Three consistent approaches of the multiple cracking process in 1D composites

Most modellings found in literature for the multiple cracking process of 1D composites can be categorised into three different approaches: a Continuous Approach (CA) that assumes an infinitely long composite, and two random approaches that consider composites of finite length. The Random Strength Approach (RSA) rests on a spatial discretization of the composite on which a strength distribution is applied, whereas the Random Crack Approach (RCA) generates the location and the strength of each new crack without any discretization. The first part of the paper lays the model and its statistical foundations. They are used to demonstrate that the three approaches should provide consistent results. The three approaches are then introduced, with special emphasis on the RCA as it is implemented for the first time without any approximation. Finally, the results provided by the three approaches are compared, confirming their full consistency