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.
Supplemental Material
Available for Download
Supplemental movie, appendix, image and software files for, Volume Preserving Simulation of Soft Tissue with Skin
- 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 Scholar
Cross Ref
- Douglas N. Arnold, Franco Brezzi, and Michel Fortin. 1984. A stable finite element for the Stokes equations. Calcolo 21, 4 (1984), 337--344.Google Scholar
Cross Ref
- Ilya Baran and Jovan Popović. 2007. Automatic rigging and animation of 3d characters. In ACM Transactions on graphics (TOG), Vol. 26. ACM, 72.Google Scholar
- Klaus-Jürgen Bathe. 2001. The inf-sup condition and its evaluation for mixed finite element methods. Computers & structures 79, 2 (2001), 243--252.Google Scholar
- Klaus-Jürgen Bathe. 2006. Finite Element Procedures. Prentice Hall. https://books.google.ca/books?id=rWvefGICfO8CGoogle Scholar
- 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 Scholar
Cross Ref
- 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 Scholar
- Dietrich Braess. 2007. Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press.Google Scholar
- Enrique Cerda and Lakshminarayanan Mahadevan. 2003. Geometry and physics of wrinkling. Physical review letters 90, 7 (2003), 074302.Google Scholar
- 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 Scholar
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
- Mihai Frâncu, Arni Asgeirsson, M. Rønnow, and K. Erleben. 2021. Locking-proof Tetrahedra. ACM Transactions on Graphics 40 (2021), 2.Google Scholar
Digital Library
- Yuan-cheng Fung. 2013. Biomechanics: mechanical properties of living tissues. Springer Science & Business Media.Google Scholar
- 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 Scholar
Cross Ref
- 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 Scholar
Cross Ref
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- Doug L James and Christopher D Twigg. 2005. Skinning mesh animations. In ACM Transactions on Graphics (TOG), Vol. 24. ACM, 399--407.Google Scholar
Digital Library
- Peter Kaufmann. 2012. Discontinuous Galerkin FEM in Computer Graphics. Ph.D. Dissertation. ETH Zurich.Google Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- Melvin Mooney. 1940. A theory of large elastic deformation. Journal of applied physics 11, 9 (1940), 582--592.Google Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- Mike A. Puso and Jerome M. Solberg. 2006. A stabilized nodally integrated tetrahedral. Internat. J. Numer. Methods Engrg. 67, 6 (2006), 841--867.Google Scholar
Cross Ref
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- 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 Scholar
Cross Ref
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- 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 Scholar
Digital Library
- 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 Scholar
Digital Library
- 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 Scholar
- Holger Wendland. 2004. Scattered data approximation. Vol. 17. Cambridge university press.Google Scholar
- 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 Scholar
Index Terms
Volume Preserving Simulation of Soft Tissue with Skin
Recommendations
Mass conservation of finite element methods for coupled flow-transport problems
This paper gives an overview of the mass conservation properties of finite element discretisations applied to coupled flow-transport problems. The system is described by the instationary, incompressible Navier Stokes equations and the time-dependent ...
Benchmarking FEniCS for mantle convection simulations
This paper evaluates the usability of the FEniCS Project for mantle convection simulations by numerical comparison to three established benchmarks. The benchmark problems all concern convection processes in an incompressible fluid induced by temperature ...
Explicit mixed strain---displacement finite elements for compressible and quasi-incompressible elasticity and plasticity
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The ...






Comments