|
Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
Publication 14-CNA-030
Stable Disarrangement Phases Arising from Expansion/Contraction or from Simple Shearing of a Model Granular Medium L. Deseri D. R. Owen Abstract: A principal challenge in modelling granular media is to connect the macroscopic deformation of the aggregate of grains with the average deformation of a small number of individual grains. We used in previous research the two-scale geometry of structured deformations ($g,G$) and the theory of elastic bodies undergoing disarrangements (non-smooth submacroscopic geometrical changes) to obtain an algebraic tensorial consistency relation between the macroscopic deformation $F = grad g$ and the grain deformation $G$, as well as an accommodation inequality $detF >= detG > 0$ that guarantees that the aggregate provides enough room at each point for the deformation of the grains. These two relations determine all of the disarrangement phases $G$ corresponding to a given $F$. We use the term stable disarrangement phase to denote a grain deformation $G$ thatminimizes the stored energy density for the aggregate among all the disarrangement phases G' corresponding to $F$.
In this article we determine for a model aggregate and for two familiar families of macroscopic deformation - - simple shearing and uniform
expansion/contraction - - all of the stable disarrangement phases of the model aggregate, as well as the corresponding connections between
aggregate deformation and grain deformation. We showed in an earlier article that each stable disarrangement phase of this model aggregate
cannot support tensile tractions, and our present results confirm the no-tension property for the two families of macroscopic deformation
treated here. Get the paper in its entirety as |
