A study of fragmentation processes using a discrete element method

We present a model of solids made from polygonal cells connected via beams. We calculate the macroscopic elastic moduli from the beam and cell parameters. This modellisation is particularly suited for the simulation of fragmentation processes. We study the effects of an explosion inside a circular disk and the impact of a projectile and obtain the fragment size distribution. We find that if breaking only happens under tensile forces a layer on the free wall opposed to impact is first ejected. In that case the distribution follows a power-law with an exponent that in most cases is around two.Comment: 16 pages in LaTex format, 17 PostScript figures. Figures are available upon request from the authors. Submitted to Int. J. of Mod. Phys.

A discrete element method representation of an anisotropic elastic continuum

A method for modeling cubically anisotropic elasticity within the discrete element method is presented. The discrete element method (DEM) is an approach originally intended for modeling granular materials (sand, soil, and powders); however, recent developments have usefully extended it to model stochastic mechanical processes in monolithic solids which, to date, have been assumed to be elastically isotropic. The method presented here for efficiently capturing cubic elasticity in DEM is an important prerequisite for further extending DEM to capture the influence of elastic anisotropy on the mechanical response of polycrystals, composites, etc. The system demonstrated here uses a directionally assigned stiffness in the bonds between adjacent elements and includes separate schemes for achieving anisotropy with Zener ratios greater and smaller than one. The model framework is presented along with an analysis of the accessible space of elastic properties that can be modeled and an artificial neural network interpolation scheme for mapping input parameters to model elastic behavior

Analysis of Sample Acquisition Dynamics Using Discrete Element Method

The analysis presented in this paper is conducted in the framework of the Ocean Worlds Autonomy Testbed for Exploration Research and Simulation (OceanWATERS) project, currently under development at NASA Ames Research Center. OceanWATERS aims at designing a simulation environment which allows for testing autonomy of scientific lander missions to the icy moons of our solar system. Mainly focused on reproducing the end effector interaction with the inherent terrain, this paper introduces a novel discrete element method (DEM)-based approach to determine forces and torques acting on the landers scoop during the sample acquisition process. An accurate force feedback from the terrain on the scoop is required by fault-detection and autonomous decision-making algorithms to identify when the requested torque on the robotic arms joints exceeds the maximum available torque. Knowledge of the terrain force feedback significantly helps evaluating the arms links structural properties and properly selecting actuators for the joints. Models available in literature constitute a partial representation of the dynamics of the interaction. As an example, Balovnev derived an analytical expression of the vertical and horizontal force acting on a bucket while collecting a sample as a function of its geometry and velocity, soil parameters and reached depth. Although the model represents an adequate approximation of the two force components, it ignores the direction orthogonal to the scoop motion and neglects the torque. This work relies on DEM analysis to compensate for analytical models deficiencies and inaccuracies, i. e. provide force and torque 3D vectors, defined in the moving reference (body) frame attached to the scoop, at each instant of the sample collection process. Results from the first presented analysis relate to the specific OceanWATERS sampling strategy, which consists of collecting the sample through five consecutive passes with increasing depth, each pass following the same circularlinear- circular trajectory. Data is collected given a specific scoop design interacting with two types of bulk materials, which may characterize the surface of icy planetary bodies: snow and ice. Although specifically concerned with the OceanWATERS design, this first analysis provides the expected force trends for similar sampling strategies and allows to deduce phenomenological information about the general scooping process. In order to further instruct the community on the use of DEM tools as a solution to the sampling collection problem, two more analyses have been carried out, mainly focused on reducing the DEM computation time, which increases with a decrease in particle size. After running a set of identical simulations, where the only changing parameter is the size of the spherical particle, it is observed that the resulting force trajectories, starting from a given particle size, converge to the true trend. It is deducible that a further decrease in size yields negligible improvements in the accuracy, while it sensibly increases computation time. A final analysis aims at discussing limitations of approximating bulk material particles having a complex shape, e. g. ice fragments, with spheres, by comparing force trends resulting in the two cases for the same simulation scenario

Application of discrete element method in agricultural engineering

Basic principle of discrete element method was summarized, and commonly used software and its characteristics were introduced. Application of discrete element method in tillage, planting, harvesting and other agricultural machinery R & D was reviewed. Typical examples of application of discrete element method in agricultural machinery research and design at home and abroad were discussed and analyzed. Application prospect and trend of discrete element method in the field of agricultural engineering were prospected, in order to provide reference for further development of modern agricultural equipment digital design

Girkmann problem with a Discrete Element Method

Cells of Voronoï are used as particles in the Discrete Element code CeaMka3D. This type of meshing does not leave geometrical space like that can be the case with spherical particles. This method has already been used successfully to simulate the propagation of seismic waves in a linear elastic medium in 2D or in 3D. In this paper, a specific axisymmetric formulation is presented. In a first part, the calculation of the volumetric deformation of a particle and the forces between particles are described. In a second part, the specific forces for the axisymmetric formulation are described. At last, this formulation is tested for the Girkmann problem. This axisymmetric benchmark has been presented in January 2008 by the International Association of Computational Mechanics (IACM) in order to test the singularity at the junction between shell and beam. The accuracy of the axisymmetric formulation for this Discrete Element Method is evaluated by this benchmark. The results of this Discrete Element Method are compared with others numerical methods

A discrete element method for polyhedral particles

The following paper presents a new approach for the Discrete Element Method (DEM) with polyhedral particles. The geometry of convex polyhedra is represented by a set of half spaces. An algorithm for contact detection for these particles is developed. Furthermore a model for the interaction forces of polyhedra in contact is suggested. The model includes elastic and damping forces in normal direction, as well as Coulomb friction in tangential direction. The feasibility of DEM with sharp edged particles is demonstrated by some engineering applications

Simulating Fractures with Bonded Discrete Element Method

Along with motion and deformation, fracture is a fundamental behaviour for solid materials, playing a critical role in physically-based animation. Many simulation methods including both continuum and discrete approaches have been used by the graphics community to animate fractures for various materials. However, compared with motion and deformation, fracture remains a challenging task for simulation, because the material's geometry, topology and mechanical states all undergo continuous (and sometimes chaotic) changes as fragmentation develops. Recognizing the discontinuous nature of fragmentation, we propose a discrete approach, namely the Bonded Discrete Element Method (BDEM), for fracture simulation. The research of BDEM in engineering has been growing rapidly in recent years, while its potential in graphics has not been explored. We also introduce several novel changes to BDEM to make it more suitable for animation design. Compared with other fracture simulation methods, the BDEM has some attractive benefits, e.g. efficient handling of multiple fractures, simple formulation and implementation, and good scaling consistency. But it also has some critical weaknesses, e.g. high computational cost, which demand further research. A number of examples are presented to demonstrate the pros and cons, which are then highlighted in the conclusion and discussion