Physical systems comprised of discrete, macroscopic particles or grains which are not bonded to one another are important in civil, chemical, and agricultural engineering, as well as in natural geological and planetary environments. Granular systems are observed in rock slides, sand dunes, clastic sediments, snow avalanches, and planetary rings. In engineering and industry they are found in connection with the processing of cereal grains, coal, gravel, oil shale, and powders, and are well known to pose important problems associated with the movement of sediments by streams, rivers, waves, and the wind.
The standard approach to the theoretical modelling of multiparticle systems in physics has been to treat the system as a continuum and to formulate the model in terms of differential equations. As an example, the science of soil mechanics has traditionally focussed mainly on quasi-static granular systems, a prime objective being to define and predict the conditions under which failure of the granular soil system will occur. Soil mechanics is a macroscopic continuum model requiring an explicit constitutive law relating, for example, stress and strain. While very successful for the low-strain quasi-static applications for which it is intended, it is not clear how it can be generalized to deal with the high-strain, explicitly time-dependent phenomena which characterize a great many other granular systems of interest. Attempts at obtaining a generalized theory of granular systems using a differential equation formalism [Johnson:87a] have met with limited success.
An alternate approach to formulating physical theories can be found in the concept of cellular automata , which was first proposed by Von Neumann in 1948. In this approach, the space of a physical problem would be divided up into many small, identical cells each of which would be in one of a finite number of states. The state of a cell would evolve according to a rule that is both local (involves only the cell itself and nearby cells) and universal (all cells are updated simultaneously using the same rule).
The Lattice Grain Model [Gutt:89a] (LGrM) we discuss here is a microscopic, explicitly time-dependent, cellular automata model, and can be applied naturally to high-strain events. LGrM carries some attributes of both particle dynamics models [Cundall:79a], [Haff:87a;87b], [Walton:84a], [Werner:87a] (PDM), which are based explicitly on Newton's second law, and lattice gas models [Frisch:86a], [Margolis:86a] (LGM), in that its fundamental element is a discrete particle, but differs from these substantially in detail. Here we describe the essential features of LGrM, compare the model with both PDM and LGM, and finally discuss some applications.