Title: Simulation of Granular Flow using the Material Point Method

Author (Talk): Sachith Dunatunga, MIT

Abstract:

While granular flows are common in everyday life, several factors complicate the numerical simulation of such a flow. Viewed as a bulk continuum, the elastic stress-strain relation is nonlinear and the total deformation requires plasticity to properly describe. Traditional solvers for solids (e.g. finite element) do not work well with the large plastic deformations involved in flow due to mesh distortion issues, whereas the elastic part of the constitutive relation presents a challenge for fluid solvers (e.g. finite volume, finite difference). The discrete element method -- which is preferred for granular flow -- treats grains as individual particles and considers interactions between them, but is too computationally intensive to be practical for even medium-scale problems. The material point method (MPM) is a recent development in mesh-free computational methods aimed at solids that seeks to combine the strengths of DEM and FEM. To this end, MPM uses mobile ``material points'' to capture the state of the system. These are not grains, but rather a representation of the continuum at certain points. At every time increment, data from these material points is projected onto a background computational domain. The equations of motion are solved on this domain, and the information is then projected back onto the material points, which updates other material quantities such as stress and strain through a constitutive relation. We have implemented a basic MPM solver for 2D problems. We investigated the usage of second order elements to improve accuracy, particularly in the stress calculation. Although second order elements do provide more accurate results when material points are favorably distributed, integration errors from failing to consider the volumetric extent of a particle can result in substantial loss of accuracy and even instability. First order elements are theoretically less accurate, but do not become unstable for this reason. Using first order elements and a Drucker-Prager based constitutive model, we show that results from simulations, such as collapse of a sand pile and discharge of a silo, produce the physically expected behavior even when the strains become extremely large. We are currently exploring methods to simulate moving boundaries, as in indentation, in the context of MPM, as well as adding capabilities to our code such as refinement of the background domain. In addition, we are investigating implementation of different material models, such as critical state theory and non-local material models, many of which involve solving a diffusion-like set of equations coupled with the original equations of motion.