Abstract
The partial differential equation (PDE) is often the tool of choice for describing the behavior of complicated fluid or solid mechanical systems. Sometimes, however, mechanical systems are composed of physically distinct elements that are not so large in number that a continuum description of the entire system is feasible or possible, or, although large in number, cannot be linked to macroscopic behavior through presently known constitutive laws. If interaction forces between individual elements are known or can be estimated and modeled, then the behavior of these elements or “particles” can be studied by solving the Newtonian equations of motion for each particle in the group simultaneously. This method (Cundall and Strack, 1979; Walton, 1983), variously called the distinct element method (DEM) or the particle dynamics method (PDM), is one example of several approaches that seek to follow the motion of selected “elementary” mechanical entities composing a larger system, and constitutes one approach to what we call here “discrete mechanics.” The purpose of this chapter is not to review the field of discrete mechanics, but to address in an eclectic way issues and problems arising in the implementation and application of these methods. For reviews see the articles by Campbell (1990) and by Cundall and Hart (1989).
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Haff, P.K. (1994). Discrete Mechanics. In: Mehta, A. (eds) Granular Matter. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4290-1_5
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DOI: https://doi.org/10.1007/978-1-4612-4290-1_5
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