A Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue

Journal of Computational Physics

Volumn 227, Issue 21, 2008, Pages 9195-9215

  Hieber, Simone E ^a   Koumoutsakos, Petros ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Lagrangian particle methods; Linear and nonlinear elasticity; Liver tissue simulation

Indexed keywords

LAGRANGE MULTIPLIERS; NUMERICAL METHODS; STRAIN; STRESS-STRAIN CURVES; TISSUE;

LAGRANGIAN FORMULATIONS; LAGRANGIAN PARTICLE METHOD; LINEAR AND NONLINEAR ELASTICITY; LINEAR ELASTIC MODEL; LIVER TISSUE; LIVER TISSUE SIMULATION; NONLINEAR ELASTIC MODEL; PARTICLE SIMULATIONS; SOFT TISSUE; TISSUE SIMULATIONS;

FINITE ELEMENT METHOD;

EID: 51449119853     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.05.016     Document Type: Article

References (51)

1. Beale J.T. A convergent 3-D vortex method with grid-free stretching. Math. Comput. 46 (1986) 401-424
2. Chaniotis A.K., Poulikakos D., and Koumoutsakos P. Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. J. Comput. Phys. 182 1 (2002) 67-90
3. Christensen R.M. Theory of Viscoelasticity. second ed. (2003), Dover Publications
4. Cottet G.-H. Artificial viscosity models for vortex and particle methods. J. Comput. Phys. 127 (1996) 299-308
5. Cottet G.-H., and Koumoutsakos P. Vortex Methods - Theory and Practice (2000), Cambridge University Press, New York
6. Danielson K.T., Hao S., Liu W.K., Uras R.A., and Li S. Parallel computation of meshless methods for explicit dynamic analysis. Int. J. Numer. Methods Eng. 47 (2000) 1323-1341
7. G. Debunne, M. Desbrun, M.-P. Cani, A. Barr, Dynamic real-time deformations using space and timing adaptive sampling, in: Eugene Fiume (Ed.), Conference Proceedings SIGGRAPH, ACM Press/ACM SIGGRAPH, 2001, pp. 31-36.
8. Degond P., and Mas-Gallic S. The weighted particle method for convection-diffusion equations. Part 1: The case of an isotropic viscosity. Math. Comput. 53 188 (1989) 485-507
9. Doblare M., Cueto E., Calvo B., Martinez M.A., Garcia J.M., and Cegonino J. On the employ of meshless methods in biomechanics. Comput. Meth. Appl. Mech. Eng. 194 (2005) 801-821
10. Eldredge J.D., Colonius T., and Leonard A. A vortex particle method for two-dimensional compressible flow. J. Comput. Phys. 179 (2002) 371-399
11. Eldredge J.D., Leonard A., and Colonius T. A general deterministic treatment of derivatives in particle methods. J. Comput. Phys. 180 2 (2002) 686-709
12. Fung Y.C. Biomechanics, Mechanical Properties of Living Tissues. second ed. (1993), Springer-Verlag
13. Gingold R.A., and Monaghan J.J. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181 (1977) 375-389
14. Gingold R.A., and Monaghan J.J. The reliability of finite-difference and particle methods for fragmentation problems. Mon. Not. R. Astron. Soc. 199 1 (1982) 115-119
15. Gray J.P., Monaghan J.J., and Swift R.P. SPH elastic dynamics. Comput. Meth. Appl. Mech. Eng. 190 (2001) 6641-6662
16. Guilkey J.E., Hoying J.B., and Weiss J.A. Computational modeling of multicellular constructs with the material point method. J. Biomech. 39 11 (2006) 2079-2086
17. Hald O.H. Convergence of vortex methods for Euler's equations, III. SIAM J. Numer. Anal. 24 3 (1987) 538-582
18. Hieber S.E., Walther J.H., and Koumoutsakos P. Remeshed smoothed particle hydrodynamics simulation of the mechanical behavior of human organs. J. Technol. Health Care 12 4 (2004) 305-314
19. Hieber S.E., and Koumoutsakos P. A Lagrangian particle level set method. J. Comput. Phys. 210 (2005) 342-367
20. Holzapfel G. Nonlinear Solid Mechanics (2000), John Wiley & Sons
21. Hoover W.G., Hoover C.G., and Merritt E.C. Smooth-particle applied mechanics: conservation of angular momentum with tensile stability and velocity averaging. Phys. Rev. E 69 1 (2004)
22. Hosseini S.M., Manzari M.T., and Hannani S.K. A fully explicit three-step SPH algorithm for simulation of non-newtonian fluid flow. Int. J. Heat Fluid Flow 17 7-8 (2007) 715-735
23. Hu X.Y., and Adams N.A. Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows. Phys. Fluids 18 10 (2006)
24. Johnson G.R., and Beissel S.R. Normalized smoothing functions for SPH impact computations. Int. J. Numer. Methods Eng. 16 (1997) 2725-2741
25. Khayyer A., Gotoh H., and Shao S.D. Corrected incompressible SPH method for accurate water-surface tracking in breaking waves. Coastel Eng. 55 (2008) 236-250
26. Koumoutsakos P. Vorticity flux control in a turbulent channel flow. Phys. Fluids 11 2 (1999) 248-250
27. Koumoutsakos P. Multiscale flow simulations using particles. Annu. Rev. Fluid Mech. 37 (2005) 457-487
28. Laigle D., Lachamp P., and Naaim M. SPH-based numerical investigation of mudflow and other complex fluid flow interactions with structures. Comput. Geo. 4 (2007) 297-306
29. Leonard A. Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17 (1985) 523-559
30. Liu W.K., Jun S., and Zhang S. Reproducing kernel particle methods. Int. J. Numer. Methods Eng. 20 8-9 (1995) 1081-1106
31. Molinari E., Fato M., DeLeo G., Riccardo D., and Beltrame F. Simulation of the biomechanical behavior of the skin in virtual surgical applications by finite element method. IEEE Trans. Biomed. Eng. 52 9 (2005) 1514-1521
32. Monaghan J.J. Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30 (1992) 543-574
33. Monaghan J.J. SPH without a tensile instability. J. Comput. Phys. 159 (2000) 290-311
34. Monaghan J.J. Smoothed particle hydrodynamics. J. Comput. Phys. 68 8 (2005) 1703-1759
35. Nava A., Mazza E., Kleinermann F., Avis N., and McClure J. Determination of the mechanical properties of soft human tissue through aspiration experiments. Lect. Notes Comput. Sci. 1878 (2003) 222-229
36. Nava A., Mazza E., Kleinermann F., Avis N., McClure J., and Bajka M. Evaluation of the mechanical properties of human liver and kidney through aspiration experiments. J. Technol. Health Care 12 (2004) 269-280
37. Osher S., and Sethian J.A. Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79 1 (1988) 12-49
38. Randles P.W., and Libersky L.D. Smoothed particle hydrodynamics: some recent improvements and applications. Comput. Meth. Appl. Mech. Engng. 139 (1996) 375-408
39. Randles P.W., and Libersky L.D. Normalized SPH with stress points. Int. J. Numer. Methods Eng. 48 (2000) 1445-1462
40. Reddy J.N. Finite Element Method. second ed. (1993), McGraw Hill, Inc.
41. Richardson L.F. The approximate arithmetical solution by finite differences of physical problems including differential equations, with an application to the stresses in a masonry dam. Phil. Trans. Roy. Soc. Lond. 210 (1910) 307-357
42. Sbalzarini I.F., Walther J.H., Bergdorf M., Hieber S.E., Kotsalis E.M., and Koumoutsakos P. PPM - a highly efficient parallel particle-mesh library for the simulation of continuum systems. J. Comput. Phys. 215 (2006) 566-588
43. Sethian J.A. A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. USA 93 4 (1996) 1591-1595
44. D. Shiels, A. Leonard, A. Stagg, Computational investigation of drag reduction on a rotationally oscillating cylinder, in: Yves Gagnon, Georges-Henri Cottet, David G. Dritschel, Ahmed F. Ghoniem, Eckart Meiburg, (Eds.), ESAIM: Proceedings: Vortex Flows and Related Numerical Methods II, 1996, pp. 307-323.
45. Sulsky D., Zhou S.-J., and Schreyer H.L. Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87 (1995) 236-252
46. Swegle J.W., Hicks D.L., and Attaway S.W. Smoothed particle hydrodynamics stability analysis. J. Comput. Phys. 116 1 (1995) 123-134
47. Szekely G., Bajka M., Brechbuhler C.H., Dual J., Enzeler R., Haller U., Hug J., Hutter R., Ionmenger N., Kauer M., Meier P., Niederer P., and Trister G. Virtual reality based simulation of endoscopic surgery. Presence 9 3 (2000) 310-333
48. Szekely G., and Satava R.M. Virtual reality in medicine. Brit. Med. J. 319 (1999) 1305-1315
49. D. Terzopoulos, J. Platt, A. Barr, K. Fleischer, Elastically deformable models, in: ACM SIGGRAPH Computer Graphics, 1987, pp. 205-214.
50. Terzopoulous D., and Fleischer K. Deformable models. Visual Comput. 4 (1988) 306-331
51. M. Teschner, B. Heidelberger, M. Muller, M. Gross, A versatile and robust model for geometrically complex deformable solids, in: Proceedings of Computer Graphics International, 2004, pp. 312-319.