Assessing continuum postulates in simulations of granular flow Page: 4 of 24
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
theory, which can predict a variety of experimental flow profiles, again us-
ing the same length scale (and no other fitting parameters) (40). Assuming
stresses at incipient yield, the coaxial flow rule is replaced by a "stochastic
flow rule" (SFR) in which spots of mobilized material perform random walks
along slip lines, biased by local stress imbalances. The resulting theory is the
first to predict both gravity-driven flow in a silo and shear flow in a Couette
cell (40; 41), so a major motivation for this work is to directly test its basic
assumptions.
This prompts us to study rheological properties of granular media over vol-
ume elements of size comparable to the width of dynamical correlations, 3d to
5d. By "element", we are referring to an approximate Representative Volume
Element (RVE) (44). A uniform stress state expressed at the boundaries of an
RVE should couple to a predictable homogeneous boundary deformation. But
to be technically precise, full determinism of this coupling is deducible only for
an element containing infinitely many microconstituents, so that average be-
havior over all microevents approaches a Dirac-delta function about the mean.
Realistically, all materials possess a finite micro-length, so any RVE behavior
must be interpreted within some acceptable noise tolerance. Hierarchical rela-
tionships for such noise bounds have been deduced by Ostoja-Starzewski (45)
in terms of the ratio 6 = Lmeso/Lmicro, where averaging is over random re-
alizations of a heterogeneous continuum material. For finite 6, the element
is more aptly referred to as a Statistical Volume Element (SVE), which ap-
proaches RVE in the limit 6 -- oo. While we use the term RVE throughout
this work, in some sense we mean a granular SVE with some acceptably small,
and quantifiable, level of noise. However, we stress that randomness in our
simulations comes from packing constraints and discrete rearrangements of a
homogeneous model material consisting of frictional, viscoelastic spheres; as
in molecular materials which are routinely described by continuum mechan-
ics, we will show that meaningful continuum averages, satisfying predictable
relations with controlled fluctuations, can be defined at the scale of observed
dynamical correlations.
The RVE must be small compared to the macroscopic length of the flow,
allowing the granular domain to deform as a network of RVEs, each one ex-
periencing close to uniform boundary conditions. If gradients in the stress or
deformation fields become too sharp, the noise in the element response must
inevitably increase. This may pose an issue for materials that can form shear
bands. Granular media are known to exhibit shear-banding phenomena in cer-
tain circumstances, though it should be noted that 3D bands tend to have a
width of 10d to 15d (46), suggesting a 3d to 5d wide element may still suffice.
This also supports our major belief that unless conditions are exotic enough
to change the dynamical correlation length (e.g. large applied gradients in
loading or shear), an element at this 3d to 5d length scale should be small
enough to describe a "standard" set of dense flows.4
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Rycroft, Chris; Kamrin, Ken & Bazant, Martin. Assessing continuum postulates in simulations of granular flow, article, August 26, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc928337/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.