Ulm, Franz Josef ^c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

^c Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Drainage; Elasticity; Foundations; Material properties; Pore pressures

Indexed keywords

ANISOTROPIC EFFECTS; BONE TISSUES; COLLAGEN MOLECULES; ELASTIC MODELS; FLUID MASS; LOADING DIRECTIONS; MATERIAL PROPERTIES; MICRO MECHANICALS; MULTI-SCALE; PORE SPACES; STRUCTURED MATERIALS;

BONE; COMPOSITE MICROMECHANICS; ELASTICITY; MINING; PORE PRESSURE;

BIOLOGICAL MATERIALS;

BIOMECHANICS; BONE; CONFERENCE PROCEEDING; MICROMECHANICS; PORE PRESSURE; POROELASTICITY;

EID: 65449131575     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)EM.1943-7889.0000001     Document Type: Conference Paper

References (57)

1. Beck, B., Qin, Y.-X., McLeod, K., and Otter, M. (2002). "On the relationship between streaming potential and strain in an in vivo bone preparation." Calcif. Tissue Int. CTINDZ0171-967X, 71, 335-343.
2. Bonar, L., Lees, S., and Mook, H. (1985). "Neutron diffraction studies of collagen in fully mineralized bone." J. Mol. Biol. JMOBAK0022-283610.1016/0022-2836(85)90090-7, 181, 265-270.
3. Bryant, J. (1983). "The effect of impact on the marrow pressure of long bones in vitro." J. Biomech. JBMCB50021-929010.1016/ 0021-9290(83)90117-3, 16(8), 659-665.
4. Bryant, J. (1988). "On the mechanical function of marrow in long bones." Eng. Med. ZZZZZZ0046-2039, 17(2), 55-58.
5. Buechner, P., Lakes, R., Swan, C., and Brand, R. (2001). "A broadband viscoelastic spectroscopic study of bovine bone: Implications for fluid flow." Ann. Biomed. Eng. ABMECF0090-696410.1114/ 1.1385813, 29, 719-728.
6. Chateau, X., and Dormieux, L. (1998). "Homogenization of a non-saturated porous medium: Hill's lemma and applications." C. R. Acad. Sci., Ser. IIb Mec. Phys. Astron. CRSMF21287-4620, 320, 627-634.
7. Chateau, X., and Dormieux, L. (2002). "Micromechanics of saturated and unsaturated porous media." Int. J. Numer. Analyt. Meth. Geomech. IJNGDZ0363-906110.1002/nag.227, 26, 831-844.
8. Cheng, A. H.-D. (1997). "Material coefficients of anisotropic poroelasticity." Int. J. Rock Mech. Min. Sci. ZZZZZZ1365-1609, 34(2), 199-205.
9. Coussy, O. (1995). Mechanics of porous continua, Wiley, Chichester, U.K.
10. Coussy, O. (2004). Poromechanics, Wiley, Chichester, U.K.
11. Cowin, S. (1999). "Bone poroelasticity." J. Biomech.JBMCB50021-929010.1016/S0021-9290(98)00161-4, 32, 217-238.
12. Cowin, S., Weinbaum, S., and Zeng, Y. (1995). "A case for bone canaliculi as the anatomical site of strain generated potentials." J. Biomech. JBMCB50021-929010.1016/0021-9290(95)00058-P, 28(11), 1281-1297.
13. Cusack, S., and Miller, A. (1979). "Determination of the elastic constants of collagen by Brillouin light scattering." J. Mol. Biol. JMOBAK0022-283610.1016/0022-2836(79)90339-5, 135, 39-51.
14. Dormieux, L., Kondo, D., and Ulm, F.-J. (2006). Microporomechanics, Wiley, New York.
15. Dormieux, L., and Ulm, F.-J., eds. (2005). CISM courses and lectures, Volume 480: Applied micromechanics of porous media, Springer, New York.
16. Eppell, S., Tong, W., Katz, J., Kuhn, L., and Glimcher, M. (2001). "Shape and size of isolated bone mineralites measured using atomic force microscopy." J. Orthop. Res. JOREDR0736-026610.1016/ S0736-0266(01)00034-1, 19, 1027-1034.
17. Fornells, P., Garcia-Aznar, J., and Doblaré, M. (2007). "Modeling tracer transport in an osteon under cyclic loading." Ann. Biomed. Eng. ABMECF0090-696410.1007/s10439-007-9351-5, 35(10), 1687-1698.
18. Fritsch, A., and Hellmich, C. (2007). "'Universal' microstructural patterns in cortical and trabecular, extracellular and extravacular bone materials: Micromechanics-based prediction of anisotropic elasticity." J. Theor. Biol. JTBIAP0022-519310.1016/ j.jtbi.2006.09.013, 244, 597-620.
19. Goldsztein, G. (2005). "Transport of nutrients in bone." SIAM J. Appl. Math. SMJMAP0036-139910.1137/040616632, 65(6), 2128-2140.
20. Gururaja, S., Kim, H., Swan, C., Brand, R., and Lakes, R. (2005). "Modeling deformation-induced fluid flow in cortical bone's canalicular-lacunar system." Ann. Biomed. Eng. ABMECF0090-696410.1007/s10439-005-8959-6, 33(1), 7-25.
21. Hellmich, C. (2005). Microelasticity of bone, 289-332.
22. Hellmich, C., Barthélémy, J.-F., and Dormieux, L. (2004a). "Mineral-collagen interactions in elasticity of bone ultrastructure-A continuum micromechanics approach." Eur. J. Mech. A/Solids EJASEV0997-753810.1016/j.euromechsol.2004.05.004, 23, 783-810.
23. Hellmich, C., and Ulm, F.-J. (2002). "Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments." J. Biomech. 1199-1212
24. Hellmich, C., and Ulm, F.-J. (2003). "Average hydroxyapatite concentration is uniform in extracollageneous ultrastructure of mineralized tissue." Biomech. Model. Mechanobiol. BMMICD1617-7959, 2, 21-36.
25. Hellmich, C., and Ulm, F.-J. (2005a). "Drained and undrained poroelastic properties of healthy and pathological bone: A poro-micromechanical investigation." Transp. Porous Media TPMEEI0169-391310.1007/s11242-004-6298-y, 58, 243-268.
26. Hellmich, C., and Ulm, F.-J. (2005b). "Micro-porodynamics of bones: Prediction of the 'Frenkel-Biot' slow compressional wave." J. Eng. Mech. JENMDT0733-939910.1061/(ASCE)0733-9399(2005)131:9(918), 131(9), 918-927.
27. Hellmich, C., Ulm, F.-J., and Dormieux, L. (2004b). "Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions?-Arguments from a multiscale approach." Biomech. Model. Mechanobiol. BMMICD1617-7959, 2, 219-238.
28. Hill, R. (1963). "Elastic properties of reinforced solids: Some theoretical principles." J. Mech. Phys. Solids JMPSA80022-509610.1016/0022-5096(63)90036-X, 11, 357-362.
29. Kafka, V. (1983). "On hydraulic strengthening of bones." Biorheology BRHLAU0006-355X, 20, 789-793.
30. Kafka, V. (1993). "On hydraulic strengthening of bones." J. Biomech. JBMCB50021-929010.1016/0021-9290(93)90038-G, 26, 761-762.
31. Katz, E., and Li, S.-T. (1973). "Structure and function of bone collagen fibrils." J. Mol. Biol. JMOBAK0022-2836, 80, 1-15.
32. Katz, J., and Ukraincik, K. (1971). "On the anisotropic elastic properties of hydroxyapatite." J. Biomech. JBMCB50021-929010.1016/ 0021-9290(71)90007-8, 4, 221-227.
33. Knothe Tate, M. (2003). "Whither flows the fluid in bone? An osteocyte's perspective." J. Biomech. JBMCB50021-929010.1016/ S0021-9290(03)00123-4, 36, 1409-1424.
34. Knothe Tate, M., Niederer, P., and Knothe, U. (1998). "In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading." Bone BONEDL8756-328210.1016/S8756-3282(97)00234-2, 22(2), 107-117.
35. Lees, S. (1987). "Considerations regarding the structure of the mammalian mineralized osteoid from viewpoint of the generalized packing model." Connect. Tissue Res. CVTRBC0300-8207, 16, 281-303.
36. Lees, S., Bonar, L., and Mook, H. (1984a). "A study of dense mineralized tissue by neutron diffraction." Int. J. Biol. Macromol. IJBMDR0141-813010.1016/0141-8130(84)90017-5, 6, 321-326.
37. Lees, S., Hanson, D., and Page, E. (1995). "Some acoustical properties of the otic bones of a fin whale." J. Acoust. Soc. Am. JASMAN0001-496610.1121/1.415430, 99(4), 2421-2427.
38. Lees, S., Heeley, J., and Cleary, P. (1979). "A study of some properties of a sample of bovine cortical bone using ultrasound." Calcif. Tissue Int. CTINDZ0171-967X, 29, 107-117.
39. Lees, S., Pineri, M., and Escoubes, M. (1984b). "A generalized packing model for type I collagen." Int. J. Biol. Macromol. IJBMDR0141-813010.1016/0141-8130(84)90053-9, 6, 133-136.
40. Lees, S., Prostak, K., Ingle, V., and Kjoller, K. (1994). "The loci of mineral in turkey leg tendon as seen by atomic force microscope and electron microscopy." Calcif. Tissue Int. CTINDZ0171-967X10.1007/ BF00425873, 55, 180-189.
41. Levin, V. (1967). "Thermal expansion coefficients of heterogeneous materials." Mech. Mater. MSMSD30167-6636, 2(1), 58-61.
42. Martin, R., Burr, D., and Sharkey, N. (1998). Skeletal tissue mechanics, Springer, New York.
43. Ochoa, J., Sanders, A., Heck, D., and Hillberry, B. (1991). "Stiffening of the femoral head due to intertrabecular fluid and intraosseous pressure." J. Biomed. Eng. JBIEDR0141-5425, 113, 259-262.
44. Pollack, S., Petrov, N., Salzstein, R., Brankov, G., and Blagoeva, R. (1984). "An anatomical model for streaming potentials in osteons." J. Biomech. JBMCB50021-929010.1016/0021-9290(84)90094-0, 17(8), 627-636.
45. Salzstein, R., and Pollack, S. (1987). "Electromechanical potentials in cortical bone-II. Experimental analysis." J. Biomech. JBMCB50021-929010.1016/0021-9290(87)90294-6, 20(3), 271-280.
46. Salzstein, R., Pollack, S., Mak, A., and Petrov, N. (1987). "Electromechanical potentials in cortical bone-I. A continuum approach." J. Biomech. JBMCB50021-929010.1016/0021-9290(87)90293-4, 20(3), 261-270.
47. Schmidt, S., McCready, M., and Ostafin, A. (2005). "Effect of oscillating fluid shear on solute transport in cortical bone." J. Biomech. JBMCB50021-929010.1016/j.jbiomech.2004.09.034, 38, 2237-2343.
48. Smit, T., Burger, E., and Huyghe, J. (2002a). "A case for strain-induced fluid flow as a regulator of BMU-coupling and osteonal alignment." J. Bone Miner. Res. JBMREJ0884-043110.1359/ jbmr.2002.17.11.2021, 17(11), 2021-2029.
49. Smit, T., Huyghe, J., and Cowin, S. (2002b). "Estimation of the poroelastic parameters of cortical bone." J. Biomech. JBMCB50021-929010.1016/S0021-9290(02)00021-0, 35, 829-835.
50. Swan, C., Lakes, R., Brand, R., and Stewart, K. (2003). "Micromechanically based poroelastic modeling of fluid flow in haversian bone." J. Biomech. Eng. JBENDY0148-073110.1115/1.1535191, 125, 25-37.
51. Tong, W., Glimcher, M., Katz, J., Kuhn, L., and Eppell, S. (2003). "Size and shape of mineralites in young bovine bone measured by atomic force microscopy." Calcif. Tissue Int. CTINDZ0171-967X10.1007/s00223-002-1077-7, 72, 592-598.
52. Torabia, S. (2004). "Identification of a relationship between the chemical constituents of mineralized tissues: Bridging computed tomography and micromechanical modeling, for noninvasive determination of elastic properties of bone." Master's thesis, Vienna Univ. of Technology, Vienna, Austria.
53. Urist, M., DeLange, R., and Finerman, G. (1983). "Bone cell differentiation and growth factors." Science SCIEAS0036-807510.1126/ science.6403986, 220, 680-686.
54. Wang, L., Cowin, S., Weinbaum, S., and Fritton, S. (2000). "Modeling tracer transport in an osteon under cyclic loading." Ann. Biomed. Eng. ABMECF0090-696410.1114/1.1317531, 28, 1200-1209.
55. Weinbaum, S., Cowin, S., and Zeng, Y. (1994). "A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses." J. Biomech. JBMCB50021-929010.1016/0021-9290(94)90010-8, 27, 339-3660.
56. Weiner, S., and Wagner, H. (1998). "The material bone: Structure-Mechanical function relations." Annu. Rev. Mater. Sci. ARMSCX0084-660010.1146/annurev.matsci.28.1.271, 28, 271-298.
57. You, L., Cowin, S., Schaffler, M., and Weinbaum, S. (2001). "A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix." J. Biomech. JBMCB50021-929010.1016/S0021-9290(01)00107-5, 34, 1375-1386.