Cost - Effective and Sufficiently Precise Integration Method Adapted to the FEM Calculations of Bone Tissue

• Autorzy: Mazur K , Dąbrowski L.

Identyfikatory

DOI

10.12921/cmst.2014.20.03.101-108

• Języki publikacji: EN

Abstrakty

EN

The technique of Young’s modulus variation in the finite element is not spread in biomechanics. Our future goal is to adapt this technique to bone tissue strength calculations. The aim of this paper is to present the necessary studies of the element’s integration method that takes into account changes in material properties. For research purposes, a virtual sample with the size and distribution of mechanical properties similar to these in a human femoral wall, was used. WinPython, an environment of Python programming language was used to perform simulations. Results with the proposed element were compared with ANSYS element PLANE42 (with constant Young modulus). The modeled sample was calculated with five different integration methods at five different mesh densities. Considered integration methods showed a very high correlation of results. Two-point Gauss Quadrature Rule proved to be the most advantageous. Results obtained by this method deviate only slightly from the pattern, while the computing time was significantly lower than others. Performed studies have shown that accuracy of the solution depends largely on the mesh density of the sample. Application of the simplest integration method in combination with four times coarser mesh density than in ANSYS with a standard component still allowed to obtain better results.

Słowa kluczowe

EN

FEM; bone; variable Young’s modulus

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2014
• Tom: Vol. 20, No. 3
• Strony: 101--108
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Mazur K

• Faculty of Mechanical Engineering, Gdansk University of Technology Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland

autor

Dąbrowski L.

• Faculty of Mechanical Engineering, Gdansk University of Technology Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland

Bibliografia

• [1] J-H. Kim, G. H. Paulino, Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic, Journal of Applied Mechanics 69(4), 502-514 (2002).
• [2] J-H. Kim, G. H. Paulino, T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms, International Journal of Fracture 126(4), 345-384 (2004).
• [3] L. Grassi, E. Schileo, F. Taddei, L. Zani, M. Juszczyk, L. Cristofolini, M. Viceconti, Accuracy of finite element predictions in sideways load configurations for the proximal human femur, Journal of Biomechanics 45(2), 394-399 (2012).
• [4] R. Fedida, Z. Yosibash, Ch. Milgrom, L. Joskowicz, Femur mechanical stimulation using high-order FE analysis with continuous mechanical properties, II International Conference on Computational Bioengineering (2005).
• [5] K. Mazur, L. Da˛browski, Young’s Modulus Distribution In The Fem Models Of Bone Tissue, National Conference on Applications of Mathematics in Biology and Medicine (2013).
• [6] E. Błazik-Borowa, J. Podgórski, Introduction to the finite element method in static of engineering structures, IZT, Lublin 2001.
• [7] W.P. Martins, Questionable value of absolute mean gray value for clinical practice, Ultrasound in Obstetrics & Gynecology 41(5), 595-597 (2013).
• [8] D.Ch. Wirtz, N. Schiffers, T. Pandorf, K. Radermacher, D. Weichert, R. Forst, Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur, Journal of Biomechanics 33(10), 1325-1330 (2000).
• [9] O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, Butterworth-Heinemann, Oxford 2000.