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

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 ɛ. 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 Xiɛ, i⩾1) are described. We prove that the sequence {(Xiɛ,Yiɛ),1⩽i⩽n} is a “conditional renewal process”, where Yiɛ is the value of the stress at which Xiɛ forms. The approaches “in the Palm sense” and “one-sided process” merge when n→+∞. The saturation case (ɛ=+∞) is also investigated.