LAYERED WATER IN CRYSTAL INTERFACES AS SOURCE FOR BONE VISCOELASTICITY: ARGUMENTS FROM A MULTISCALE APPROACH

Lukas Eberhardsteiner

References

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  31. [32]: (a) experimental setup, as well as experimentalresults versus model predictions for (b) fully saturated bone specimens and (c) partially dried bone specimens[4] K.S. Prostak and S. Lees. Visualization of crystal-matrix structure. In situ demineralization of mineral-ized turkey leg tendon and bone. Calcified Tissue In-ternational, 59(6):474–479, 1996.[5] S. Lees. Considerations regarding the structure ofthe mammalian mineralized osteoid from viewpointof the generalized packing model. Connective TissueResearch, 16(4):281–303, 1987.[6] N. Sasaki, A. Tagami, T. Goto, M. Taniguchi,M. Nakata, and K. Hikichi. Atomic force micro-scopic studies on the structure of bovine femoral cor-tical bone at the collagen fibril-mineral level. Jour-nal of Materials Science: Materials in Medicine,13(3):333–337, 2002.[7] B. Aoubiza, J.M. Crolet, and A. Meunier. On the me-chanical characterization of compact bone structureusing homogenization theory. Journal of Biomechan-ics, 29(6):1539–1547, 1996.[8] Ch. Hellmich and F.-J. Ulm. Micromechanicalmodel for ultra-structural stiffness of mineralized tis-sues. Journal of Engineering Mechanics (ASCE),128(8):898 – 908, 2002.[9] A. Fritsch and C. Hellmich. ‘Universal’ microstruc-tural patterns in cortical and trabecular, extracellularand extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. Journal ofTheoretical Biology, 244(4):597–620, 2007.[10] A.G. Reisinger, D.H. Pahr, and P.K. Zysset. Sensitiv-ity analysis and parametric study of elastic propertiesof an unidirectional mineralized bone fibril-array us-ing mean field methods. Biomechanics and Modelingin Mechanobiology, 9(5):499–510, 2010.[11] D. Zahn and O. Hochrein. Computational study ofinterfaces between hydroxyapatite and water. Phys-ical Chemistry Chemical Physics, 5(18):4004–4007,2003.[12] H. Pan, J. Tao, T. Wu, and R. Tang. Molecular simula-tion of water behaviors on crystal faces of hydroxyap-atite. Frontiers of Chemistry in China, 2(2):156–163,2007.[13] A. Fritsch, C. Hellmich, and L. Dormieux. Ductilesliding between mineral crystals followed by ruptureof collagen crosslinks: experimentally supported mi-711cromechanical explanation of bone strength. Journalof Theoretical Biology, 260(2):230–252, 2009.[14] A. Zaoui. Continuum micromechanics: survey. Jour-nal of Engineering Mechanics (ASCE), 128(8):808–816, 2002.[15] R. Hill. Elastic properties of reinforced solids: sometheoretical principles. Journal of Mechanics andPhysics of Solids, 11(5):357–372, 1963.[16] P.M. Suquet. Continuum Micromechanics, volume377 of CISM Courses and Lectures. Springer Verlag,Wien New York, 1997.[17] A. Zaoui. Structural Morphology and ConstitutiveBehavior of Microheterogeneous Materials, chap-ter 6, pages 291 – 347. Springer-Verlag, WienNew York, 1997. In [16].[18] C. Donolato. Analytical and numerical inver-sion of the Laplace-Carson transform by a differ-ential method. Computer Physics Communications,145(2):298 – 309, 2002.[19] A. Fritsch, L. Dormieux, and Ch. Hellmich. Porouspolycrystals built up by uniformly and axisymmet-rically oriented needles: homogenization of elasticproperties. Comptes Rendus Mecanique, 334(3):151– 157, 2006.[20] D. Ter Haar. A phenomenological theory of visco-elastic behaviour. Physica, 16(9):719 – 737, 1950.[21] N. Laws and R. McLaughlin. Self-consistent esti-mates for the viscoelastic creep compliances of com-posite materials. Proceedings of the Royal SocietyLondon, Series A, 359:251 – 273, 1978.[22] J. Eshelby. The determination of the elastic field of anellipsoidal inclusion, and related problems. Proceed-ings of the Royal Society London, Series A, 241:376 –396, 1957.[23] N. Laws. The determination of stress and strainconcentrations at an ellipsoidal inclusion in ananisotropic material. Journal of Elasticity, 7(1):91 –97, 1977.[24] A. Stroud. Approximate Calculation of Multiple Inte-grals. Prentice-Hall Englewood Cliffs, 1971.[25] B. Pichler, C. Hellmich, and J. Eberhardsteiner.Spherical and acicular representation of hydrates in amicromechanical model for cement paste: Predictionof early-age elasticity and strength. Acta Mechanica,203(3-4):137–162, 2009.[26] J.C. Nadeau and M. Ferrari. Invariant tensor-to-matrix mappings for evaluation of tensorial expres-sions. Journal of Elasticity, 52(1):43–61, 1998.[27] P. Helnwein. Some remarks on the compressed matrixrepresentation of symmetric second-order and fourth-order tensor. Computer Methods in Applied Mechan-ics and Engineering, 190(22-23):2753–2770, 2001.[28] S.C. Cowin. A recasting of anisotropic poroelastic-ity in matrices of tensor components. Transport inPorous Media, 50(1-2):35–56, 2003.[29] J. Abate and P.P. Valk´o. Multi-precision Laplacetransform inversion. International Journal for Nu-merical Methods in Engineering, 60(5):979 – 993,2004.[30] S. Scheiner and C. Hellmich. Continuum microvis-coelasticity model for aging basic creep of early-ageconcrete. Journal of Engineering Mechanics (ASCE),135(4):307–323, 2009.[31] T. Iyo, Y. Maki, N. Sasaki, and M. Nakata.Anisotropic viscoelastic properties of cortical bone.Journal of Biomechanics, 37(9):1433–1437, 2004.[32] N. Sasaki, Y. Nakayama, M. Yoshikawa, and A. Enyo.Stress relaxation function of bone and bone collagen.Journal of Biomechanics, 26(12):1369–1376, 1993.
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