This is the author's final version of the contribution published as:[M. Fraldi, G. Perrella, M. Ciervo, F. Bosia, N.M. Pugno, A hybrid deterministicprobabilistic approach to model the mechanical response of helically arranged hierarchical strands, Journal of the Mechanics
AbstractVery recently, a Weibull-based probabilistic strategy has been successfully applied to bundles of wires to determine their overall stress-strain behaviour, also capturing previously unpredicted nonlinear and post-elastic features of hierarchical strands. This approach is based on the so-called "Equal Load Sharing (ELS)" hypothesis by virtue of which, when a wire breaks, the load acting on the strand is homogeneously redistributed among the surviving wires. Despite the overall effectiveness of the method, some discrepancies between theoretical predictions and in silico Finite Element-based simulations or experimental findings might arise when more complex bundle structures are analysed, e.g. helically arranged bundles. To overcome these limitations, an enhanced hybrid approach is proposed in which the probability of rupture is combined with a deterministic mechanical model of a strand constituted by helically-arranged and hierarchically-organized wires. The results show that generalized stress-strain responses -incorporating tensile/torsion couplingare naturally found and, once one or more elements break, the competition between geometry and mechanics of the strand microstructure, i.e. the different cross sections and helical angles of the wires belonging to the different hierarchical levels of the strand, determines the no longer homogeneous stress redistribution among the surviving wires whose fate is hence governed by an "Unequal Load Sharing" criterion.