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I am doing a project on some properties of granular materials. I might have to face people who ask the definition of granular material. How can we define granular materials? One answer is "it is sand-like materials," which is true but not enough. Wikipedia gives lower limit for a material size to accept it as granular as 1 micro meter. And there is no upper limit. Is that true? What ever people are not satisfied with these definitions how should we define them?

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    $\begingroup$ I would think a granular material is one containing particles too large to satisfy the continuum assumption and too small (i.e., too numerous) to be worth characterizing individually when analyzing the system through constitutive equations. $\endgroup$ Jan 11 '18 at 19:08
  • $\begingroup$ Thanks...it is clear Then it is significant ony when large number is present.isn't it?.then is it necessary to specify how much large number.can we define an accurate boundary. I think it is not needed,but people often ask for clarification. What should i say them? $\endgroup$
    – fahd
    Jan 13 '18 at 4:57
  • $\begingroup$ You could tell them that the system size criterion is subjective. If you don't have the computational power to model the stresses, orientation, and displacement of each particle, then you need the constitutive equations for a granular material. $\endgroup$ Jan 13 '18 at 20:18
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Granular materials (GM) are primarily defined as being athermal - thermal fluctuations/energies are negligible compared with grain-grain or grain-environment interaction energies - disordered, and dissipative (frictional effects, coefficient of restitution for collisions).

Consider a sand grain (about 1 mm in diameter), and estimate the gravitational potential energy associated with lifting the grain by 1 diameter. Compare with kT at room temperature and you'll see that the thermal energy is comparatively negligible - typical statistical mechanics approaches cannot be used to characterize these systems, which is why they are so interesting and still a relatively young field. The lower limit you present (microns) makes sense for typical particle densities, but of primary importance is the mass, not just the size. Obviously, though, the concept of a granular "material" makes the most sense when you have a collection of these bodies, not a single classical grain.

A description of these ideas can be found in the first chapter of Granular Media: Between fluid and solid (B. Andreotti, Y. Forterre, and O. Pouliquen).

An idea I haven't found in the literature or GM textbooks: An upper limit on size may be the size scale at which contact repulsion (which primarily characterizes grain-grain interactions) is no longer dominant. If a bunch of terrestrial planets were placed in a compression cell, for instance, their mutual attraction might be so strong as to cause attraction and elastic deformations even without applied a pressure or shear stress. (I don't know if planets are actually massive enough for this, haven't done this computation.) In fact, they would be in a "jammed" (solid) state because attractive interactions would dominate. I have not seen this idea presented in the literature or textbooks, but it seems reasonable to me. With some simple calculations one could estimate the crossover from contact-repulsion dominance to attraction-dominance and see where the transitional size scale lays - maybe at the planetary size, maybe not.

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The first line of An Introduction to Granular Flow by K. Kesava Rao and Prabhu R. Nott (2008):

A granular material is a collection of solid particles or grains, such that most of the particles are in contact with at least some of their neighboring particles.

A good way to get a definition is to look for a textbook on the subject.

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