A damage model based on failure threshold weakening

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

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 7, 1269-1278

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.

Keywords: Damage; Slider-block model; Scaling; Percolation; Critical point (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:7:p:1269-1278

DOI: 10.1016/j.physa.2010.12.004

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