Comparison with Other Methods

Some common questions asked about 3DEC are: Is 3DEC a distinct element or discrete element program? What is the difference, and what is 3DEC ’s relation to other programs? We provide a definition here which we hope will clarify these matters.

Many finite element, boundary element and Lagrangian finite difference programs have interface elements or “slide lines” that enable them to model a discontinuous material to some extent. However, their formulation is usually restricted in one or more of the followingways: first, the logic may break down when many intersecting interfaces are used; second, there may not be an automatic scheme for recognizing new contacts; and third, the formulation may be limited to small displacements and/or rotation. Such programs are usually adapted from existing continuum programs.

The name discrete element method applies to a computer program only if it:

1. allows finite displacements and rotations of discrete bodies, including complete detachment; and
2. recognizes new contacts automatically as the calculation progresses.

Without the first attribute, a program cannot reproduce some important mechanisms in a discontinuous medium; without the second, the program is limited to small numbers of bodies for which the interactions are known in advance. The term distinct element method was coined by Cundall and Strack (1979) to refer to the particular discrete-element scheme that uses deformable contacts and an explicit, time-domain solution of the original equations of motion (not the transformed, modal equations).

There are four main classes of computer programs that conform to the proposed definition of a discrete element method. (The classes and representative programs are discussed further in Section 1.1.1 in Theory and Background.)

1. Distinct Element Programs – These programs use explicit time-marching to solve the equations of motion directly. Bodies may be rigid or deformable (by subdivision into elements); contacts are deformable. 3DEC falls into this category.
2. Modal Methods – The method is similar to the distinct element method in the case of rigid bodies, but for deformable bodies modal superposition is used.
3. Discontinuous Deformation Analysis – Contacts are rigid, and bodies may be rigid or deformable. The condition of no-interpenetration is achieved by an iteration scheme; the body deformability comes from superposition of strain modes.
4. Momentum-Exchange Methods – Both the contacts and the bodies are rigid: momentum is exchanged between two contacting bodies during an instantaneous collision. Frictional sliding can be represented.

There are several published schemes that appear to resemble discrete element methods but are different in character, or are lacking one or more essential ingredients. For example, many publications are concerned with the stability of one or more rigid bodies, using the limit equilibrium method (Hoek (1973); Warburton (1981); Goodman and Shi (1985); Lin and Fairhurst (1988)). This method computes the static force equilibrium of the bodies, and does not address the changes in force distribution that accompany displacements of the bodies.