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arXiv · 1009.4166

A damage model based on failure threshold weakening

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

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BibTeXRIS

Joseph D. Gran, John B. Rundle, Donald L. Turcotte, James R. Holliday, William Klein. 2010-09-21. A damage model based on failure threshold weakening. https://doi.org/10.1016/j.physa.2010.12.004

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