Statistical and renewal results for the random sequential adsorption model applied to a unidirectional multicracking problem

Pierre Calka, André Mézin and Pierre Vallois

Stochastic Processes and their Applications, 2005, vol. 115, issue 6, 983-1016

Abstract: We work out a stationary process on the real line to represent the positions of the multiple cracks which are observed in some composites materials submitted to a fixed unidirectional stress [var epsilon]. Our model is the one-dimensional random sequential adsorption. We calculate the intensity of the process and the distribution of the inter-crack distance in the Palm sense. Moreover, the successive crack positions of the one-sided process (denoted by , i[greater-or-equal, slanted]1) are described. We prove that the sequence is a "conditional renewal process", where is the value of the stress at which forms. The approaches "in the Palm sense" and "one-sided process" merge when n-->+[infinity]. The saturation case ([var epsilon]=+[infinity]) is also investigated.

Keywords: Brittleness; Car-parking; model; Coating; Composite; material; Crack; Fibre; Markov; chain; Packing; model; Palm; measure; Poisson; point; process; Random; sequential; adsorption; Relaxation; of; stress; Renewal; process; Rupture; Stationary; processes (search for similar items in EconPapers)
Date: 2005
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