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Constitutive modelling of PMMA-based bone cement: a functional model of viscoelasticity and its approximation for time domain investigations

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
To represent the mechanical behaviour of polyethylmethacrylate-based bone cement, a constitutive approach of finite linear viscoelasticity is formulated and identified. Motivated by the experimental data of storage and loss modulus, the model is based on a three-dimensional functional in integral representation. In the investigated frequency range, the master curve of the loss modulus is constant and that of the storage modulus increases linearly with the logarithm of the frequency. This behaviour corresponds to a viscoelastic fluid, and can be described by a continuous relaxation spectrum. For numerical simulations which are planned in future, the constitutive functional is approximated by a discrete spectrum. To this end, an earlier-developed method to approximate continuous relaxation spectra in limited time or frequency ranges by discrete ones is applied.
Słowa kluczowe
Rocznik
Strony
221--242
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
autor
autor
autor
  • Institute of Mechanics, Department of Aerospace Engineering, University of the Federal Armed Forces Munich, D-85577 Neubiberg, Germany
Bibliografia
  • 1. G. BAROUD, J. NEMES, P.P. HEINI, T. STEFFEN, Load shift on the intervertebral disc a vertebroplasty: a finite element study, Eur. Spine J., 12, 421-426, 2003.
  • 2. G. BAROUD, M. BOHNER, P.P. HEINI, T. STEFFEN, Injection biomechanics of bone cem used in vertebroplasty, Bio-Medical Materials and Engineering, 14, 487-504, 2004.
  • 3. G. BAROUD, C. VANT, Long-term effects of vertebroplasty: adjacent vertebral fracti Journal of Long-Term Effects of Medical Implants, 15, 499-514, 2005.
  • 4. G. BAROUD, M. CROOKSHANK, M. BOHNER, High-viscosity cement significantly enho uniformity of cement filling in vertebroplasty: an experimental model and study on cei leakage, Spine, 31, 2562-2568, 2006.
  • 5. H. BERTILSSON, J.F. JANSSON, The limits of linear viscoelasticity in Poly-Methyl-Methacrylate and Poly-Ethyl-Methacrylate, Journal of Applied Polymer Science, 1971-1978, 1975.
  • 6. G. BOHME, Stromwigsmechanik nichtnewtonscher Fluide, Teubner Verlag, 2000.
  • 7. S.V. DOROZHKIN, Calcium, orthophosphate cements for biomedical application, Jouri Material Science, 43, 3028-3057, 2008.
  • 8. E.J. HARPER, M. BRADEN, W. BONFIELD, Mechanical properties of hydroxyapatite inforced polyethylmethacrylate bone cement after immersion in a physiological solution influence of a silane coupling agent, Journal of Materials Science: Materials in Med 11, 491-497, 2000.
  • 9. P. HAUPT, Continuum mechanics and theory of materials, Springer, Berlin 2000.
  • 10. P. HAUPT, A. LION, E. BACKHAUS, On the dynamic behaviour of polymers under finite strains: constitutive modelling and identification of parameters, Int. J. Solids Struct., 37, 3633-3646, 2000.
  • 11. P. HAUPT, A. LION, On finite linear viscoelasticity of incompressible isotropic materials, Acta Mechanica, 159, 87-124, 2002.
  • 12. P.P. HEINI, U. BERLEMANN, M. KAUFMANN, K. LIPPUNER, C. FANKHAUSER, P.V. LANDUYT, Augmentation of mechanical properties in osteoporotic vertebral bones: a biomechanical investigation of vertebroplasty with different bone cements, Eur. Spine Journal, 10, 164-171, 2001.
  • 13. D.G. KIM, M.A. MILLER, K.A. MANN, Creep dominates tensile fatigue damage of the bone-cement interface, Journal of Orthopaedic Research, 22, 633-640, 2004.
  • 14. A.B. LENNON, P.J. PRENDERGAST, Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence, Journal of Biomechanics, 35, 311-321, 2002.
  • 15. C. Li, S. KOTHA, C.H. HUANG, S. SCHMID, J. MASON, D. YAKIMICKI, M. HAWKINS, Finite element simulation of thermal behaviour of prothesis-cement-bone-system, BED, 50, Bioengineering Conference, ASME, 235-236, 2001.
  • 16. A. LlON, Thermomechanik von Elastomeren, Habilitation, Bericht 1/2000, Institute of Mechanics, Faculty of Mechanical Engineering, University of Kassel, 2000.
  • 17. A. LION, P. HOFER, On the phenomenological representation of curing phenomena in continuum mechanics, Archives of Mechanics, 59, 59-89, 2007.
  • 18. S. MAZZULLO, M. PAOLINI, C. VERDI, Numerical simulation of thermal bone necrosis during cementation of femoral prothesis, Journal of Mathematical Biology, 29, 475-494, 1991.
  • 19. A. ROHLMANN, T. ZANDER, T. JONY, U. WEBER, G. BERGMANN, Einfluss der Wirbelkor-persteifigkeit auf den intradiskalen Druck, Biomed. Technik, 50, 148-152, 2005.
  • 20. A. ROHLMANN, T. ZANDER, G. BERGMANN, Spinal loads after osteoporotic vertebral fractures by vertebroplasty of kyphoplasty, Eur. Spine J., 15, 1255-1264, 2006.
  • 21. M. STANCZYK, Study on modelling of PMMA bone cement polymerization, Journal of Biomechanics, 38, 1397-1403, 2005.
  • 22. A.V. TOBOLSKY, Mechanische Eigenschaften und Struktur von Polymeren, Berliner Union, 1967.
  • 23. N. VERDONSHOT, R. HUISKES, Dynamic creep behaviour of acrylic bone cement, Journal of Biomedical Materials Research, 29, 575-581, 1995.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0012-0036
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