Critical Importance of Both Bond Breakage and Network Heterogeneity in Hysteresis Loop on Stress–Strain Curves and Scattering Patterns

This study demonstrates the importance of both breakable bond potentials and the heterogeneity of cross-linked network structures in reproducing hysteresis loops on stress–strain curves through coarse-grained molecular dynamics simulations. We prepared a parametrized bond breakage model in coarse-grained molecular dynamics simulations for flexible polymers. As a simple model of a heterogeneous network structure, we present a diamond lattice-like bimodal network wherein the number of particles between cross-links was randomly set as (N_s ± N_b), where N_s and N_b represent the average number and bimodal amplitude, respectively. For a regular network (N_b = 0) under uniaxial stretching, total failure occurred at a certain strain at which multiple bonds broke instantaneously. By contrast, the heterogeneous network (N_b ≃ N_s/2) broke down gradually and locally. Analyses through two-dimensional scattering patterns (2DSPs) and local bond statistics revealed the failure behaviors of the network. For the shorter links between cross-links, the bond was broken by the smallest strain. Bond breakage generates large voids, which can be observed as a characteristic behavior of 2DSPs. We confirmed that the stress–strain curves for multiple cycles showed hysteresis loops that originated from bond breakage. Systematic change of bond breakage criteria was confirmed to be important in controlling the shape of the hysteresis loop, which is required for comparison with experiments.