Cost-Effective and Sufficiently Precise Integration Method Adapted to the FEM Calculations of Bone Tissue
Mazur Katarzyna *, Dąbrowski Leszek **
Faculty of Mechanical Engineering, Gdansk University of Technology
Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
E-mail: ∗ katarzyna.mazur@pg.gda.pl, ∗∗ldabrows@pg.gda.pl
DOI: 10.12921/cmst.2014.20.03.101-108
Abstract:
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.
Key words:
References:
[1] J-H. Kim, G. H. Paulino, Isoparametric Graded Finite Ele-
ments for Nonhomogeneous Isotropic and Orthotropic, Jour-
nal 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, Interna-
tional 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 predic-
tions 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 Confer-
ence on Computational Bioengineering (2005).
[5] K. Mazur, L. Dabrowski, Young’s Modulus Distribution In
The Fem Models Of Bone Tissue, National Conference on Ap-
plications of Mathematics in Biology and Medicine (2013).
[6] E. Błazik-Borowa, J. Podgórski, Introduction to the finite ele-
ment 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 & Gyne-
cology 41(5), 595-597 (2013).
[8] D.Ch. Wirtz, N. Schiffers, T. Pandorf, K. Radermacher, D.
Weichert, R. Forst, Critical evaluation of known bone ma-
terial 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.
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.
Key words:
References:
[1] J-H. Kim, G. H. Paulino, Isoparametric Graded Finite Ele-
ments for Nonhomogeneous Isotropic and Orthotropic, Jour-
nal 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, Interna-
tional 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 predic-
tions 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 Confer-
ence on Computational Bioengineering (2005).
[5] K. Mazur, L. Dabrowski, Young’s Modulus Distribution In
The Fem Models Of Bone Tissue, National Conference on Ap-
plications of Mathematics in Biology and Medicine (2013).
[6] E. Błazik-Borowa, J. Podgórski, Introduction to the finite ele-
ment 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 & Gyne-
cology 41(5), 595-597 (2013).
[8] D.Ch. Wirtz, N. Schiffers, T. Pandorf, K. Radermacher, D.
Weichert, R. Forst, Critical evaluation of known bone ma-
terial 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.
