Trabecular bone numerical homogenization with the use of buffer zone

• Autorzy: Makowski P. , Kuś W.
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to calculation of effective orthotropic material parameters for trabecular bone tissue. The finite element method (FEM) numerical model of bone sample was created on the basis of microcomputed tomography (µCT) data. The buffer zone surrounding the tissue was created to apply the periodic boundary conditions. Numerical homogenization algorithm was implemented in FEM software and used to calculate the elasticity matrix coefficients of the considered bone sample.

Słowa kluczowe

EN

trabecular bone; numerical homogenization; multiscale modeling; FEM

PL

kość beleczkowa; homogenizacja numeryczna; modelowanie wieloskalowe; MES

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2014
• Tom: Vol. 21, no. 2
• Strony: 113--121
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Makowski P.

• Institute of Computational Mechanics and Engineering Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland

autor

Kuś W.

• Institute of Computational Mechanics and Engineering Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland

Bibliografia

• [1] M. Binkowski, G. Davis, Z. Wrobel, A. Goodship. Quantitative measurement of the bone density by X-ray micro vomputed tomography. IFMBE Proceedings, 31: 856–859, 2010.
• [2] T. Burczyński, W. Kuś. Microstructure optimisation and identification in multi-scale modeling. Computational Methods in Applied Sciences, 14: 169–181, 2009.
• [3] T. Burczyński, W. Kuś, A. Brodacka. Multiscale modeling of osseous tissues. Journal of Theoretical and Applied Mechanics, 48: 855–870, 2010.
• [4] S. Hollister, R. Maddox, J. Taboas. Optimal design and fabrication of scaffolds to mimic tissue properties and satisfy biological constraints. Biomaterials, 23: 4095–4103, 2002.
• [5] Y. Holdstein, L. Podshivalov, A. Fischer. Geometric modeling and analysis of bone micro-structures as a base for scaffold design. Computational Methods in Applied Sciences, 20: 91–109, 2011.
• [6] A. John, M. Duda, P. Makowski. The influence of material parameters modeling method on stress and strain state in human femur. Proceedings of Biomechanics 2012, International conference of the Polish Society of Biomechanics, 119–120, 2012.
• [7] J. Kabel, B. Van Rietbergen, M. Dalstra, A. Odgaard, R. Huiskes. The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone. Journal of Biomechanics, 32: 673–680, 1999.
• [8] G. Kokot. Evaluation of bone mechanical properties using digital image correlation, nanoindentation and numerical simulations (in Polish). Monograph 484, Silesian University of Technology, Gliwice, 2013.
• [9] G. Kokot, M. Binkowski, A. John, B. Gzik-Zroska. Advanced mechanical testing methods in determining bone material properties. Mechanika, 18: 139–143, 2012.
• [10] S.R. Lorenzetti. New method to determine the Young’s modulus of single trabeculae. DSc Dissertation, Zurich, 2006.
• [11] Ł. Madej, A. Mrozek, W. Kuś, T. Burczyński, M. Pietrzyk. Concurrent and upscaling methods in multi-scale modelling – case studies. Computer Methods in Material Science, 8: 1–15, 2008.
• [12] P. Makowski. Trabecular bone homogenization with use of MSC.Marc user subroutines. International Conference on Computer Methods in Mechanics CMM 2013 Proceedings, Poznań, 2013.
• [13] P. Makowski, A. John, W. Kuś, G. Kokot. Multiscale modeling of the simplified trabecular bone structure. Proceedings of 18th International Conference Mechanika 2013, 156–161, 2013.
• [14] P. Makowski, W. Kuś, G. Kokot. Evolutionary identification of trabecular bone properties. ECCOMAS International Conference IPM 2013 Proceedings, 35–36, 2013.
• [15] J. Szyndler, Ł. Madej. Effect of number of grains and boundary conditions on digital material representation deformation under plane strain. Archives of Civil and Mechanical Engineering, 2013.
• [16] K. Terada, M. Hori, T. Kyoya, N. Kikuchi. Simulation of the multi-scale convergence in computational homogenization approaches. International Journal of Solids and Structures, 37: 2285–2311, 2000.
• [17] D. Trias, J. Costa, J.A. Mayugo, J.E. Hurtado. Random models versus periodic models for fibre reinforced composites. Computational Materials Science, 38: 316–324, 2006.
• [18] B. Van Rietbergen, R. Huiskes. Elastic constants of cancellous bone. In: Cowin, S.C. (Ed.), Bone Mechanics Handbook, 2nd Edition, CRC Press, Boca Raton, FL, 2001.
• [19] B. Van Rietbergen, A. Odgaard, J. Kabel, R. Huiskes. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. Journal of Biomechanics, 29: 1653–7, 1996.
• [20] B. Van Rietbergen, A. Odgaard, J. Kabel, R. Huiskes. Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions. Journal of Orthopaedic Research, 16: 23–28, 1998.
• [21] G. Yang, J. Kabel, B. Van Rietbergen, A. Odgaard, R. Huiskes, S.C Cowin. The anisotropic Hooke’s law for cancellous bone and wood. Journal of Elasticity, 53: 125–146, 1999.