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The beam-film model.

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posted on 2014-01-30, 03:29 authored by Liangran Zhang, Zhangyi Liang, John Hutchinson, Nancy Kleckner

(A) Beam-film model [3]. CO-designation is promoted by stress. Each stress-promoted CO-designation reduces the stress level to zero at the designation point. That effect redistributes in the vicinity, decreasing exponentially with distance, correspondingly reducing the probability of subsequent designation(s) in the immediate vicinity. Subsequent CO-designations will tend to occur in regions with higher remaining stress levels, thus giving an even distribution. More specifically: with a film attached to a beam, if the beam expands relative to the film, stress arises along the film, causing it to crack at the positions of flaws. A crack at one position will release the stress nearby (with a distance L that is characteristic of the materials) thus reducing the probability that another crack occurs nearby. Assuming a maximal possible stress level of σ0, if a crack occurs at an isolated position that is unaffected by any prior cracks, then the stress level at any distance “x” to either side is σ = σ0 (1−e−x/L). If two cracks occur near one another, the stress levels at positions between them is the sum of their individual effects, with additional considerations also coming into play at the ends of the beam as described [3]. (B) A generalized version of the beam-film model involving sequential rounds of event designation and spreading interference as described by the mathematical expressions of the BF model.

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