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A damage model based on failure threshold weakening

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  • Gran, Joseph D.
  • Rundle, John B.
  • Turcotte, Donald L.
  • Holliday, James R.
  • Klein, William

Abstract

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency–magnitude scaling relationship and the ergodic behavior of the model.

Suggested Citation

  • Gran, Joseph D. & Rundle, John B. & Turcotte, Donald L. & Holliday, James R. & Klein, William, 2011. "A damage model based on failure threshold weakening," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1269-1278.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:7:p:1269-1278
    DOI: 10.1016/j.physa.2010.12.004
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    References listed on IDEAS

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