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GPU-Based Fast Finite Element Solution for Nonlinear Anisotropic Material Behavior and Comparison of Integration Strategies

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Computational Biomechanics for Medicine

Abstract

We present a study of accuracy and execution speed using a novel implementation of a nonlinear anisotropic fiber-reinforced material model within a Total Lagrangian Explicit Dynamic (TLED) finite element (FE) framework, developed for execution on Graphics Processing Units. Full integration and selective-reduced integration have been developed for tri-linear hexahedral elements and tested in comparison to the classical under-integrated TLED scheme. Comparison is performed with respect to an established FE code. Results indicate that by using the presented method, excellent accuracy can be retained while greatly accelerating solution times.

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References

  1. F. Migliavacca, L. Petrini, M. Colombo, F. Auricchio, R. Pietrabissa, Mechanical behavior of coronary stents investigated through the finite element method. J. Biomech. 35(6), 803–811 (2002) [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0021929002000337

  2. C. Conway, F. Sharif, J. McGarry, P. McHugh, A computational test-bed to assess coronary stent implantation mechanics using a population-specific approach. Cardiovasc. Eng. Technol. 3(4), 374–387 (2012) [Online]. Available: http://dx.doi.org/10.1007/s13239-012-0104-8

  3. N. Famaey, G. Sommer, J.V. Sloten, G.A. Holzapfel, Arterial clamping: finite element simulation and in vivo validation. J. Mech. Behav. Biomed. Mater. 12, 107–118 (2012) [Online]. Available: http://www.sciencedirect.com/science/article/pii/S1751616112000902

  4. V. Strbac, J. Vander Sloten, N. Famaey, Analyzing the potential of GPGPUs for real-time explicit finite element analysis of soft tissue deformation using CUDA. Finite Elem. Anal. Des. (2015, submitted)

    Google Scholar 

  5. G.R. Joldes, A. Wittek, M. Couton, S.K. Warfield, K. Miller, Real-time prediction of brain shift using nonlinear finite element algorithms. Med. Image Comput. Comput. Assist. Interv. 12(2), 300–307 (2009)

    Google Scholar 

  6. E.D. Cris Cecka, Adrian J. Lew, Assembly of finite element methods on graphics processors. Int. J. Numer. Methods Eng. 85, 640–669 (2011)

    Google Scholar 

  7. Z.A. Taylor, M. Cheng, S. Ourselin, High-speed nonlinear finite element analysis for surgical simulation using graphics processing units. IEEE Trans. Med. Imaging 27(5), 650–663 (2008) [Online]. Available: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4388142

  8. S.F. Johnsen, Z.A. Taylor, M.J. Clarkson, J. Hipwell, M. Modat, B. Eiben, L. Han, Y. Hu, T. Mertzanidou, D.J. Hawkes, S. Ourselin, Niftysim: a GPU-based nonlinear finite element package for simulation of soft tissue biomechanics. Int. J. Comput. Assist. Radiol. Surg. 10(7), 1077–1095 (2014)

    Article  Google Scholar 

  9. K. Miller, G. Joldes, D. Lance, A. Wittek, Total Lagrangian explicit dynamics finite element algorithm for computing soft tissue deformation. Commun. Numer. Methods Eng. 23(2), 121–134 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Belytschko, W.K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures (Wiley, New York, 2000)

    MATH  Google Scholar 

  11. G.R. Joldes, A. Wittek, K. Miller, Real-time nonlinear finite element computations on GPU - application to neurosurgical simulation. Comput. Methods Appl. Mech. Eng. 199(49–52), 3305–3314 (2010) [Online]. Available: http://dx.doi.org/10.1016/j.cma.2010.06.037

  12. G. Joldes, A. Wittek, K. Miller, Real-time nonlinear finite element computations on GPU: handling of different element types, in Computational Biomechanics for Medicine (Springer, New York, 2011), pp. 73–80

    Google Scholar 

  13. D.P. Flanagan, T. Belytschko, A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. Int. J. Numer. Methods Eng. 17, 679–706 (1981)

    Article  MATH  Google Scholar 

  14. G.R. Joldes, A. Wittek, K. Miller, An efficient hourglass control implementation for the uniform strain hexahedron using the total Lagrangian formulation. Commun. Numer. Methods Eng. 24, 1315–1323 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. T. Belytschko, L.P. Bindeman, Assumed strain stabilization of the eight node hexahedral element. Comput. Methods Appl. Mech. Eng. 105, 225–260 (1993)

    Article  MATH  Google Scholar 

  16. T.C. Gasser, R.W. Ogden, G.A. Holzapfel, Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6), 15–35 (2006)

    Article  Google Scholar 

  17. G.R. Joldes, A. Wittek, K. Miller, An adaptive dynamic relaxation method for solving nonlinear finite element problems. application to brain shift estimation. Int. J. Numer. Methods Biomed. Eng. 27(2), 173–185 (2011) [Online]. Available: http://dx.doi.org/10.1002/cnm.1407

  18. C. Sansour, On the physical assumptions underlying the volumetric-isochoric split and the case of anisotropy. Eur. J. Mech. A Solids 27, 28–39 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Helfenstein, M. Jabareen, E. Mazza, S. Govindjee, On non-physical response in models for fiber-reinforced hyperelastic materials. Int. J. Solids Stuct. 47, 2056–2061 (2010)

    Article  MATH  Google Scholar 

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Acknowledgements

This research was funded by an FP7 STREP project, CASCADE, by an interdisciplinary research project of KU Leuven (IDO), and by the Research Foundation Flanders (FWO).

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Correspondence to Vukašin Štrbac .

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Štrbac, V., Pierce, D.M., Sloten, J.V., Famaey, N. (2016). GPU-Based Fast Finite Element Solution for Nonlinear Anisotropic Material Behavior and Comparison of Integration Strategies. In: Joldes, G., Doyle, B., Wittek, A., Nielsen, P., Miller, K. (eds) Computational Biomechanics for Medicine. Springer, Cham. https://doi.org/10.1007/978-3-319-28329-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-28329-6_9

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