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Smoothed Particle Hydrodynamics-Based Viscous Deformable Object Modelling

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Robot Dynamic Manipulation

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 144))

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Abstract

Materials like fluids are long since important research objects of continuum mechanics as well as of computer graphics. Smoothed particle hydrodynamics(SPH) is one of the representation methods employed for continuous materials. Its simplicity in implementation and its realistic representation are drastically improved during the last decades. More recently, highly viscous fluids like honey, jam, and bread dough based on the SPH formulation have gained attention with impressive results. In this chapter, a novel implicit viscosity method is proposed. The internal viscosity forces are recursively calculated from the difference of the nearby velocities of the particles until they are small enough to be neglected. The proposed approach has longer time-steps compared with existing explicit viscosity methods, resulting in shorter computation time. Besides, the proposed method uses a physical viscosity coefficient, not an artificial one like in existing implicit viscosity methods, which helps predict the viscous behavior of continuous materials more accurately. The obtained results show that the computational time for the proposed approach is predictable, while the accuracy in modelling the viscosity behaviour is similar or higher than existing methods.

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Notes

  1. 1.

    https://eigen.tuxfamily.org/.

  2. 2.

    https://opencv.org.

  3. 3.

    http://www.openscenegraph.org.

  4. 4.

    https://www.sidefx.com.

  5. 5.

    https://www.blender.org.

  6. 6.

    https://www.openmp.org.

References

  1. T.J. Chung. Computational Fluid Dynamics (Cambridge University Press, 2010)

    Google Scholar 

  2. R. Eymard, T. Gallouët, R. Herbin, Finite volume methods. Handb. Numer. Anal. 7, 713–1018 (2000)

    MathSciNet  MATH  Google Scholar 

  3. G. Irving, J. Teran, R. Fedkiw, Invertible finite elements for robust simulation of large deformation, in 2004 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 131–140 (2004)

    Google Scholar 

  4. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. The Finite Element Method Set (Butterworth-Heinemann, 2005)

    Google Scholar 

  5. G.R. Liu, J. Zhang, K.Y. Lam, H. Li, G. Xu, Z.H. Zhong, G.Y. Li, X. Han, A gradient smoothing method (GSM) with directional correction for solid mechanics problems. Comput. Mech. 41(3), 457–472 (2008)

    Article  Google Scholar 

  6. M.B. Liu, G.R. Liu, Smoothed Particle Hydrodynamics (SPH): an overview and recent developments. Arch. Comput. Methods Eng. 17(1), 25–76 (2010)

    Article  MathSciNet  Google Scholar 

  7. J.J. Monaghan, Smoothed particle hydrodynamics. Rep. Prog. Phys. 68(1), 1703–1759 (2005)

    Article  MathSciNet  Google Scholar 

  8. J.U. Brackbill, H.M. Ruppel, FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J. Comput. Phys. 65(2), 314–343 (1986)

    Article  MathSciNet  Google Scholar 

  9. J. Cornelis, M. Ihmsen, A. Peer, M. Teschner, IISPH-FLIP for incompressible fluids. Comput. Gr. Forum 33(2), 255–262 (2014)

    Article  Google Scholar 

  10. A. Stomakhin, C. Schroeder, L. Chai, J. Teran, A. Selle, A material point method for snow simulation. ACM Trans. Gr. 32(4), 102:1–102:10 (2013)

    Google Scholar 

  11. D. Sulsky, S.-J. Zhou, H.L. Schreyer, Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87(1), 236–252 (1995)

    Article  Google Scholar 

  12. M. Macklin, M. Müller, Position based fluids. ACM Trans. Graph. 32(4), 104:1–104:12 (2013)

    Google Scholar 

  13. M. Müller, B. Heidelberger, M. Hennix, J. Ratcliff, Position based dynamics. J. Vis. Commun. Image Represent. 18(2), 109–118 (2007)

    Article  Google Scholar 

  14. F.H. Harlow, The particle-in-cell method for numerical solution of problems in fluid dynamics Los Alamos Scientific Lab., N. Mex, Technical report (1962)

    Google Scholar 

  15. Y. Zhu, R. Bridson, Animating sand as a fluid. ACM Trans. Gr. 24(3), 965–972 (2005)

    Article  Google Scholar 

  16. T. Takahashi, Y. Dobashi, I. Fujishiro, T. Nishita, Volume preserving viscoelastic fluids with large deformations using position-based velocity corrections. Vis. Comput. 32(1), 57–66 (2016)

    Article  Google Scholar 

  17. R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics-theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)

    Article  Google Scholar 

  18. L.B. Lucy, A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024 (1977)

    Article  Google Scholar 

  19. J.J. Monaghan, R.A. Gingold, Shock simulation by the particle method SPH. J. Comput. Phys. 52(2), 374–389 (1983)

    Article  Google Scholar 

  20. J.J. Monaghan, Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys. 30(1), 543–574 (1992)

    Article  Google Scholar 

  21. J.J. Monaghan, Simulating free surface flows with SPH. J. Comput. Phys. 110(2), 399–406 (1994)

    Article  Google Scholar 

  22. M. Desbrun, M.-P. Gascuel, Smoothed particles: A new paradigm for animating highly deformable bodies, in Eurographics Workshop on Computer Animation and Simulation ’96, pp. 61–76 (1996)

    Google Scholar 

  23. S.J. Cummins, M. Rudman, An SPH projection method. J. Comput. Phys. 152(2), 584–607 (1999)

    Article  MathSciNet  Google Scholar 

  24. S. Shao, E.Y.M. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Res. 26(7), 787–800 (2003)

    Article  Google Scholar 

  25. M. Becker, M. Teschner, Weakly compressible SPH for free surface flows, in 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 209–217 (2007)

    Google Scholar 

  26. B. Solenthaler, R. Pajarola, Predictive-corrective incompressible SPH. ACM Trans. Gr..s, 28(3), 40:1–40:6 (2009)

    Google Scholar 

  27. B. Solenthaler, R. Pajarola, Predictive-corrective incompressible SPH, in ACM SIGGRAPH 2009 Papers, pp. 40:1–40:6 (2009)

    Google Scholar 

  28. M. Ihmsen, J. Cornelis, B. Solenthaler, C. Horvath, M. Teschner, Implicit incompressible SPH. IEEE Trans. Vis. Comput. Gr. 20(3), 426–435 (2014)

    Article  Google Scholar 

  29. J. Bender, D. Koschier, Divergence-free smoothed particle hydrodynamics, in 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 147–155 (2015)

    Google Scholar 

  30. J.P. Morris, P.J. Fox, Y. Zhu, Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997)

    Article  Google Scholar 

  31. S. Clavet, P. Beaudoin, P. Poulin, Particle-based viscoelastic fluid simulation, in 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 219–228 (2005)

    Google Scholar 

  32. Y. Chang, K. Bao, J. Zhu, E. Wu, High viscosity fluid simulation using particle-based method, in 2011 IEEE International Symposium on VR Innovation, pp. 199–205 (2011)

    Google Scholar 

  33. M. Müller, D. Charypar, M. Gross, Particle-based fluid simulation for interactive applications, in ACM Eurographics/SIGGRAPH Symposium on Computer Animation, pp. 154–159 (2003)

    Google Scholar 

  34. M.M. Cross, Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems. J. Colloid Sci. 20, 417–437 (1965)

    Article  Google Scholar 

  35. L.F.d.S. Andrade, M. Sandim, F. Petronetto, P. Pagliosa, A. Paiva, SPH fluids for viscous jet buckling, in 27th SIBGRAPI Conference on Graphics, Patterns and Images, pp. 65–72 (2014)

    Google Scholar 

  36. L.F.d.S. Andrade, M. Sandim, F. Petronetto, P. Pagliosa, A. Paiva. Particle-based fluids for viscous jet buckling. Comput. Gr. 52, 106–115 (2015)

    Google Scholar 

  37. T. Takahashi, Y. Dobashi, I. Fujishiro, T. Nishita, M.C. Lin, Implicit formulation for SPH-based viscous fluids. Comput. Gr. Forum 34(2), 493–502 (2015)

    Article  Google Scholar 

  38. A. Peer, M. Ihmsen, J. Cornelis, M. Teschner, An implicit viscosity formulation for SPH fluids. ACM Trans. Gr. 34(4), 114:1–114:10 (2015)

    Google Scholar 

  39. J. Bender, D. Koschier, Divergence-free SPH for incompressible and viscous fluids. IEEE Trans. Visual Comput. Gr. 23, 1193–1206 (2017)

    Article  Google Scholar 

  40. H. Barreiro, I. García-Fernández, I. Alduán, M.A. Otaduy, Conformation constraints for efficient viscoelastic fluid simulation. ACM Trans. Gr. 36(6), 221:1–221:11 (2017)

    Google Scholar 

  41. M. Weiler, D. Koschier, M. Brand, J. Bender, A physically consistent implicit viscosity solver for SPH fluids. Comput. Gr. Forum 37(2), 145–155 (2018)

    Article  Google Scholar 

  42. M. Carlson, P.J. Mucha, R.B. Van Horn III, G. Turk, Melting and flowing, in 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 167–174 (2002)

    Google Scholar 

  43. C. Batty, R. Bridson, Accurate viscous free surfaces for buckling, coiling, and rotating liquids, in 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 219–228 (2008)

    Google Scholar 

  44. A. Peer, M. Ihmsen, Prescribed velocity gradients for highly viscous SPH fluids with vorticity diffusion. IEEE Trans. Visual Comput. Gr. 23(12), 2656–2662 (2016)

    Article  Google Scholar 

  45. E. Rossi, A. Colagrossi, D. Durante, G. Graziani, Simulating 2D viscous flow around geometries with vertices through the diffused vortex hydrodynamics method. Comput. Methods Appl. Mech. Eng. 302, 147–169 (2016)

    Article  MathSciNet  Google Scholar 

  46. A.E. Chorin. A Mathematical Introduction to Fluid Mechanics (Springer, 1992)

    Google Scholar 

  47. A. Powell, MIT materials science and engineering. 3.21 Lectures on Fluid Flow and Kinectics (2003)

    Google Scholar 

  48. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis (AMS Chelsea Publishing, 1977)

    Google Scholar 

  49. M. Ihmsen, J. Orthmann, B. Solenthaler, A. Kolb, M. Teschner, SPH fluids in computer graphics, in EUROGRAPHICS 2014 — State of The Art Report, pp. 21–42 (2014)

    Google Scholar 

  50. M. Kelager, Lagrangian fluid dynamics using smoothed particle hydrodynamics. Master’s thesis, University of Copenhagen (2006)

    Google Scholar 

  51. M. Gomez-Gesteira, B.D. Rogers, R.A. Dalrymple, A. Crespo, State-of-the-art of classical SPH for free-surface flows. J. Hydraul. Res. 48, 6–27 (2010)

    Article  Google Scholar 

  52. F. Colin, R. Egli, F.Y. Lin, Computing a null divergence velocity field using smoothed particle hydrodynamics. J. Comput. Phys. 217(2), 680–692 (2006)

    Article  MathSciNet  Google Scholar 

  53. H.-S. Dou, B. Khoo, Investigation of turbulent transition in plane Couette flows using energy gradient method. Adv. Appl. Math. Mech. 3, 165–180 (2005)

    Article  MathSciNet  Google Scholar 

  54. X. X, J. Ouyang, W. Li, Q. Liu, SPH simulations of 2D transient viscoelastic flows using brownian configuration fields. J. Non-Newtonian Fluid Mech. 208, 59–71 (2014)

    Google Scholar 

  55. L. Trefethen, A.E. Trefethen, S.C. Reddy, T. Driscoll, Hydrodynamic stability without eigenvalues. Science 261(5121), 578–584 (1993)

    Article  MathSciNet  Google Scholar 

  56. E. Mitsoulis, Numerical simulation of calendering viscoplastic fluids. J. Nonnewton. Fluid Mech. 154(2–3), 77–88 (2008)

    Article  Google Scholar 

  57. E. Mitsoulis, S.G. Hatzikiriakos, Rolling of bread dough: Experiments and simulations. Food Bioprod. Process. 87(2), 124–138 (2009)

    Article  Google Scholar 

  58. S. Sofou, E.B. Muliawan, S.G. Hatzikiriakos, E. Mitsoulis, Rheological characterization and constitutive modeling of bread dough. Rheol. Acta 47(4), 369–381 (2008)

    Article  Google Scholar 

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Kim, JT., Ruggiero, F., Lippiello, V., Siciliano, B. (2022). Smoothed Particle Hydrodynamics-Based Viscous Deformable Object Modelling. In: Siciliano, B., Ruggiero, F. (eds) Robot Dynamic Manipulation. Springer Tracts in Advanced Robotics, vol 144. Springer, Cham. https://doi.org/10.1007/978-3-030-93290-9_3

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