A Semi-Implicit Material Point Method for the Continuum Simulation of Granular Materials
ACM Transactions on Graphics, July 2016 (Proceedings of the ACM SIGGRAPH 2016
Conference, to appear)
Abstract
We present a new continuum-based method for the realistic simulation
of large-scale free-flowing granular materials. We derive a compact
model for the rheology of the material, which accounts for the exact
nonsmooth Drucker-Prager yield criterion combined with a varying
volume fraction. Thanks to a semi-implicit time-stepping scheme and
a careful spatial discretization of our rheology built upon the
Material-Point Method, we are able to preserve at each time step the
exact coupling between normal and tangential stresses, in a stable
way. This contrasts with previous approaches which either regularize
or linearize the yield criterion for implicit integration, leading
to unrealistic behaviors or visible grid artifacts. Remarkably, our
discrete problem turns out to be very similar to the discrete
contact problem classically encountered in multibody dynamics, which
allows us to leverage robust and efficient nonsmooth solvers from
the literature. We validate our method by successfully capturing
typical macroscopic features of some classical experiments, such as
the discharge of a silo or the collapse of a granular column.
Finally, we show that our method can be easily extended to
accommodate more complex scenarios including two-way rigid body
coupling as well as anisotropic materials.
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Acknowledgments
We would like to thank Pierre-Yves Lagrée for his help in reviewing the literature on granular simulation, Rahul Narain for sharing his original code with us, as well as the anonymous reviewers for their insightful feedbacks.
This work was supported in part by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) funded by the French program Investissement d Avenir.