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Volume Preserving Simulation of Soft Tissue with Skin

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Published:27 September 2021Publication History
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Abstract

Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods employ compressible elasticity models and achieve incompressibility indirectly by setting Poisson's ratio to be close to 0.5. This approach can produce results that are plausible qualitatively but inaccurate quantatively. This approach also causes numerical instabilities and locking in coarse discretizations or otherwise poses a prohibitive restriction on the size of the time step. We propose a novel approach to alleviate these issues by replacing indirect volume preservation using Poisson's ratios with direct enforcement of zonal volume constraints, while controlling fine-scale volumetric deformation through a cell-wise compression penalty. To increase realism, we propose an epidermis model to mimic the dramatically higher surface stiffness on real skinned bodies. We demonstrate that our method produces stable realistic deformations with precise volume preservation but without locking artifacts. Due to the volume preservation not being tied to mesh discretization, our method also allows a resolution consistent simulation of incompressible materials. Our method improves the stability of the standard neo-Hookean model and the general compression recovery in the Stable neo-Hookean model.

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References

  1. Alexis Angelidis, Marie-Paule Cani, Geoff Wyvill, and Scott King. 2004. Swirling-sweepers: constant-volume modeling. In 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings. 10--15.Google ScholarGoogle ScholarCross RefCross Ref
  2. Douglas N. Arnold, Franco Brezzi, and Michel Fortin. 1984. A stable finite element for the Stokes equations. Calcolo 21, 4 (1984), 337--344.Google ScholarGoogle ScholarCross RefCross Ref
  3. Ilya Baran and Jovan Popović. 2007. Automatic rigging and animation of 3d characters. In ACM Transactions on graphics (TOG), Vol. 26. ACM, 72.Google ScholarGoogle Scholar
  4. Klaus-Jürgen Bathe. 2001. The inf-sup condition and its evaluation for mixed finite element methods. Computers & structures 79, 2 (2001), 243--252.Google ScholarGoogle Scholar
  5. Klaus-Jürgen Bathe. 2006. Finite Element Procedures. Prentice Hall. https://books.google.ca/books?id=rWvefGICfO8CGoogle ScholarGoogle Scholar
  6. Javier Bonet and A.J. Burton. 1998. A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications. Communications in Numerical Methods in Engineering 14, 5 (1998), 437--449.Google ScholarGoogle ScholarCross RefCross Ref
  7. Javier Bonet and Richard D. Wood. 2008. J. Bonet, R. D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, Cambridge, UK. Vol. 24. https://doi.org/10.1017/CBO9780511755446Google ScholarGoogle Scholar
  8. Dietrich Braess. 2007. Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press.Google ScholarGoogle Scholar
  9. Enrique Cerda and Lakshminarayanan Mahadevan. 2003. Geometry and physics of wrinkling. Physical review letters 90, 7 (2003), 074302.Google ScholarGoogle Scholar
  10. Oscar Civit-Flores and Antonio Susín. 2014. Robust treatment of degenerate elements in interactive corotational fem simulations. In Computer Graphics Forum, Vol. 33. Wiley Online Library, 298--309.Google ScholarGoogle Scholar
  11. Eduardo Alberto de Souza Neto, Francisco M. Andrade Pires, and D.R.J. Owen. 2005. F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking. Internat. J. Numer. Methods Engrg. 62, 3 (2005), 353--383.Google ScholarGoogle ScholarCross RefCross Ref
  12. Raphael Diziol, Jan Bender, and Daniel Bayer. 2011. Robust Real-Time Deformation of Incompressible Surface Meshes. Proceedings - SCA 2011: ACM SIGGRAPH / Eurographics Symposium on Computer Animation, 237--246.Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Cormac Flynn and Brendan AO McCormack. 2009. A three-layer model of skin and its application in simulating wrinkling. Computer methods in biomechanics and biomedical engineering 12, 2 (2009), 125--134.Google ScholarGoogle Scholar
  14. Mihai Frâncu, Arni Asgeirsson, M. Rønnow, and K. Erleben. 2021. Locking-proof Tetrahedra. ACM Transactions on Graphics 40 (2021), 2.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Yuan-cheng Fung. 2013. Biomechanics: mechanical properties of living tissues. Springer Science & Business Media.Google ScholarGoogle Scholar
  16. Stefan Hartmann and Patrizio Neff. 2003. Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility. International journal of solids and structures 40, 11 (2003), 2767--2791.Google ScholarGoogle ScholarCross RefCross Ref
  17. Gentaro Hirota, Renee Maheshwari, and Ming C. Lin. 2000. Fast volume-preserving free-form deformation using multi-level optimization. Computer-Aided Design 32, 8 (2000), 499--512. https://doi.org/10.1016/S0010-4485(00)00038-5Google ScholarGoogle ScholarCross RefCross Ref
  18. Min Hong, Sunhwa Jung, Min-Hyung Choi, and Samuel W.J. Welch. 2006. Fast Volume Preservation for a Mass-Spring System. IEEE Computer Graphics and Applications 26, 5 (Sept 2006), 83--91. https://doi.org/10.1109/MCG.2006.104Google ScholarGoogle Scholar
  19. Geoffrey Irving, Craig Schroeder, and Ronald Fedkiw. 2007. Volume Conserving Finite Element Simulations of Deformable Models. ACM Trans. Graph. 26, 3, Article 13 (July 2007). https://doi.org/10.1145/1276377.1276394Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Geoffrey Irving, Joseph Teran, and Ronald Fedkiw. 2004. Invertible Finite Elements for Robust Simulation of Large Deformation. In Proceedings of the 2004 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Grenoble, France) (SCA '04). Eurographics Association, Goslar Germany, Germany, 131--140. https://doi.org/10.1145/1028523.1028541Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Alec Jacobson, Ilya Baran, Ladislav Kavan, Jovan Popović, and Olga Sorkine. 2012. Fast automatic skinning transformations. ACM Transactions on Graphics (TOG) 31, 4 (2012), 77.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Doug L James and Christopher D Twigg. 2005. Skinning mesh animations. In ACM Transactions on Graphics (TOG), Vol. 24. ACM, 399--407.Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Peter Kaufmann. 2012. Discontinuous Galerkin FEM in Computer Graphics. Ph.D. Dissertation. ETH Zurich.Google ScholarGoogle Scholar
  24. Ryo Kikuuwe, Hiroaki Tabuchi, and Motoji Yamamoto. 2009. An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements. ACM Transactions on Graphics (TOG) 28, 1 (2009), 8.Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Duo Li, Shinjiro Sueda, Debanga R. Neog, and Dinesh K. Pai. 2013. Thin Skin Elastodynamics. ACM Trans. Graph. (Proc. SIGGRAPH) 32, 4 (July 2013), 49:1--49:9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Pengbo Li and Paul G. Kry. 2014. Multi-layer Skin Simulation with Adaptive Constraints. In Proceedings of the Seventh International Conference on Motion in Games (Playa Vista, California) (MIG '14). ACM, New York, NY, USA, 171--176. https://doi.org/10.1145/2668084.2668089Google ScholarGoogle Scholar
  27. Tiantian Liu, Sofien Bouaziz, and Ladislav Kavan. 2017. Quasi-Newton Methods for Real-Time Simulation of Hyperelastic Materials. ACM Trans. Graph. 36, 3, Article 116a (May 2017). https://doi.org/10.1145/2990496Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Andreas Longva, Fabian Löschner, Tassilo Kugelstadt, José Antonio Fernández-Fernández, and Jan Bender. 2020. Higher-order finite elements for embedded simulation. ACM Transactions on Graphics (TOG) 39, 6 (2020), 1--14.Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Ives Macêdo, João Paulo Gois, and Luiz Velho. 2009. Hermite interpolation of implicit surfaces with radial basis functions. In 2009 XXII Brazilian Symposium on Computer Graphics and Image Processing. IEEE, 1--8.Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Nadia Magnenat-Thalmann, Prem Kalra, Jean Luc Lévêque, Roland Bazin, Dominique Batisse, and Bernard Querleux. 2002. A computational skin model: fold and wrinkle formation. IEEE Transactions on Information Technology in Biomedicine 6, 4(2002), 317--323.Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. 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. https://doi.org/10.1145/2010324.1964932Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Melvin Mooney. 1940. A theory of large elastic deformation. Journal of applied physics 11, 9 (1940), 582--592.Google ScholarGoogle ScholarCross RefCross Ref
  33. Matthias Müller, Julie Dorsey, Leonard McMillan, Robert Jagnow, and Barbara Cutler. 2002. Stable Real-time Deformations. In Proceedings of the 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (San Antonio, Texas) (SCA '02). ACM, New York, NY, USA, 49--54. https://doi.org/10.1145/545261.545269Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Dinesh K. Pai, Austin Rothwell, Pearson Wyder-Hodge, Alistair Wick, Ye Fan, Egor Larionov, Darcy Harrison, Debanga Raj Neog, and Cole Shing. 2018. The Human Touch: Measuring Contact with Real Human Soft Tissues. ACM Trans. Graph. 37, 4, Article 58 (July 2018), 12 pages. https://doi.org/10.1145/3197517.3201296Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Emmanuel Promayon, Pierre Baconnier, and Claude Puech. 1996. Physically Based Deformations Constrained in Displacements and Volume. Computer Graphics Forum (Proc. of Eurographics '96) 15 (08 1996). https://doi.org/10.1111/1467-8659.1530155Google ScholarGoogle Scholar
  36. Mike A. Puso and Jerome M. Solberg. 2006. A stabilized nodally integrated tetrahedral. Internat. J. Numer. Methods Engrg. 67, 6 (2006), 841--867.Google ScholarGoogle ScholarCross RefCross Ref
  37. Ronald S. Rivlin and Eric K. Rideal. 1948. Large elastic deformations of isotropic materials IV. further developments of the general theory. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 241, 835 (1948), 379--397. https://doi.org/10.1098/rsta.1948.0024arXiv:https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1948.0024Google ScholarGoogle Scholar
  38. Damien Rohmer, Stefanie Hahmann, and Marie-Paule Cani. 2009. Exact Volume Preserving Skinning with Shape Control. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (New Orleans, Louisiana) (SCA '09). ACM, New York, NY, USA, 83--92. https://doi.org/10.1145/1599470.1599481Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. 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 2012 Courses (Los Angeles, California) (SIGGRAPH '12). ACM, New York, NY, USA, Article 20, 50 pages. https://doi.org/10.1145/2343483.2343501Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Breannan Smith, Fernando De Goes, and Theodore Kim. 2018. Stable Neo-Hookean Flesh Simulation. ACM Trans. Graph. 37, 2, Article 12 (March 2018), 15 pages. https://doi.org/10.1145/3180491Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Alexey Stomakhin, Russell Howes, Craig Schroeder, and Joseph M. Teran. 2012. Energetically Consistent Invertible Elasticity. In Proceedings of the 11th ACM SIGGRAPH / Eurographics Conference on Computer Animation (Lausanne, Switzerland) (EUROSCA'12). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 25--32. https://doi.org/10.2312/SCA/SCA12/025-032Google ScholarGoogle Scholar
  42. Theodore Sussman and Klaus-Jürgen Bathe. 1987. A finite element formulation for nonlinear incompressible elastic and inelastic analysis. Computers & Structures 26, 1-2 (1987), 357--409.Google ScholarGoogle ScholarCross RefCross Ref
  43. Joseph Teran, Eftychios Sifakis, Geoffrey Irving, and Ronald Fedkiw. 2005. Robust Quasistatic Finite Elements and Flesh Simulation. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Los Angeles, California) (SCA 05). ACM, New York, NY, USA, 181--190. https://doi.org/10.1145/1073368.1073394Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Rodolphe Vaillant, Loïc Barthe, Gaël Guennebaud, Marie-Paule Cani, Damien Rohmer, Brian Wyvill, Olivier Gourmel, and Mathias Paulin. 2013. Implicit skinning: real-time skin deformation with contact modeling. ACM Transactions on Graphics (TOG) 32, 4 (2013), 125.Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Wolfram von Funck, Holger Theisel, and Hans-Peter Seidel. 2007. Explicit Control of Vector Field Based Shape Deformations. In 15th Pacific Conference on Computer Graphics and Applications (PG'07). 291--300. https://doi.org/10.1109/PG.2007.26Google ScholarGoogle Scholar
  46. Andreas Wächter and Lorenz T. Biegler. 2006. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming 106, 1 (01 Mar 2006), 25--57. https://doi.org/10.1007/s10107-004-0559-yGoogle ScholarGoogle ScholarDigital LibraryDigital Library
  47. Huamin Wang and Yin Yang. 2016. Descent methods for elastic body simulation on the GPU. ACM Transactions on Graphics (TOG) 35, 6 (2016), 1--10.Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. Ofir Weber, Olga Sorkine, Yaron Lipman, and Craig Gotsman. 2007. Context-aware skeletal shape deformation. In Computer Graphics Forum, Vol. 26. Wiley Online Library, 265--274.Google ScholarGoogle Scholar
  49. Holger Wendland. 2004. Scattered data approximation. Vol. 17. Cambridge university press.Google ScholarGoogle Scholar
  50. Seung-Hyun Yoon and Myung-Soo Kim. 2006. Sweep-based Freeform Deformations. Comput. Graph. Forum 25 (09 2006), 487--496. https://doi.org/10.1111/j.1467-8659.2006.00968.xGoogle ScholarGoogle Scholar

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