1. Jiang, C., Gast, T., and Teran, J. 2017. Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact. ACM Trans. Graph. 36, 4.

    The typical elastic surface or curve simulation method takes a Lagrangian approach and consists of three components: time integration, collision detection and collision response. The Lagrangian view is beneficial because it naturally allows for tracking of the codimensional manifold, however collision must then be detected and resolved separately. Eulerian methods are promising alternatives because collision processing is automatic and while this is effective for volumetric objects, advection of a codimensional manifold is too inaccurate in practice. We propose a novel hybrid Lagrangian/Eulerian approach that preserves the best aspects of both views. Similar to the Drucker-Prager and Mohr-Coulomb models for granular materials, we define our collision response with a novel elastoplastic constitutive model. To achieve this, we design an anisotropic hyperelastic constitutive model that separately characterizes the response to manifold strain as well as shearing and compression in the directions orthogonal to the manifold. We discretize the model with the Material Point Method and a novel codimensional Lagrangian/Eulerian update of the deformation gradient. Collision intensive scenarios with millions of degrees of freedom require only a few minutes per frame and examples with up to one million degrees of freedom run in less than thirty seconds per frame.

    @article{Jiang_SIGGRAPH_2017,
      author = {Jiang, Chenfanfu and Gast, Theodore and Teran, Joseph},
      title = {Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact},
      journal = {ACM Trans. Graph.},
      issue_date = {July 2017},
      volume = {36},
      number = {4},
      month = jul,
      year = {2017},
      articleno = {152},
      numpages = {14},
      url = {http://doi.acm.org/10.1145/3072959.3073623},
      doi = {10.1145/3072959.3073623},
      acmid = {3073623},
      publisher = {ACM},
      address = {New York, NY, USA},
      video = {https://www.youtube.com/watch?v=eGtB0VXJsuI}
    }
    
  2. Pradhana Tampubolon, A., Gast, T., Klár, G., et al. 2017. Multi-species simulation of porous sand and water mixtures. ACM Trans. Graph. 36, 4.

    We present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use a two-grid Material Point Method to discretize the governing equations. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop an improved return mapping for sand plasticity that prevents volume gain artifacts in the traditional Drucker-Prager model.

    @article{Tampubolon_SIGGRAPH_2017,
      author = {Pradhana Tampubolon, Andre and Gast, Theodore and Kl\'{a}r, Gergely and Fu, Chuyuan and Teran, Joseph and Jiang, Chenfanfu and Museth, Ken},
      title = {Multi-species simulation of porous sand and water mixtures},
      journal = {ACM Trans. Graph.},
      issue_date = {July 2017},
      volume = {36},
      number = {4},
      month = jul,
      year = {2017},
      articleno = {105},
      numpages = {11},
      url = {http://doi.acm.org/10.1145/3072959.3073651},
      doi = {10.1145/3072959.3073651},
      acmid = {3073651},
      publisher = {ACM},
      address = {New York, NY, USA},
      video = {https://www.youtube.com/watch?v=HDjV4DOIq0E}
    }
    
  3. Klár, G., Gast, T., Pradhana, A., et al. 2016. Drucker-prager Elastoplasticity for Sand Animation. ACM Trans. Graph. 35, 4, 103:1–103:12.

    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.

    @article{Klar_SIGGRAPH_2016,
      author = {Kl\'{a}r, Gergely and Gast, Theodore and Pradhana, Andre and Fu, Chuyuan and Schroeder, Craig and Jiang, Chenfanfu and Teran, Joseph},
      title = {Drucker-prager Elastoplasticity for Sand Animation},
      journal = {ACM Trans. Graph.},
      issue_date = {July 2016},
      volume = {35},
      number = {4},
      month = jul,
      year = {2016},
      issn = {0730-0301},
      pages = {103:1--103:12},
      articleno = {103},
      numpages = {12},
      url = {http://doi.acm.org/10.1145/2897824.2925906},
      doi = {10.1145/2897824.2925906},
      acmid = {2925906},
      publisher = {ACM},
      address = {New York, NY, USA},
      video = {https://www.youtube.com/watch?v=Bqme4WWuIVQ}
    }
    
  4. Ram, D., Gast, T., Jiang, C., et al. 2015. A Material Point Method for Viscoelastic Fluids, Foams and Sponges. Proceedings of the 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation, ACM, 157–163.

    We present a new Material Point Method (MPM) for simulating viscoelastic fluids, foams and sponges. We design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd-B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). Lastly, we show that implicit time stepping can be achieved in a manner similar to [Stomakhin et al. 2013] and that this allows for high resolution simulations at practical simulation times.

    @inproceedings{Ram_SCA_2015,
      author = {Ram, Daniel and Gast, Theodore and Jiang, Chenfanfu and Schroeder, Craig and Stomakhin, Alexey and Teran, Joseph and Kavehpour, Pirouz},
      title = {A Material Point Method for Viscoelastic Fluids, Foams and Sponges},
      booktitle = {Proceedings of the 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation},
      series = {SCA '15},
      year = {2015},
      isbn = {978-1-4503-3496-9},
      location = {Los Angeles, California},
      pages = {157--163},
      numpages = {7},
      url = {http://doi.acm.org/10.1145/2786784.2786798},
      doi = {10.1145/2786784.2786798},
      acmid = {2786798},
      publisher = {ACM},
      address = {New York, NY, USA},
      video = {https://www.youtube.com/embed/nXck0xs7oyw}
    }
    
  5. Gast, T.F., Schroeder, C., Stomakhin, A., Jiang, C., and Teran, J.M. 2015. Optimization Integrator for Large Time Steps. Visualization and Computer Graphics, IEEE Transactions on 21, 10, 1103–1115.

    Practical time steps in today’s state-of-the-art simulators typically rely on Newton’s method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. We show that recasting backward Euler as a minimization problem allows Newton’s method to be stabilized by standard optimization techniques with some novel improvements of our own. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. We show how simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. We also present novel penalty collision formulations for self collisions and collisions against scripted bodies designed for the unique demands of this solver. Finally, we show that these techniques improve the behavior of Material Point Method (MPM) simulations by recasting it as an optimization problem.

    @article{Gast_TVCG_2015,
      author = {Gast, T.F. and Schroeder, C. and Stomakhin, A. and Jiang, Chenfanfu and Teran, J.M.},
      journal = {Visualization and Computer Graphics, IEEE Transactions on},
      title = {Optimization Integrator for Large Time Steps},
      year = {2015},
      volume = {21},
      number = {10},
      pages = {1103-1115},
      doi = {10.1109/TVCG.2015.2459687},
      issn = {1077-2626},
      month = oct,
      video = {https://www.youtube.com/embed/f3F20tRs-tU}
    }
    
  6. Gast, T.F. and Schroeder, C. 2014. Optimization Integrator for Large Time Steps. Eurographics/ACM SIGGRAPH Symposium on Computer Animation, Eurographics Association.
    [Best Paper Honorable Mention]

    Practical time steps in today’s state-of-the-art simulators typically rely on Newton’s method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. We show that recasting backward Euler as a minimization problem allows Newton’s method to be stabilized by standard optimization techniques with some novel improvements of our own. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. We show how simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. We also present novel penalty collision formulations for self collisions and collisions against scripted bodies designed for the unique demands of this solver.

    @inproceedings{Gast_SCA_2014,
      title = {Optimization Integrator for Large Time Steps},
      author = {Gast, Theodore F. and Schroeder, Craig},
      booktitle = {Eurographics/ACM SIGGRAPH Symposium on Computer Animation},
      year = {2014},
      address = {Copenhagen, Denmark},
      publisher = {Eurographics Association},
      url = {http://diglib.eg.org/EG/DL/WS/SCA/SCA14/031-040.pdf},
      doi = {10.2312/sca.20141120},
      note = {Best Paper Honorable Mention},
      video = {https://www.youtube.com/embed/oFItQtbqSe0}
    }