Journal of Biomechanics
Volume 35, Issue 1 , Pages 1-17 , January 2002

Anisotropic bone remodelling model based on a continuum damage-repair theory

,Accepted 2 September 2001.

References 

  1. Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous ware technique for the measurement of the elastic properties of bone. Journal of Biomechanics. 1984;17:349–361
  2. Beaupré GS, Orr TE, Carter DR. An approach for time-dependent bone modeling and remodeling-theoretical development. Journal of Orthopaedic Research. 1990;8:551–651
  3. Beaupré GS, Orr TE, Carter DR. An approach for time-dependent bone modeling and remodeling-application (a preliminary remodeling simulation). Journal of Orthopaedic Research. 1990;8:662–670
  4. Carter DR. Mechanical loading history and skeletal biology. Journal of Biomechanics. 1987;20:1095–1109
  5. Carter DR, Orr TE, Pyhrie DP. Relationships between loading history and femoral cancellous bone architecture. Journal of Biomechanics. 1989;22:231–244
  6. Ciarlet, P.G., 1988. Mathematical elasticity.In: J.L. Lions, G. Papanicolaon, H. Fuyta, H.B. Keller (Eds.), Three-Dimensional Elasticity, Vol I. Elsevier, Amsterdam, p. 20.
  7. Cordebois JP, Sideroff F. Damage induced elastic anisotropy. Mechanical behavior of anisotropic solids. Proceedings of the EUROMECH Colloque. 1982;115:761–774
  8. Cowin SC. Wolff's law of trabecular architecture at remodeling equilibrium. Journal of Biomechanical Engineering. 1986;108:83–88
  9. Cowin SC, Sadegh AM, Luo GM. An evolutionary Wolff's law for trabecular architecture. Journal of Biomechanical Engineering. 1992;114:129–136
  10. Fernandes, P., Rodrigues, H., Jacobs, C.R., 1998. A model of bone adaptation using a global optimisation criterion based on the trajectorial theory of Wolff. Computer Methods in Biomechanics and Biomedical Engineering.
  11. Fridez, P., 1996. Modélisation de l’adaptation osseuse externe. Physics Department, EPFL, Lausanne.
  12. Garcı́a, J.M., 1999. Modelos de Remodelación Ósea: Análisis numérico y aplicaciones al diseño de fijaciones de fracturas del fémur proximal. Tesis Doctoral, Universidad de Zaragoza.
  13. Harrigan TP, Mann RW. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. Journal of Material Science. 1984;19:761–767
  14. Huiskes, et al., 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis. Journal of Biomechanics 20, 1135–1150.
  15. Jacobs, C.R., 1994. Numerical Simulation of Bone Adaptation to Mechanical Loading. Dissertation for the Degree of Doctor of Philosophy, Stanford University.
  16. Jacobs CR, et al.  Adaptive bone remodeling incorporating simultaneous density and anisotropy considerations. Journal of Biomechanics. 1997;30:603–613
  17. Kachanov LM. Time of the rupture process under creep conditions, IVZ Akad. Naukovi S.S.R. Otd Tech Nauka. 1958;8:26–31
  18. Karlsson, L.M., Cruz-Orive, L.M., 1993. Application of the star volume distribution to characterize structural anisotropy of a duplex stainless steel. In: Stereology in Materials Science: Demostration of Some Methods, Royal Institute of Technology, Stockholm.
  19. Koiter, 1953. Stress–strain relations, uniqueness and variational theorems for elastoplastic materials with a singular yield surface. Quarterly of Applied Mathematics 11, 350, 354.
  20. Lekhnitskii SG. Theory of Elasticity of an Anisotropic Body. Moscow: Mir Publishers; 1981;
  21. Lemaitre J. A continuous damage mechanics model for ductile fracture. Journal of Engineering Materials and Technology. 1985;107:83–89
  22. Martin RB. Porosity and specific surface of bone. CRC Critical Reviews in Biomedical Engineering. 1984;10(3):179–222
  23. McClintock, F., 1968. A criterion for ductile fracture by the growth of holes. Journal of Applied Mechanics 35.
  24. Mikic B, Carter DR. Bone strain gage date and theoretical models of functional adaptation. Journal of Biomechanics. 1995;28:465–469
  25. Odgaard A, Jensen EB, Gundersen HJG. Estimation of structural anisotropy based on volume orientation. A new concept. Journal of Microscopy. 1990;157:149–182
  26. Odgaard, et al., 1997. Fabric and elastic principal directions of cancellous bone are closely related. Journal of Biomechanics 30, 487–495.
  27. Pettermann HE, Reiter TJ, Rammerstorfer FG. Computational simulation of internal bone remodeling. Archives of Computational Methods in Engineering. 1997;4:295–323
  28. Prendergast PJ, Taylor D. Prediction of bone adaptation using damage accumulation. Journal of Biomechanics. 1994;27:1067–1076
  29. Reilly TD, Burstein AH. The mechanical properties of cortical bone. Journal of Bone and Joint Surgery. 1974;56:1001–1022
  30. Reilly TD, Burstein AH. The elastic and ultimate properties of compact bone tissue. Journal of Biomechanics. 1975;8(6):393–405
  31. Resende L, Martin JB. A progressive damage continuum model for granular materials. Computational Methods in Applied Mechanical Engineering. 1984;42:1–18
  32. Rice J, Tracey D. On ductile enlargement of voids in triaxial stress fields. Journal of Mechanics and Physics of Solids. 1969;17:201–217
  33. Rodrigues, H., et al., 1998. Global and local material optimization models applied to anisotropic bone adaptation. Iutam Symposium—Synthesis in Bio Solid Mechanics.
  34. Simo JC, Hughes TJR. Computational Inelasticity. New York: Springer; 1998;
  35. Simo JC, Ju JW. Strain- and stress-based continuum damage models. I. Formulation. International Journal of Solids Structures. 1987;23:821–840
  36. van Rietbergen, et al., 1996. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. Journal of Biomechanics 29, 1653–1657.
  37. Weinans H, Huiskes R, Grootenboer HJ. The behaviour of adaptive bone-remodeling simulation models. Journal of Biomechanics. 1992;25:1425–1441
  38. Whalen RT, Carter DR. Influence of physical activity on the regulation of bone density. Journal of Biomechanics. 1988;21(10):825–837
  39. Whitehouse WJ. The quantitative morphology of anisotropic trabecular bone. Journal of Microscopy. 1974;101:153–168
  40. Wolff J. Das gesetz der transformation der knochen. Berlin: Hirschwald; 1892;
  41. Yoon HS, Katz JL. Ultrasonic have propagation in human cortical bone (II measurements of elastic properties and micro-hardness). Journal of Biomechanics. 1976;9:459–464
  42. Zysset PK, Goulet RW, Hollister SJ. A global relationship between trabecular bone morphology and homogenized elastic properties. Journal of Biomechanical Engineering. 1998;120:640–646

PII: S0021-9290(01)00178-6

Journal of Biomechanics
Volume 35, Issue 1 , Pages 1-17 , January 2002