In the ninetys, I developped SDEC, a code using the Discrete Element Method. This code is based on a newtonian approach which uses rigid bodies. These elements are described in terms of their mass, volume and their interactions. The code herein uses spherical elements. Two elements may be considered as interacting while not touching. Any element within an interaction range of another element defined as a radius around this element will be interacting with the latter. The interactions are known as "soft sphere" interactions because the interaction forces are linked to the displacements of the elements which implies that the elements may penetrate or overlap one another.

Newton's second law of motion describes the motion of each element as the sum of all forces  applied on this element.The dynamic behavior of the system is solved numerically by a time  algorithm in which the velocities and the accelerations are constant at each time step. The system evolves and an explicit finite difference algorithm is used to reproduce this  evolution.

Until now,  this code has been used to study geomechanical problems in both quasi-static and dynamical applications.

The ultimate Discrete Element Sofware : YADE

Yade is an extensible open-source framework for discrete numerical models, focused on Discrete Element Method. The project started as an offspring from SDEC during Olivier Galizzi's Phd thesis and major additional contributions were made by Janek Kozicki and Vaclav Smilauer. It is now being developed at multiple research institutes and has active and helpful user community.

The computation parts are written in c++ using flexible object model, allowing independent implementation of new alogrithms, interfaces with other software packages (e.g. flow simulation), data import/export routines. Python can be used to create and manipulate the simulation or for postprocessing.

Bruno Chareyre and Anton Gladky are currently leading the project.

It is a free software with a GPL open source licence.  You can down load this software at the following address :

http://yade.wikia.com/wiki/Yade

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From: Kozicki, J. & F.V. Donze, YADE-OPEN DEM: an open--source software using a discrete element method to simulate granular material, Engineering Computations, 26(7), pp. 786-805, 2009.

Purpose - Develop an open source software based on the Discrete Element Method and using object oriented programming techniques. The paper describes the software arhitecture.

Design/methodolgy/approach - The DEM chosen uses position, orientation, velocity and angular velocity as independent variables of simulated particles which are subject to explicit leapfrog time–integration scheme (Lagrangian method).  The three–dimensional dynamics equations based on the classical Newtonian approach for the second law of motion are used. The track of forces and moments acting on each particle is kept at every time–step.  Contact forces depend on the particle geometry overlap and material properties. The normal, tangential and moment components of interaction force are included.
Findings - An effort has been undertaken to extract the underlying object oriented abstractions in the Discrete Element Method. These abstractions were implemented in C++, conform to object oriented design principles and use design patterns. Based on that, a software framework was developed in which the abstractions provide the interface where the modelling methods can be plugged–in.

Originality/value - The resulting YADE-OPEN DEM framework is designed in a generic way which provides great flexibility when adding new scientific simulation code. Some of the advantages are that numerous simulation methods can be coupled within the same framework while plug–ins can import data from other software.  In addition, this promotes code improvement through open source development and allows feedback from the community. However implementing such models requires that one adheres to the framework design and the YADE framework is a new emerging software.To download the software see http://yade.wikia.com webpage.

Other references -

• Kozicki, J. & F.V. Donze, Applying an open--source software for numerical simulations using finite element or discrete modelling methods. Computer Methods in Applied Mechanics and Engineering, 197(49-50), pp. 4429-4443, 2008
• Smilauer, V., E. Catalano, B. Chareyre, S. Dorofeenko, J. Duriez, A. Gladky, J. Kozicki, C. Modenese, L. Scholtes, L. Sibille, J. Stransky, and K. Thoeni, Yade Documentation (V. Šmilauer, ed.), The Yade Project, 1st ed., 2010. http://yade-dem.org/doc/.