HR: 0800h
AN: NG31A-0845    [Abstracts]
TI: Connecting the Microscale to the Macroscale in Earthquake Processes: Scaling and its Relationship to Nucleation in Damage Mechanics
AU: * Rundle, J B
EM: jbrundle@ucdavis.edu
AF: Center for Computational Science and Engineering, One Shields Ave University of California, Davis, CA 95616 United States
AU: Shcherbakov, R
EM: roshch@physics.ucdavis.edu
AF: Center for Computational Science and Engineering, One Shields Ave University of California, Davis, CA 95616 United States
AU: Turcotte, D
EM: turcotte@geology.ucdavis.edu
AF: Department of Geology, One Shields Ave University of California, Davis, CA 95616 United States
AU: Klein, W
EM: klein@bu.edu
AF: Department of Physics, 590 Commonwealth Ave Boston University, Boston, MA 02215 United States
AB: The process of earthquake initiation and failure typically involves a range of scales, inasmuch as the foreshocks and aftershocks are significantly smaller in magnitude than the mainshock. The physics of these processes are similar to the processes involved in damage mechanics in materials, which can be studied in the laboratory. Material damage occurs when microscopic processes of dislocation dynamics and microcrack formation are produced in association with strain and fracture mechanisms operating on the macroscopic scale. Here we discuss the physics of self-organization and damage at the "microscopic" scale, and how it relates to the "macroscopic" scale of the fracture. We begin by writing a free energy functional that connects the microscale with the macroscale processes. Since damage represents a modification of a brittle elastic system, we expect to find that the interactions produce the mean field dynamics characteristic of elastic systems. Sudden transitions in the state of these systems can be understood in the context of first order phase transitions, where the influence of the classical limit of stability, or spinodal, is felt. The appearance of a mean field spinodal leads to a general coarse-grained equation, which expresses the balance between rate of stress supplied, and rate of stress dissipated in the processes leading to surface damage. We can use ideas from thermodynamics and kinetics of phase transitions to develop the form of standard equations for material damage, giving clear physical meaning to all terms and variables. Ultimately, the self-organizing dynamics arise from the appearance of an energy landscape in these systems, which in turn arises from the strong correlations and mean field nature of the physics. We demonstrate that these ideas lead to dynamical equations, and we derive the scaling properties of the solutions. Our theory has the novel feature that, while the initial nucleation process occurs in a non-classical spinodal mode, the final crack or "droplet" has a classical profile, as a result of the decreasing range of interaction as damage increases. We also compare with laboratory data and show reasonable agreement in certain cases.
DE: 5104 Fracture and flow
DE: 7209 Earthquake dynamics and mechanics
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting