“Stable Neo-Hookean Flesh Simulation” by Smith, Goes and Kim

  • ©Breannan Smith, Fernando de Goes, and Theodore Kim



Session Title:

    Deep Thoughts on How Things Move


    Stable Neo-Hookean Flesh Simulation




    Nonlinear hyperelastic energies play a key role in capturing the fleshy appearance of virtual characters. Real-world, volume-preserving biological tissues have Poisson’s ratios near 1/2, but numerical simulation within this regime is notoriously challenging. In order to robustly capture these visual characteristics, we present a novel version of Neo-Hookean elasticity. Our model maintains the fleshy appearance of the Neo-Hookean model, exhibits superior volume preservation, and is robust to extreme kinematic rotations and inversions. We obtain closed-form expressions for the eigenvalues and eigenvectors of all of the system’s components, which allows us to directly project the Hessian to semipositive definiteness, and also leads to insights into the numerical behavior of the material. These findings also inform the design of more sophisticated hyperelastic models, which we explore by applying our analysis to Fung and Arruda-Boyce elasticity. We provide extensive comparisons against existing material models.


    1. Ellen M. Arruda and Mary C. Boyce. 1993. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids 41, 2 (1993), 389–412.
    2. David Baraff and Andrew Witkin. 1998. Large steps in cloth simulation. In Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’98). 43–54. 
    3. Adam W. Bargteil and Elaine Cohen. 2014. Animation of deformable bodies with quadratic bézier finite elements. ACM Trans. Graph. 33, 3, Article 27 (June 2014), 10 pages. 
    4. Jan Bender, Matthias Müller, and Miles Macklin. 2015. Position-based simulation methods in computer graphics. In Eurographics Tutorials. Eurographics Association.
    5. Silvia S. Blemker, Peter M. Pinsky, and Scott L. Delp. 2005. A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii. J. Biomechanics 38, 4 (2005), 657–665.
    6. Javier Bonet and Richard D. Wood. 2008. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.
    7. Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective dynamics: Fusing constraint projections for fast simulation. ACM Trans. Graph. 33, 4, Article 154 (July 2014), 11 pages. 
    8. Allan F. Bower. 2009. Applied Mechanics of Solids. CRC Press.
    9. James R. Bunch, Christopher P. Nielsen, and Danny C. Sorensen. 1978. Rank-one modification of the symmetric eigenproblem. Numer. Math. 31, 1 (1978), 31–48. 
    10. Isaac Chao, Ulrich Pinkall, Patrick Sanan, and Peter Schröder. 2010. A simple geometric model for elastic deformations. ACM Trans. Graph. 29, 4, Article 38 (2010), 6 pages. 
    11. Oscar Civit-Flores and Antonio Susín. 2014. Robust treatment of degenerate elements in interactive corotational FEM simulations. Comput. Graph. Forum 33, 6 (2014), 298–309. 
    12. Pradeep Dubey, Pat Hanrahan, Ronald Fedkiw, Michael Lentine, and Craig Schroeder. 2011. PhysBAM: Physically based simulation. In ACM SIGGRAPH Courses. Article 10, 22 pages. 
    13. Yuan-cheng Fung. 2013. Biomechanics: Mechanical Properties of Living Tissues. Springer Science 8 Business Media.
    14. Joachim Georgii and Rüdiger Westermann. 2008. Corotated finite elements made fast and stable. In Proceedings of the Fifth Workshop on Virtual Reality Interaction and Physical Simulation (VRIPHYS’08). 11–19.
    15. Gene H. Golub and Charles F. Van Loan. 2012. Matrix Computations. Vol. 3. JHU Press.
    16. George Neville Greaves, A. L. Greer, R. S. Lakes, and T. Rouxel. 2011. Poisson’s ratio and modern materials. Nat. Mater. 10, 11 (2011), 823–837.
    17. Nicholas J. Higham. 2008. Functions of Matrices: Theory and Computation. SIAM. 
    18. Gentaro Hirota, Susan Fisher, A. State, Chris Lee, and Henry Fuchs. 2001. An implicit finite element method for elastic solids in contact. In Proceedings of the Fourteenth Conference on Computer Animation (Computer Animation’01). 136–254.
    19. Geoffrey Irving, Joseph Teran, and Ronald Fedkiw. 2004. Invertible finite elements for robust simulation of large deformation. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’04). 131–140. 
    20. Michael A. Jenkins and Joseph F. Traub. 1970. A three-stage variable-shift iteration for polynomial zeros and its relation to generalized rayleigh iteration. Numer. Math. 14, 3 (1970), 252–263. 
    21. Ryan Kautzman, Jiayi Chong, and Patrick Coleman. 2012. Stable, art-directable skin and flesh using biphasic materials. In ACM SIGGRAPH Talks.
    22. Ryo Kikuuwe, Hiroaki Tabuchi, and Motoji Yamamoto. 2009. An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements. ACM Trans. Graph. 28, 1, Article 8 (2009), 13 pages. 
    23. Allen Knutson and Terence Tao. 2001. Honeycombs and sums of hermitian matrices. Notices Amer. Math. Soc 48, 2 (2001), 175–186.
    24. Tamara G. Kolda and Brett W. Bader. 2009. Tensor decompositions and applications. SIAM Rev. 51, 3 (2009), 455–500. 
    25. Tiantian Liu, Ming Gao, Lifeng Zhu, Eftychios Sifakis, and Ladislav Kavan. 2016. Fast and robust inversion-free shape manipulation. Comput. Graph. Forum 35, 2 (2016), 1–11.
    26. Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, and Markus Gross. 2011. Example-based elastic materials. ACM Trans. Graph. 30, 4, Article 72 (July 2011), 8 pages. 
    27. Aleka McAdams, Yongning Zhu, Andrew Selle, Mark Empey, Rasmus Tamstorf, Joseph Teran, and Eftychios Sifakis. 2011. Efficient elasticity for character skinning with contact and collisions. ACM Trans. Graph. 30, 4, Article 37 (July 2011), 12 pages. 
    28. Nathan Mitchell, Mridul Aanjaneya, Rajsekhar Setaluri, and Eftychios Sifakis. 2015. Non-manifold level sets: A multivalued implicit surface representation with applications to self-collision processing. ACM Trans. Graph. 34, 6, Article 247 (Oct. 2015), 9 pages. 
    29. Melvin Mooney. 1940. A theory of large elastic deformation. J. Appl. Phys. 11, 9 (1940), 582–592.
    30. Matthias Müller, Julie Dorsey, Leonard McMillan, Robert Jagnow, and Barbara Cutler. 2002. Stable real-time deformations. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’02). 49–54. 
    31. Matthias Müller, Jos Stam, Doug James, and Nils Thürey. 2008. Real time physics. In ACM SIGGRAPH Classes. Article 88, 90 pages.
    32. Rahul Narain, Matthew Overby, and George E. Brown. 2016. ADMM ⊇ projective dynamics: Fast simulation of general constitutive models. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’16). 21–28. 
    33. Matthieu Nesme, Paul G. Kry, Lenka Jeřábková, and François Faure. 2009. Preserving topology and elasticity for embedded deformable models. ACM Trans. Graph. 28, 3, Article 52 (July 2009), 9 pages.
    34. Raymond W. Ogden. 1997. Non-linear Elastic Deformations. Dover Publications.
    35. Zherong Pan, Hujun Bao, and Jin Huang. 2015. Subspace dynamic simulation using rotation-strain coordinates. ACM Trans. Graph. 34, 6, Article 242 (2015), 12 pages. 
    36. Ronald Rivlin. 1948. Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philos. Trans. Roy. Soc. London A: Math. Phys. Eng. Sci. 241, 835 (1948), 379–397.
    37. Karl Rupp, Florian Rudolf, and Josef Weinbub. 2010. ViennaCL – A high level linear algebra library for GPUs and multi-core CPUs. In International Workshop on GPUs and Scientific Applications. 51–56.
    38. Ruediger Schmedding and Matthias Teschner. 2008. Inversion handling for stable deformable modeling. Vis. Comput. 24, 7 (2008), 625–633. 
    39. Christian Schüller, Ladislav Kavan, Daniele Panozzo, and Olga Sorkine-Hornung. 2013. Locally injective mappings. In Eurographics/ACMSIGGRAPH Symposium on Geometry Proceedings (SGP’13). 125–135. 
    40. Eftychios Sifakis and Jernej Barbic. 2012. FEM simulation of 3D deformable solids: A practitioner’s guide to theory, discretization and model reduction. In ACM SIGGRAPH Courses. Article 20, 50 pages. 
    41. James G. Simmonds. 2012. A Brief on Tensor Analysis. Springer Science 8 Business Media.
    42. Alexey Stomakhin, Russell Howes, Craig Schroeder, and Joseph M. Teran. 2012. Energetically consistent invertible elasticity. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’12). 25–32. 
    43. Joseph Teran, Eftychios Sifakis, Geoffrey Irving, and Ronald Fedkiw. 2005. Robust quasistatic finite elements and flesh simulation. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’05). 181–190. 
    44. Matthias Teschner, Bruno Heidelberger, Matthias Muller, and Markus Gross. 2004. A versatile and robust model for geometrically complex deformable solids. In Proceedings of Computer Graphics International (CGI’04). 312–319. 
    45. Christopher D. Twigg and Zoran Kačić-Alesić. 2010. Point cloud glue: Constraining simulations using the procrustes transform. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’10). 45–54. 
    46. Nobuyuki Umetani, Ryan Schmidt, and Jos Stam. 2014. Position-based elastic rods. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA’14). 21–30. 
    47. Huamin Wang and Yin Yang. 2016. Descent methods for elastic body simulation on the GPU. ACM Trans. Graph. 35, 6, Article 212 (Nov. 2016), 10 pages.
    48. Hongyi Xu, Funshing Sin, Yufeng Zhu, and Jernej Barbič. 2015. Nonlinear material design using principal stretches. ACM Trans. Graph. 34, 4, Article 75 (July 2015), 11 pages.