“Nonlinear material design using principal stretches” by Xu, Sin, Zhu and Barbic

  • ©Hongyi Xu, FunShing Sin, Yufeng Zhu, and Jernej Barbic

Conference:


Type(s):


Title:

    Nonlinear material design using principal stretches

Session/Category Title:   Deform Me a Solid


Presenter(s)/Author(s):


Moderator(s):



Abstract:


    The Finite Element Method is widely used for solid deformable object simulation in film, computer games, virtual reality and medicine. Previous applications of nonlinear solid elasticity employed materials from a few standard families such as linear corotational, nonlinear St.Venant-Kirchhoff, Neo-Hookean, Ogden or Mooney-Rivlin materials. However, the spaces of all nonlinear isotropic and anisotropic materials are infinite-dimensional and much broader than these standard materials. In this paper, we demonstrate how to intuitively explore the space of isotropic and anisotropic nonlinear materials, for design of animations in computer graphics and related fields. In order to do so, we first formulate the internal elastic forces and tangent stiffness matrices in the space of the principal stretches of the material. We then demonstrate how to design new isotropic materials by editing a single stress-strain curve, using a spline interface. Similarly, anisotropic (orthotropic) materials can be designed by editing three curves, one for each material direction. We demonstrate that modifying these curves using our proposed interface has an intuitive, visual, effect on the simulation. Our materials accelerate simulation design and enable visual effects that are difficult or impossible to achieve with standard nonlinear materials.

References:


    1. Allard, J., Marchal, M., Cotin, S., et al. 2009. Fiber-based fracture model for simulating soft tissue tearing. Studies in health technology and informatics 142, 13–18.Google Scholar
    2. Ball, J. 1976. Convexity conditions and existence theorems in nonlinear elasticity. Archive for Rational Mechanics and Analysis 63, 4, 337–403.Google ScholarCross Ref
    3. Becker, M., and Teschner, M. 2007. Robust and efficient estimation of elasticity parameters using the linear finite element method. In Simulation und Visualisierung Conf. (SimVis), 15–28.Google Scholar
    4. Bickel, B., Baecher, M., Otaduy, M., Matusik, W., Pfister, H., and Gross, M. 2009. Capture and modeling of non-linear heterogeneous soft tissue. ACM Trans. on Graphics (SIGGRAPH 2009) 28, 3, 89:1–89:9. Google ScholarDigital Library
    5. Bonet, J., and Burton, A. 1998. A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations. Computer Methods in Applied Mechanics and Engineering 162, 151–164.Google ScholarCross Ref
    6. Bonet, J., and Wood, R. D. 1997. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge Univ. Press.Google Scholar
    7. Bower, A. 2011. Applied Mechanics of Solids. Taylor & Francis.Google Scholar
    8. Capell, S., Green, S., Curless, B., Duchamp, T., and Popović, Z. 2002. Interactive skeleton-driven dynamic deformations. ACM Trans. on Graphics (SIGGRAPH 2002) 21, 3, 586–593. Google ScholarDigital Library
    9. Carmichael, A., and Holdaway, H. 1961. Phenomenological elastomechanical behavior of rubbers over wide ranges of strain. Journal of Applied Physics 32, 2, 159–166.Google ScholarCross Ref
    10. Chao, I., Pinkall, U., Sanan, P., and Schröder, P. 2010. A Simple Geometric Model for Elastic Deformations. ACM Trans. on Graphics (SIGGRAPH 2010) 29, 3, 38:1–38:6. Google ScholarDigital Library
    11. Civit-Flores, O., and Susín, A. 2014. Robust Treatment of Degenerate Elements in Interactive Corotational FEM Simulations. Computer Graphics Forum 33, 6, 298–309.Google ScholarDigital Library
    12. Drucker, D. C. 1957. A definition of stable inelastic material. Tech. rep., DTIC Document.Google Scholar
    13. Gao, Z., Kim, T., James, D. L., and Desai, J. P. 2009. Semi-automated soft-tissue acquisition and modeling for surgical simulation. In Proc. of the 5th IEEE Int. Conf. on Automation Science and Engineering, 268–273. Google ScholarDigital Library
    14. Hahn, F., Thomaszewski, B., Coros, S., Sumner, R., and Gross, M. 2013. Efficient simulation of secondary motion in rig-space. In Symp. on Computer Animation (SCA), 165–171. Google ScholarDigital Library
    15. Hernandez, F., Cirio, G., Perez, A., and Otaduy, M. 2013. Anisotropic strain limiting. In Proc. of Congreso Español de Informática Gráfica, vol. 2.Google Scholar
    16. Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible Finite Elements for Robust Simulation of Large Deformation. In Symp. on Computer Animation (SCA), 131–140. Google ScholarDigital Library
    17. Kikuuwe, R., Tabuchi, H., and Yamamoto, M. 2009. An edge-based computationally efficient formulation of saint venant-kirchhoff tetrahedral finite elements. ACM Trans. on Graphics 28, 1, 1–13. Google ScholarDigital Library
    18. Lee, H.-P., and Lin, M. 2012. Fast optimization-based elasticity parameter estimation using reduced models. The Visual Computer 28, 6-8, 553–562. Google ScholarDigital Library
    19. Li, Y., and Barbič, J. 2014. Stable orthotropic materials. In Symp. on Computer Animation (SCA), 41–46.Google Scholar
    20. Li, S., Huang, J., de Goes, F., Jin, X., Bao, H., and Desbrun, M. 2014. Space-time editing of elastic motion through material optimization and reduction. ACM Trans. on Graphics (SIGGRAPH 2014) 33, 4, 108:1–108:10. Google ScholarDigital Library
    21. McAdams, A., Zhu, Y., Selle, A., Empey, M., Tamstorf, R., Teran, J., and Sifakis, E. 2011. Efficient elasticity for character skinning with contact and collisions. ACM Trans. on Graphics (SIGGRAPH 2011) 30, 4, 37:1–37:11. Google ScholarDigital Library
    22. Mooney, M. 1940. A theory of large elastic deformation. Journal of applied physics 11, 9, 582–592.Google ScholarCross Ref
    23. Müller, M., and Gross, M. 2004. Interactive Virtual Materials. In Proc. of Graphics Interface 2004, 239–246. Google ScholarDigital Library
    24. O’Brien, J., and Hodgins, J. 1999. Graphical Modeling and Animation of Brittle Fracture. In Proc. of ACM SIGGRAPH 1999, 111–120. Google ScholarDigital Library
    25. Ogden, R. W. 1997. Non-linear elastic deformations. Courier Dover Publications.Google Scholar
    26. Papadopoulo, T., and Lourakis, M. I. 2000. Estimating the Jacobian of the singular value decomposition: Theory and application. In European Conf. on Computer Vision, 554–570. Google ScholarDigital Library
    27. Parker, E. G., and O’Brien, J. F. 2009. Real-time deformation and fracture in a game environment. In Symp. on Computer Animation (SCA), 156–166. Google ScholarDigital Library
    28. Perez, A., Cirio, G., Hernandez, F., Garre, C., and Otaduy, M. 2013. Strain limiting for soft finger contact simulation. In World Haptics Conference (WHC), 2013, 79–84.Google ScholarCross Ref
    29. Picinbono, G., Delingette, H., and Ayache, N. 2001. Non-linear and anisotropic elastic soft tissue models for medical simulation. In IEEE Int. Conf. on Robotics and Automation 2001.Google Scholar
    30. Shoemake, K. 1985. Animating rotation with quaternion curves. In Proc. of ACM SIGGRAPH 1985, 245–254. Google ScholarDigital Library
    31. Sifakis, E., and Barbič, J. 2012. FEM simulation of 3D deformable solids: A practitioner’s guide to theory, discretization and model reduction. In SIGGRAPH 2012 Course Notes. Google ScholarDigital Library
    32. Sifakis, E., Neverov, I., and Fedkiw, R. 2005. Automatic determination of facial muscle activations from sparse motion capture marker data. ACM Trans. on Graphics (SIGGRAPH 2005) 24, 3, 417–425. Google ScholarDigital Library
    33. Stomakhin, A., Howes, R., Schroeder, C., and Teran, J. M. 2012. Energetically consistent invertible elasticity. In Symp. on Computer Animation (SCA), 25–32. Google ScholarDigital Library
    34. Sussman, T., and Bathe, K.-J. 2009. A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension–compression test data. Communications in Numerical Methods in Engineering 25, 1, 53–63.Google ScholarCross Ref
    35. Talbot, H., Marchesseau, S., Duriez, C., Sermesant, M., Cotin, S., and Delingette, H. 2013. Towards an interactive electromechanical model of the heart. Interface focus 3, 2, 20120091.Google Scholar
    36. Ten Thije, R., Akkerman, R., and Huétink, J. 2007. Large deformation simulation of anisotropic material using an updated lagrangian finite element method. Computer methods in applied mechanics and engineering 196, 33, 3141–3150.Google Scholar
    37. Teran, J., Blemker, S., Hing, V. N. T., and Fedkiw, R. 2003. Finite volume methods for the simulation of skeletal muscle. In Symp. on Computer Animation (SCA), 68–74. Google ScholarDigital Library
    38. Teran, J., Sifakis, E., Irving, G., and Fedkiw, R. 2005. Robust Quasistatic Finite Elements and Flesh Simulation. In Symp. on Computer Animation (SCA), 181–190. Google ScholarDigital Library
    39. Thomaszewski, B., Pabst, S., and Strasser, W. 2009. Continuum-based strain limiting. Computer Graphics Forum (Eurographics 2009) 28, 2, 569–576.Google Scholar
    40. Twigg, C., and Kačić-Alesić, Z. 2010. Point cloud glue: constraining simulations using the procrustes transform. In Symp. on Computer Animation (SCA), 45–54. Google ScholarDigital Library
    41. Valanis, K., and Landel, R. 1967. The strain-energy function of a hyperelastic material in terms of the extension ratios. Journal of Applied Physics 38, 7, 2997–3002.Google ScholarCross Ref
    42. Wang, H., O’Brien, J., and Ramamoorthi, R. 2010. Multi-resolution isotropic strain limiting. ACM Trans. on Graphics (SIGGRAPH Asia 2010) 29, 6, 156:1–156:10. Google ScholarDigital Library
    43. Wang, H., O’Brien, J. F., and Ramamoorthi, R. 2011. Data-driven elastic models for cloth: modeling and measurement. ACM Trans. on Graphics (SIGGRAPH 2011) 30, 4, 71:1–71:11. Google ScholarDigital Library


ACM Digital Library Publication:



Overview Page: