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Critical Behavior of a Strain Percolation Model for Metals



Y Shim, Lyle E. Levine, R M. Thomson


Extensive simulations of a strain percolation model for a deforming metal have been performed to examine its strain behavior. We find that the total strain exhibits critical power-law behavior that is well explained by two-dimensional percolation theory. Near the critical point, most of the strained cells organize themselves around a state having the minimum or at least marginally stable strain regardless of the initial conditions. A strain much greater than the manimum stable strain generally decays to a lower value when transmitted to an unstrained cell. The universal behavior of the total strain in the system is a consequence of the self-organizing character of the strain in the critical cluster. Although the probability distributions for the total strain and cluster size appear to exhibit non-universal this may merely represent a transient response before crossover to a true asymptotic, universal behavior occurs. Other critical aspects of the model are also discussed.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
No. 4


dislocations, finite-scaling theory, percolation, self-organizing criticality


Shim, Y. , Levine, L. and Thomson, R. (2002), Critical Behavior of a Strain Percolation Model for Metals, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) (Accessed November 28, 2023)
Created March 31, 2002, Updated October 12, 2021