Abstract
The central problem of devising mathematical models of granular materials is how to define a granular medium as a continuum. This paper outlines the elements of a theory that could be incorporated in discrete models such as the Discrete-Element Method, without recourse to a continuum description. It is shown that familiar concepts from continuum mechanics such as stress and strain can be defined for interacting discrete quantities. Established concepts for constitutive equations can likewise be applied to discrete quantities. The key problem is how to define the constitutive response in terms of truncated strain measures that are a practical necessity for analysis of large granular systems.
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Peters, J.F. Some fundamental aspects of the continuumization problem in granular media. J Eng Math 52, 231–250 (2005). https://doi.org/10.1007/BF02694039
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DOI: https://doi.org/10.1007/BF02694039