Continuum modelling and simulation of granular flows through their many phases

We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic flow rule given by the $\mu(I)$ inertial rheology of granular materials. When the free volume exceeds a critical level, the material is deemed to separate and is treated as disconnected, stress-free media. A Material Point Method (MPM) procedure is written for the simulation of this model and many demonstrations are provided in different geometries. By using the MPM framework, extremely large strains and nonlinear deformations, which are common in granular flows, are representable. The method is verified numerically and its physical predictions are validated against known results

Optimization of multistage systems with nondifferentiable objective functions.

This dissertation is aimed at a class of convex dynamic optimization problems in which the transition functions are twice continuously differentiable and the stagewise objective functions are convex, although not necessarily differentiable. Two basic descent algorithms which use sequential and parallel coordinating techniques are developed. In both algorithms the nondifferentiability of the objective function is accounted for by using subgradient information. The objective of the subproblems generated consists of successive piecewise linear approximations of the stagewise objective function and the value function. In the parallel algorithm, an incentive coordination method is used to coordinate the subproblems. We provide proofs of convergence for these algorithms. Two variations, namely, subgradient selection and subgradient aggregation, of the basic algorithms are also discussed. In practice while subgradient selection seems to perform well, computational results with subgradient aggregation are rather disappointing. Computational results of the basic algorithms and variants based on subgradient selection are given. The effect of number of stages on performance of these algorithms is compared with a general nonlinear programming package (NPSOL)

neocpp89/mpm-2d: Old but relatively stable version.

A 2D implementation of the Material Point Method and supporting code

A framework for continuum simulation of granular flow

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 119-124).Granular materials have eluded continuum modeling attempts for centuries. A significant chunk of the complexity lies in the trans-phase behavior of granular media; while the material has a yield stress and can therefore act as a solid body, grains may also flow quickly much like a liquid. At low pressures and high velocities, the grains may even become disconnected from each other, resulting in a gas-like state where the only stresses are essentially due to occasional collisions between grains. Moreover, all three states are commonly found simultaneously in many industrial and natural processes, and individual grains may switch between these phases readily. A further complication is that typically the grain size is large compared to the geometries in which we are interested; these size effects can lead to mispredictions when purely local models (without an intrinsic length scale) are used. Due to these complexities, a highly favored technique is the discrete element method, which tracks each grain individually and updates the forces and displacements when grains contact each other. While extremely accurate, discrete methods require incredible amounts of computational power, severely restricting the sizes of problems that can be simulated. Continuum techniques can potentially scale better, as individual grain-grain interactions are no longer tracked, but require a constitutive model. Recent continuum models, such as in Jop, Forterre, and Pouliquen (2006) and Kamrin and Koval (2012) show promise in capturing many observed phenomena, yet current numerical techniques limit the applicability of these models due to computational or numerical issues. In this thesis, we explore a continuum framework for simulation of granular materials in the context of the material point method, which allows us to test these material models further than many existing continuum techniques and pave the way for efficient simulation of large-scale processes involving granular media.by Sachith Anurudde Dunatunga.Ph. D

A nonlocal dense granular flow model implemented in the material point method

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2014.Cataloged from PDF version of thesis.Includes bibliographical references (pages 63-65).A nonlocal model for dense granular flow is implemented in the material point method (MPM), an extension of the finite element method (FEM) for solid mechanics. The nonlocal model used has shown great predictive capability for dense flows when implemented in the finite element framework, but limitations of FEM prevent application of the model to truly large scale, inhomogeneous deformations. We show that these FEM results may be replicated in the MPM framework through the solution of a vertical chute flow, and allows for future work utilizing the strengths of MPM for larger and more complex flows.by Sachith Anurudde Dunatunga.S.M

Continuum modeling of projectile impact and penetration in dry granular media

© 2016 Elsevier Ltd Modeling of impact into granular substrates is a topic of growing interest over the last decade. We present a fully continuum approach for this problem, which is shown to capture an array of experimentally observed behavior with regard to the intruder penetration dynamics as well as the flow and stress response of the granular media. The intruder is modeled as a stiff elastic body and the dry granular bulk is modeled using a ‘trans-phase’ constitutive relation. This relation has an elasto-viscoplastic response with pressure- and rate-sensitive yield behavior given by the μ(I) inertial rheology when the granular free volume is below a critical value. Above this critical value, the material is deemed to separate and is treated as a disconnected, stress-free medium. The Material Point Method is used to implement the impact problem numerically. Validations are conducted against a wide set of experimental data with a common granular material, which allows use of a single model calibration to test the agreement. In particular, continuum simulations of projectile impact with different shaped intruders and different impact energies show good agreement with experiments regarding of time-of-flight, penetration depth, and Poncelet drag force coefficients. Simultaneously, good agreement with experiments is found regarding the response of the granular media during impact, such as the pressure wave propagation process during the initial stage of impact, the flow fields that develop under the moving intruder, and the free-surface dynamics

Amplitude-dependent attenuation of compressive waves in curved granular crystals constrained by elastic guides

We study the wave propagation in a curved chain of spherical particles constrained by elastic guides under the axial impact of a falling mass. We characterize the force transmission properties of the chain by varying the striker’s mass and the chain’s curvature. Experimental tests demonstrate amplitude-dependent attenuation of compressive waves propagating through the curved chain. In particular, we observe that the curved systems present an improved transmission of small dynamic disturbances relative to that of strong excitations, resulting from the close interplay between the granular particles and the softer elastic medium. We also find that the transmission of the compressive waves through the chains is dependent on the initial curvature imposed to the system. Numerical simulations, based on an approach that combines discrete element and finite element methods, corroborate the experimental results. The findings suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of pressure amplitudes

A generative statistical model for tracking multiple smooth trajectories

We present a general model for tracking smooth trajec-tories of multiple targets in complex data sets, where tracks potentially cross each other many times. As the number of overlapping trajectories grows, exploiting smoothness be-comes increasingly important to disambiguate the associa-tion of successive points. However, in many important prob-lems an effective parametric model for the trajectories does not exist. Hence we propose modeling trajectories as in-dependent realizations of Gaussian processes with kernel functions which allow for arbitrary smooth motion. Our generative statistical model accounts for the data as com-ing from an unknown number of such processes, together with expectations for noise points and the probability that points are missing. For inference we compare two methods: A modified ver-sion of the Markov chain Monte Carlo data association (MCMCDA) method, and a Gibbs sampling method which is much simpler and faster, and gives better results by be-ing able to search the solution space more efficiently. In both cases, we compare our results against the smoothing provided by linear dynamical systems (LDS). We test our approach on videos of birds and fish, and on 82 image sequences of pollen tubes growing in a petri dish, each with up to 60 tubes with multiple crossings. We achieve 93 % accuracy on image sequences with up to ten trajectories (35 sequences) and 88 % accuracy when there are more than ten (42 sequences). This performance sur-passes that of using an LDS motion model, and far exceeds a simple heuristic tracker. 1