Journal ArticleDOI
Ill‐posedness in three‐dimensional plastic flow
TLDR
In this article, the Critical State Theory of Soil Mechanics (CSTOM) was used to examine partial differential equations for frictional materials flowing via plastic yield, including the equations given by the critical state theory of soil mechanics.Abstract:
This paper examines partial differential equations for frictional materials flowing via plastic yield, including the equations given by the Critical State Theory of Soil Mechanics. In particular, the material density is considered as a dependent variable. In previous work we demonstrated that two-dimensional plastic flow may be ill posed due to an instability along two rays in Fourier transform space. In this paper, we show that in three dimensions the equations are linearly well posed provided all three strain rates are nonzero.read more
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ReportDOI
MFIX documentation theory guide
TL;DR: This report describes the MFIX (Multiphase Flow with Interphase exchanges) computer model, a general-purpose hydrodynamic model that describes chemical reactions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors.
Journal ArticleDOI
Physics of the Granular State
TL;DR: The generation of analogies between the physics found in a simple sandpile and that found in complicated microscopic systems, such as flux motion in superconductors or spin glasses, has prompted a number of new theories and to a new era of experimentation on granular systems.
Journal ArticleDOI
Computing granular avalanches and landslides
TL;DR: In this paper, the authors present a tool set for simulation of geophysical mass flows, which can simulate model systems of equations that contain no interstitial fluid and can be changed to allow for more complex material models, as warranted.
Journal ArticleDOI
Well-posed and ill-posed behaviour of the -rheology for granular flow
TL;DR: In this article, the Coulomb rheology is shown to be well-posed for intermediate values of, but not for high and low inertial numbers, which is not obvious from casual inspection of the equations, and suggests that additional physics such as enduring force chains and binary collisions becomes important in these limits.
Journal ArticleDOI
Viewing Earth's surface as a soft-matter landscape
TL;DR: In this article, the authors explore how a soft-matter physics perspective has helped to illuminate, and even predict, the rich dynamics of earth materials and their associated landscapes and highlight phenomena of geophysical flows that challenge, and will hopefully inspire, work on more fundamental aspects of soft matter.
References
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Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Journal ArticleDOI
Instability in the evolution equations describing incompressible granular flow
TL;DR: In this paper, the Navier-Stokes equations for the flow of an incompressible, viscous fluid are derived and analyzed, and the main result is that depending on geometric and material parameters, the equations governing granular flow may lead to a violent instability analogous to that for u, = u XI up ;
Journal ArticleDOI
Constitutive inequalities for isotropic elastic solids under finite strain
TL;DR: In this paper, the authors examined restrictions on isotropic constitutive laws for finitely deformed elastic solids from the standpoint of Hill (1968) and introduced the notion of conjugate pairs of stress and strain measures, whereby families of contending inequalities can be generated.
Book ChapterDOI
Some Mathematical and Physical Aspects of Continuum Models for the Motion of Granular Materials
TL;DR: In this article, the authors discuss mathematical and physical aspects of a continuum model for the motion of granular materials and describe some problems associated with the formulation and solution of differential equations of motion for a granular material.