A local view on the role of friction and shape

Abstract

Abstract. Leibniz said "Naturam cognosci per analogiam": nature is understood by making analogies. This statement describes a seminal epistemological principle. But one has to be aware of its limitations: quantum mechanics for example at some point had to push Bohr's model of the atom aside to make progress. This article claims that the physics of granular packings has to move beyond the analogy of frictionless spheres, towards local models of contact formation.On earth solid assemblies of granular particles are by far the most frequent phase of granular matter; we encounter granular packings everywhere from our kitchen cabinet to civil engineering textbooks. In order to make their handling, transport, and storage more efficient, we strive for a theory that predicts their mechanical properties, such as shear and bulk modulus or yield stress, starting from a few state variables only. Efforts to develop such a theory often start by modeling granular packings as an assembly of frictionless spheres. This is a rather unsuitable starting point, for a number of reasons:1. All granular particles are frictional. 2. Frictional particles have lower isostatic numbers than frictionless particles. 3. Granular physics happens at volume fractions inaccessible to frictionless particles. 4. The volume fraction of soft particles can be changed by compression. The volume fraction of frictional particles is changed by changing their geometry. 5. Friction is one reason for history dependence in granular systems. 6. Real world granular media are rarely spherical.Shape adds complexity, e.g. to history dependence.These six theses are also the outline for the following sections. They are intended to provoke discussions with a sizeable subgroup of the theoretically or numerically working scientists. Many experimentalists, applied scientist, and engineers might find them, at least in part, well-known. For simplicity, we will discuss in the following only monodisperse spheres; except for section 6.

On the metrology of interparticle contacts in sand from x-ray tomography images

“…The partial results on contact detection and orientation of spherical particles might contribute to the field of granular physics where research focusses principally on rather perfectly rounded shapes, see e.g., [21]. However, little work has been done on natural, angular particles so far.…”

Viewing Earth’s surface as a soft-matter landscape

“…For simplicity here we consider jamming (unjamming) to be a rapid increase (decrease) in rigidity that is typically associated with an increase (decrease) in volume fraction φ toward (away from) a critical value φ c . The nature of this transition, however, is sensitive to particle contacts and interactions [123][124][125] and interparticle friction [126,127], factors that are important for geophysicallyrelevant properties such as dilatancy [128].…”

Structural similarity between dry and wet sphere packings

“…It is also noteworthy that the á ñ Z values of wet packings fluctuate more strongly from preparation to preparation than those of dry packings, in contrast to the á ñ B values which display a smoother increase with f g . Dry packings are hyperstatic, i.e.the contact forces provide more constraints than what is needed to fix all the degrees of freedom of the particles [61]. In absense of a dominating mechanical constraint, the dependence of á ñ Z on f g originates from geometrical effects such as volume exclusion [62,63].…”