PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

A contribution to modelling of anisotropic behaiour of bone and bone remodelling

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Anisotropic behaviour of bones in the elastic and plastic ranges is discused. The adaptive elasticity with evolving structure is examined from the point of view of tensor functions. The equations of adaptive piezoelectricity are formulated. A general framework for bone remodelling combined with homogenization is proposed. It is suggested that the bone adaption to variable loads may be viewed as a shakedown problem. A possibility of studying bone remodelling via optimal design is considered.
PL
Przedyskutowano anizotropię tkanki kostnej w zakresie sprężystym i plastycznym. Przeanalizowano równania adaptacyjnej teorii sprężystości z ewoluującą strukturą przy zastosowaniu funkcji tensorowych. Sformułowano równania adaptacyjnej teorii piezoelektryczności. Zaproponowano ogólny model dla przebudowy kości w powiązaniu z homogenizacją. Wysunięto hipotezę, że proces adaptacji kości może być rozpatrywany w ramach teorii przystosowania. Rozpatrzono możliwość badania przebudowy kości jako zadznia optymalnego.
Słowa kluczowe
Rocznik
Tom
Strony
537--554
Opis fizyczny
Bibliogr. 48 poz.
Twórcy
autor
  • Institute of Structural Mechanics, Warsaw University of Technology
autor
  • Institute of Fundamental Technological Research, Polish Academy of Sciences
Bibliografia
  • 1. ACERBI E., CHIADO PIAT V., DAL MASO G., PERCIVALE D., 1992, An Extension Theorem from Connected Sets and Homogenization in General Periodic Domains, Nonlinear Anal, Theory, Methods and Appl., 18, 481-496.
  • 2. ALLAIRE G., 1994, Explicit Lamination Parameters for Three-Dimensional Shape Optimization, Control and Cybernetics, 23, 309-326.
  • 3. ALLAIRE G., BONNETIER E., FRANCFORT G., JOUVE F., 1997, Shape Optimization by the Homogenization Method, Numer. Math., 76, 27-68.
  • 4. ALLAIRE G., KOHN R.V., 1993, Optimal Design for Minimum Weight and Compliance in Plane Stress Using Extremal Microstructures, Eur. J. Mech., A/Solids, 12, 839-878.
  • 5. CHERKAEV A., KOHN R. (edit.), 1997, Topics in the Mathematical Modelling of Composite Materials, Birkhauser, Boston.
  • 6. CHOUNG C. J., FUNG Y.C., 1986, On Residual Stresses in Arteries, J. Biomech. Eng., 108, 189-192.
  • 7. COWIN S.C., 1979, On the Strength Anisotropy of Bone and Wood, Transactions of the ASME, J. Appl. Mech., 46, 832-838.
  • 8. COWIN S.C., 1985, The Relationship Between the Elasticity Tensor and The Fabric Tensor, Mech. Mat, 4, 137-147.
  • 9. COWIN S.C., 1986a, Fabric Dependence of an Anisotropic Strength Criterion, Mech. Mat, 5, 251-260.
  • 10. COWIN S.C., 1986b, Wolff's Law of Trabecular Architecture at Remodeling Equilibrium, J. Biomech. Eng., 108, 83-88.
  • 11. COWIN S.C., 1993, Bone Stress Adaptation Models, ASME Journal of J. Biomech. Eng., 115, 528-533.
  • 12. COWIN S.C. (edit.), 1989, Bone Mechanics, CRC Press, Inc. Boca Raton, Florida.
  • 13. COWIN S.C, 1997, The False Premise of Wolff's Law, Forma, 12, 247-262.
  • 14. COWIN S.C, ARRAMON Y.P., Luo CM., SADEGH A.M., 1993, Chaos in the Discrete-Time Algorithm for Bone-Density Remodeling Rate Equations, J. Biomech., 26, 1077-1089.
  • 15. COWIN S.C, HEGEDUS D.H., 1976a, Bone Remodeling I: Theory of Adaptive Elasticity, J. Elasticity, 6, 313-326.
  • 16. COWIN S.C, NACHLINGER R.R., 1976b, Bone Remodeling III: Uniqueness and Stability in Adaptive Elasticity Theory, J. Elasticity, 8, 285-295.
  • 17. COWIN S.C, SADEGH A.M., Luo CM., 1992, An Evolutionary Wolff's Law for Trabecular Architecture, J. Biomech. Eng., 114, 129-136.
  • 18. CURREY J.D., 1984, The Mechanical Adaptations of Bones, University Press, Princeton.
  • 19. CURREY J.D., 1997, Was Wolff Correct?, Forma, 12, 263-26.
  • 20. FRANCFORT C, MARIGO J.-J., 1993, Stable Damage Evolution in Brittle Continuous Medium, Eur. J. Mech., A/Solids, 12, 149-189.
  • 21. FRANCFORT C, MURAT F., TARTAR L., 1995, Fourt-Order Moments of Non-negative Measures on and Applications, Arch. Rat. Mech. Anal., 131, 305-333.
  • 22. GIBSON L.J., ASHBY M.F., 1988, Cellular Solids: Structure and Properties, Pergamon Press, Oxford.
  • 23. GJELSVIK A., 1973, Bone Remodelling and Piezoelectricity, Part I and Part II, Journal of Biomechanics, 6, 69-77, 187-193.
  • 24. GREENWALD S.E., MOORE J.E., RACHER A., KANE T.P.C., MEISTER J.-J., 1997, Experimental Investigation of the Distribution of Residual Strains in the Artery Wall, J. Biomech. Eng., 119, 438-444.
  • 25. GUZELSU N., SAHA S., 1984, Electro-Mechanical Behavior of Wet Bone - Part I: Theory, - Part II: Wave Propagation, ASME J. Biomech. Eng., 106, 249-271.
  • 26. HEGEDUS D.H., CowiN S.C., 1976b, Bone Remodeling II: Small Strain Adaptive Elasticity, J. Elasticity, 6, 337-352.
  • 27. JEMIOŁO S., KOWALCZYK K., 1997, Invariant Formulation and Canonical Form of the Hoffman Anisotropic Failure Criterion, Proc. V Seminarium Ukraińsko-Polskiego, Theoretical Foundations of Civil Engineering, W. Szczęśniak (edit.), Dnepropetrovsk, Oficyna Wydawnicza PW, Warszawa, 291-300, in Polish.
  • 28. JEMIOŁO S., TELEGA J.J., 1997a, Representations of Tensor Functions and Applications in Continuum Mechanics, IFTR Reports, 3.
  • 29. JEMIOŁO S., TELEGA J.J., 1997b, Fabric Tensor and Constitutive Equations for a Class of Plastic and Locking Orthotropic Materials, Arch. Mech., 49, 1041-1067.
  • 30. JEMIOŁO S., TELEGA J.J., 1998, Fabric Tensors in Bone Mechanics, Eng. Trans., 46, 3-26.
  • 31. LEVENSTON M.E., 1997, Temporal Stability of Node-Based Internal Bone Adaptation Simulations, J. Biomech., 30, 403-407.
  • 32. LIPTON R., 1994, A Saddle-Point Theorem With Application to Structural Optimization, J. Optim. Theory Appi, 81, 549-568.
  • 33. LOWET G., RUEGSEGGER P., WEINAMS H., MEUNIER A. (edit.), 1997, Bone Research in Biomechanics, IOS Press, Amsterdam.
  • 34. LUO G., COWIN S.C., SADEGH A.M., ARRAMON Y.P., 1995, Implementation of Strain Rate as a Bone Remodeling Stimulus, J. Biomech. Eng., 117, 329-338.
  • 35. MARTIN R.B., BURR D., 1989, Structure, Function and Adaptation of Compact Bone, Raven Press, New York.
  • 36. MONNIER J., TRABUCHO L., 1998, Existence and Uniqueness of Solution to an Adaptive Elasticity Model, Math. And Mech. Solids, 3, 217-228.
  • 37. MULLENDER M.G., HuiSKES R., 1995, Proposal for the Regulatory Mechanism of Wolff's Law, J. Orthopaedic Res., 13, 503-512.
  • 38. OGAARD A., WEINAMS H. (edit), 1995, Bone Structure and Remodeling, Word Scientific, Singapore.
  • 39. OLEINIK O.A., SHAMAEV A.S., YOSIFIANOV G.A., 1992, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam.
  • 40. PEDERSEN P., BENDS0E P. (edit.) 1999, Synthesis in Bio Solid Mechanics, Kulwer Academic Publishers, Dorderecht.
  • 41. RO KOTOM AN AN A R.L., CURNIER A., LEYVRAZ P.F., 1991, An Objective Anisotropic Elastic Plastic Model and Algorithm Applicable to Bone Mechanics, Eur. J. Mech., A/Solids, 10, 327-342.
  • 42. RYCHLEWSKI J., ZHANG J.M., 1989, Anisotropy Degree of Elastic Materials, Arch. Mech., 41, 697-715.
  • 43. TANAKA M., ADACHI T., 1994, Preliminary Study on Mechanical Bone Remodeling Permitting Residual Stress, JSME Int. J., 37, 87-95.
  • 44. TELEGA J.J., GAŁKA A., TOKARZEWSKI S., 1999, Application of the Reiterated Homogenization to Determination of Effective Moduli of a Compact Bone, J. Theor. Appl. Mech., 37, 3.
  • 45. TELEGA J.J., JEMIOŁO S., 1998, Fabric Tensors in Bone Mechanics, Adaptive Elasticity and Adaptive Piezoelectricity, Proc. Biomechanics - Modelling, Computational Methods, Experimental and Biomedical Applications, J. Awrejcewicz, M. Ciach, M. Kleiber (edit.), Łódź, 183-188.
  • 46. TURNER C.H., COWIN S.C., RHO J.Y., ASHMAN R.B., RICE J.C., 1990, The Fabric Dependence of the Orthotropic Elastic Constants of Cancellous Bone, J. Biomech., 23, 549-561.
  • 47. VAISHNOV R.N., VOSSONGHI J., 1983, Estimation of Residual Strain in Aortic Segments, in: Biomedical Engineering II, Recent Developments, 330-333, Pergamon Press, New York.
  • 48. ZYSSET P.K. AND CURNIER A., 1996, A 3D Damage Model for Trabecular bone based on Fabric Tensors, J. Biomech., 29, 1549-1558.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWM2-0001-0255
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.