1. 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}
    }
    
  2. 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}
    }
    
  3. 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}
    }