“Drucker-prager elastoplasticity for sand animation” by Klár, Gast, Tampubolon, Fu, Schroeder, et al. …

  • ©Gergely Klár, Theodore Gast, Andre Pradhana Tampubolon, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran

Conference:


Type:


Title:

    Drucker-prager elastoplasticity for sand animation

Session/Category Title:   PHYSICAL PHENOMENA


Presenter(s)/Author(s):


Moderator(s):



Abstract:


    We simulate sand dynamics using an elastoplastic, continuum assumption. We demonstrate that the Drucker-Prager plastic flow model combined with a Hencky-strain-based hyperelasticity accurately recreates a wide range of visual sand phenomena with moderate computational expense. We use the Material Point Method (MPM) to discretize the governing equations for its natural treatment of contact, topological change and history dependent constitutive relations. The Drucker-Prager model naturally represents the frictional relation between shear and normal stresses through a yield stress criterion. We develop a stress projection algorithm used for enforcing this condition with a non-associative flow rule that works naturally with both implicit and explicit time integration. We demonstrate the efficacy of our approach on examples undergoing large deformation, collisions and topological changes necessary for producing modern visual effects.

References:


    1. Alduán, I., and Otaduy, M. 2011. SPH granular flow with friction and cohesion. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, 25–32. Google ScholarDigital Library
    2. Alduán, I., Tena, A., and Otaduy, M. 2009. Simulation of high-resolution granular media. In Proc Cong Español Inf Graf.Google Scholar
    3. Bardenhagen, S., Brackbill, J., and Sulsky, D. 2000. The material-point method for granular materials. Comp Meth App Mech Eng 187, 3-4, 529–541.Google ScholarCross Ref
    4. Bell, N., Yu, Y., and Mucha, P. 2005. Particle-based simulation of granular materials. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, 77–86. Google ScholarDigital Library
    5. Bonet, J., and Wood, R. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.Google Scholar
    6. Chanclou, B., Luciani, A., and Habibi, A. 1996. Physical models of loose soils dynamically marked by a moving object. In Comp Anim, 27–35. Google ScholarDigital Library
    7. Chang, Y., Bao, K., Zhu, J., and Wu, E. 2012. A particle-based method for granular flow simulation. Sci China Inf Sci 55, 5, 1062–1072.Google ScholarCross Ref
    8. Chen, P., and Wong, S. 2013. Real-time auto stylized sand art drawing. In CAD Comp Graph, 439–440. Google ScholarDigital Library
    9. Cummins, S., and Brackbill, J. 2002. An implicit particle-in-cell method for granular materials. J Comp Phys 180, 2, 506–548. Google ScholarDigital Library
    10. Drucker, D., and Prager, W. 1952. Soil mechanics and plasticity analysis or limit design. Quart App Math 10, 157–165.Google ScholarCross Ref
    11. Gast, T., Schroeder, C., Stomakhin, A., Jiang, C., and Teran, J. 2015. Optimization integrator for large time steps. IEEE Trans Vis Comp Graph 21, 10, 1103–1115. Google ScholarDigital Library
    12. Gonzalez, O., and Stuart, A. 2008. A first course in continuum mechanics. Cambridge University Press.Google Scholar
    13. Ihmsen, M., Wahl, A., and Teschner, M. 2013. A lagrangian framework for simulating granular material with high detail. Comp Graph 37, 7, 800–808. Google ScholarDigital Library
    14. Jaeger, H., Nagel, S., and Behringer, R. 1996. Granular solids, liquids, and gases. Rev Mod Phys 68, 1259–1273.Google ScholarCross Ref
    15. Jiang, C., Schroeder, C., Selle, A., Teran, J., and Stomakhin, A. 2015. The affine particle-in-cell method. ACM Trans Graph 34, 4, 51:1–51:10. Google ScholarDigital Library
    16. Jiang, C. 2015. The material point method for the physics-based simulation of solids and fluids. PhD thesis, University of California, Los Angeles.Google Scholar
    17. Klár, G., Gast, T., Pradhana, A., Fu, C., Schroeder, C., Jiang, C., and Teran, J. 2016. Drucker-prager elastoplasticity for sand animation: Supplementary technical document. ACM Trans Graph. Google ScholarDigital Library
    18. Lenaerts, T., and Dutré, P. 2009. Mixing fluids and granular materials. Comp Graph Forum 28, 2, 213–218.Google ScholarCross Ref
    19. Li, X., and Moshell, J. 1993. Modeling soil: realtime dynamic models for soil slippage and manipulation. In Proc SIGGRAPH, 361–368. Google ScholarDigital Library
    20. Luciani, A., Habibi, A., and Manzotti, E. 1995. A multi-scale physical model of granular materials. In Proc Graph Int, 136–146.Google Scholar
    21. Macklin, M., Müller, M., Chentanez, N., and Kim, T. 2014. Unified particle physics for real-time applications. ACM Trans Graph 33, 4, 153:1–153:12. Google ScholarDigital Library
    22. Mast, C., Arduino, P., Mackenzie-Helnwein, P., and Miller, R. 2014. Simulating granular column collapse using the material point method. Acta Geotech 10, 1, 101–116.Google ScholarCross Ref
    23. Mast, C. 2013. Modeling landslide-induced flow interactions with structures using the Material Point Method. PhD thesis.Google Scholar
    24. Mazhar, H., Heyn, T., Negrut, D., and Tasora, A. 2015. Using Nesterov’s method to accelerate multibody dynamics with friction and contact. ACM Trans Graph 34, 3, 32:1–32:14. Google ScholarDigital Library
    25. Milenkovic, V. 1996. Position-based physics: simulating the motion of many highly interacting spheres and polyhedra. In Proc SIGGRAPH, 129–136. Google ScholarDigital Library
    26. Miller, G., and Pearce, A. 1989. Globular dynamics: a connected particle system for animating viscous fluids. Comp Graph 13, 3, 305–309.Google ScholarCross Ref
    27. Narain, R., Golas, A., and Lin, M. 2010. Free-flowing granular materials with two-way solid coupling. ACM Trans Graph 29, 6, 173:1–173:10. Google ScholarDigital Library
    28. Nkulikiyimfura, D., Kim, J., and Kim, H. 2012. A real-time sand simulation using a GPU. In Comp Tech Inf Man, vol. 1, 495–498.Google Scholar
    29. Nocedal, J., and Wright, S. 2006. Numerical Optimization. Springer series in operations research and financial engineering. Springer.Google Scholar
    30. Onoue, K., and Nishita, T. 2003. Virtual sandbox. In Proc Pac Conf Comp Graph App, 252–262. Google ScholarDigital Library
    31. Pla-Castells, M., Garcia-Fernandez, I., and Martinez, R. 2006. Interactive terrain simulation and force distribution models in sand piles. In Cellular Automata, vol. 4173 of Lecture Notes Comp Sci. 392–401. Google ScholarDigital Library
    32. Ram, D., Gast, T., Jiang, C., Schroeder, C., Stomakhin, A., Teran, J., and Kavehpour, P. 2015. A material point method for viscoelastic fluids, foams and sponges. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, 157–163. Google ScholarDigital Library
    33. Steffen, M., Kirby, R. M., and Berzins, M. 2008. Analysis and reduction of quadrature errors in the material point method (MPM). Int J Numer Meth Eng 76, 6, 922–948.Google ScholarCross Ref
    34. Stomakhin, A., Schroeder, C., Chai, L., Teran, J., and Selle, A. 2013. A material point method for snow simulation. ACM Trans Graph 32, 4, 102:1–102:10. Google ScholarDigital Library
    35. Stomakhin, A., Schroeder, C., Jiang, C., Chai, L., Teran, J., and Selle, A. 2014. Augmented MPM for phase-change and varied materials. ACM Trans Graph 33, 4, 138:1–138:11. Google ScholarDigital Library
    36. Sulsky, D., Chen, Z., and Schreyer, H. L. 1994. A particle method for history-dependent materials. Comp Meth in App Mech Eng 118, 1, 179–196.Google ScholarCross Ref
    37. Sumner, R., O’Brien, J., and Hodgins, J. 1999. Animating sand, mud and snow. Comp Graph Forum 18, 1, 17–26.Google ScholarCross Ref
    38. Yasuda, R., Harada, T., and Kawaguchi, Y. 2008. Realtime simulation of granular materials using graphics hardware. In Comp Graph Imag Vis, 28–31. Google ScholarDigital Library
    39. Yoshioka, N. 2003. A sandpile experiment and its implications for self-organized criticality and characteristic earthquake. Earth, planets and space 55, 6, 283–289.Google Scholar
    40. Yue, Y., Smith, B., Batty, C., Zheng, C., and Grinspun, E. 2015. Continuum foam: a material point method for shear-dependent flows. ACM Trans Graph 34, 5, 160:1–160:20. Google ScholarDigital Library
    41. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. ACM Trans Graph 24, 3, 965–972. Google ScholarDigital Library


ACM Digital Library Publication:



Overview Page: