Investigation of the rupture of a synthetic tape within the framework of the percolation theory

Abstract

Abstract Within the framework of the percolation theory (bond problem), a new model of breaking a complex synthetic tape is proposed as a continuous-type phase transition when the state jump is zero. The percolation threshold and accompanying characteristics are calculated for the model of rupture of a synthetic reinforced tape when flowing along the first and second neighbours. The knots of the tape form a strip of a square lattice, the width of which is fixed. All nodes are intact and cannot be damaged, links (tape threads) can be intact and broken (blocked). The dependences of the percolation threshold in the bond problem and the relative deviation of the threshold from the ribbon length are calculated. It is proved that for the simplest model of one-dimensional percolation with percolation along the nearest neighbours (the problem of nodes), the percolation threshold in the thermodynamic limit is equal to unity. It is shown that, with an accuracy of 10%, the percolation threshold for a sufficiently long ribbon is equal to unity. This indicates that the system is quasi-one-dimensional. Thus, using the method of computer simulation, the percolation threshold, root-mean-square and relative threshold deviations were calculated. The critical susceptibility index was also calculated. In contrast to the usual percolation problem, in the proposed model it makes sense to consider only the region above the percolation threshold. The proposed model can be generalized to the case when nodes are also damaged (blocked), then we come to a mixed percolation model, which is supposed to be considered in the future.