HR: 16:30h
AN: NG12C-03    [PDF]
TI: Damage Mechanics: Connecting the Microscale and Macroscale in Material Deformation
AU: * Rundle, J B
EM: jbrundle@ucdavis.edu
AF: Center for Computational Science and Engineering and Dept. of Physics, University of California One Shields Ave., Davis, CA 95616 United States
AU: Shcherbakov, R
EM: roshch@ucdavis.edu
AF: Center for Computational Science and Engineering and Dept. of Physics, University of California One Shields Ave., Davis, CA 95616 United States
AU: Turcotte, D
EM: turcotte@ucdavis.edu
AF: Dept. of Geology, University of California One Shields Ave., Davis, CA 95616 United States
AU: Klein, W
EM: klein@bu.edu
AF: Dept. of Physics, Boston University 590 Commonwealth Ave, Boston, MA 02215 United States
AB: 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. 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. We also compare with laboratory data and show reasonable agreement in certain cases.
DE: 3220 Nonlinear dynamics
DE: 5104 Fracture and flow
DE: 5112 Microstructure
DE: 5120 Plasticity, diffusion, and creep
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting