In earthquakes, at sliding interfaces and near crack tips, high stresses can precipitate the flow of otherwise solid material. This flow, or plastic deformation, is critical to many of the systems studied during the workshop. Since the onset of plastic flow can determine the nucleation of a slip event, understanding the details of this process can be important for predicting when a system will begin to rupture. In addition this process is accompanied by significant dissipation of energy, and quantifying the energy dissipation is crucial for understanding the degree of brittleness or ductility in a system during failure. These issues were discussed in the context of granular flows (Bazant, Lois, Lemaitre, Morgan, Carlson and Rice, Behringer), glassy system (Barrat, Falk, Langer, Maloney, Rottler, Schuh, Sollich) and in crystalline materials (Green, Yip, Selinger, Naimark, Miguel, Grinfeld).

Of particular interest were phenomena that lead to localization of deformation along narrow slip planes. An overview of such phenomena in materials systems was presented by Ravi-Chandar. Observations of this behavior in simulated glasses and granular media were discussed by Barrat, Falk, Maloney, Morgan and Rottler. Of particular interest were the conditions under which localized slip would occur. Both Maloneyand Morgan observed localized slip on short time-scales, but these did not organize into persistant shear bands. In the simulations of Barrat and co-workers bands localized near the walls of the simulation cell, and slip alternated between the walls. This was quite different from the behavior observed in the binary glass simulated by Falk and Shi which exhibited persistent shear localization depending on the quench time used to prepare the glass. This localization maybe akin to the development of craze zones near crack tips in polymers as simulated by Rottler and Robbins. Here the craze persists due to a structural change in the material, much as a significant change in short range order is seen in the glasses simulated by Falk and Shi. These simulation results are quite relevant to understanding localization in metallic glasses, as shown by Schuh. The connection to slip in the gouge zone as presented by Rice of an earthquake was discussed, but remains an area of development.

In homogeneously deforming glass and granular solids interesting results were reported by Barrat and Rottler. related to the effect of aging time on the apparent ultimate strength of the glass. These ageing affects are seen in a broad class of systems and discussions overlapping with the friction area explored the overlap between aging in glasses and role of ageing in contact systems. Additional effects in homogeneous deformation included work by Lois and Carlson indicating the emergence of long correlation lengths with increased packing fraction and reduced coefficient of restitution. These emerging correlation lengths provided an explaination of the observed correlations between forces. The relationship between this work and experimentally observed force chains in granular media as observed by Behringer and others remains to be explored. Bazant presented some interesting results comparing hopper flows in granular media to predictions that arise from his spot model, which provides a novel method for modeling such flows. Lemaitre described some attempts to apply theories of amorphous plasticity such as the shear transformation zone (STZ) theory to granular media. Some interesting dicussions arose regarding the relations between the STZ theory, as originated by Falk and Langer, and the soft glassy rheology model (SGR) of Sollich and Cates. However, the lack of a statistical mechanics model that could be used to extend these theories beyond the mean field currently limits progress in this area. Development of these theories beyond mean field treatments could provide a rich area for theoretical progress.

Additional discussions centered on the role of phase transformations played in some of these instances and whether the language of phase transformations applied more broadly could capture the underlying physics in some class of problems. Of particular interest were the kinds of phase transformations that cause deep earthquakes, as described by Green. In addition Ravi-Chandar provided an overview of those instances in which shear induced transformation lead to localization. Naimark provided a novel theory that attempts to apply the Ginsberg-Landau formalism to a broad array of instances. Grinfeld pointed out some of the deep unresolved problems in the thermodynamics of phase transitions that can lead to problem in understanding solid-solid phase transformations. Questions persisted as to whether transitions between flow and jamming, i.e. the emergence of a yield stress, can be described in the language commonly used to discuss phase transitions.

The deformation of crystalline materials was also considered. This was of interest as a fundamental process important for understanding the size and rate effects that may control deformation and slip, as illustrated by the simulations performed by Selinger. Also the avalanche behavior in systems with dislocations were discussed by Miguel and Yip which had implications both for plastic flow and as a model system in which long range forces lead to the spontaneous development of structure and intermittent dynamics.

22 Talks in this area

8/10, 12:00 p.m.
Gregg Lois (UCSB)
Simulations of Dense Granular Flows
8/15, 3:10pm
Anael Lemaitre (Institut Navier)
Athermal, Quasi-static Deformation of Amorphous Materials
8/16, 9:30am
Martin Bazant (MIT)
Cooperative Diffusion and Stochastic Plasticity in Granular Flow
8/16, 11:10am
Chris Schuh (MIT)
Extracting the Activation Parameters of Flow Defects from Nanoindentation Experiments
8/16, 2:00pm
Jean-Louis Barrat (Lyon)
Microscopic Simulations of Sheared Glassy Systems
8/16, 2:35pm
Michael Falk (Michigan)
The Relationship Between Localization and Percolation in Simulated Systems
8/16, 3:10pm
Joerg Rottler (Univ British Columbia)
Shear Yielding of Glassy Solids: Effects of Age, Rate and Temperature
8/16, 4:15pm
Peter Sollich (Kings College)
Recent Extensions of the Soft Glassy Rheology Model
8/16, 4:50pm
Harry Green (UC Riverside)
Reaction-induced Shearing Instabilities in High-pressure Silicates and Germanates: Implications for the Mechanics of Deep Earthquakes
8/19, 3:10pm
Sid Yip (MIT)
Atomic-Level Measures of Strength, Deformation and Reactivity
8/19, 4:15pm
Robin Selinger (Kent State)
Simulation of Plastic Deformation and Ductile Fracture: Size/Rate/Temperature Effects
8/23, 10:30 a.m.
Discussion
Constitutive Formulations of Slip and Plasticity
8/30, 10:30 a.m.
Discussion Leaders: Jean Carlson (UCSB) and James Rice (Harvard)
Discussion: Granular Media
8/31, 10:00 a.m.
Dr. Craig Maloney (UCSB)
Dissertation Defense: Amorphous Systems in Athermal Quasistatic Shear
9/06, 10:30 a.m.
Dr. James Langer (UCSB)
STZ Theory of Deformation and Failure in Amorphous Solids
9/14, 12:00 p.m.
Dr. Oleg Naimark (Institute of Continuum Media Mechanics, Russian Academy of Sciences)
Structural-Scaling Transitions in Ensembles of Defects as Mechanisms of Plasticity and Failure
9/22, 10:30 a.m.
Dr. K. Ravi-Chandar (UT Austin)
Discussion: Strain localization in a variety of materials systems
10/12, 12:00 p.m.
Discussion Leaders: J. Fineberg, P. McGuiggan
The Origins of Ageing
10/18, 10:30 a.m.
Dr. M. Carmen Miguel (University de Barcelona)
Collective Dislocation Phenomena in Nonequilibrium Systems
11/15, 10:30 a.m.
Dr. Michael Grinfeld (Army Research Lab)
Deeply Focused Earthquakes as Phase Transformations
11/29, 10:30 a.m.
Dr. Joerg Rottler (University of British Columbia)
Fracture of Glassy Polymers
12/08, 10:30 a.m.
Dr. Robert P. Behringer (Duke)
Friction, Failure and Dynamics of Granular Materials