Critical Importance\nof Both Bond Breakage and Network\nHeterogeneity in Hysteresis Loop on Stress–Strain Curves and\nScattering Patterns

This study demonstrates the importance of both breakable\nbond potentials\nand the heterogeneity of cross-linked network structures in reproducing\nhysteresis loops on stress–strain curves through coarse-grained\nmolecular dynamics simulations. We prepared a parametrized bond breakage\nmodel in coarse-grained molecular dynamics simulations for flexible\npolymers. As a simple model of a heterogeneous network structure,\nwe present a diamond lattice-like bimodal network wherein the number\nof particles between cross-links was randomly set as (<i>N</i><sub>s</sub> ± <i>N</i><sub>b</sub>), where <i>N</i><sub>s</sub> and <i>N</i><sub>b</sub> represent\nthe average number and bimodal amplitude, respectively. For a regular\nnetwork (<i>N</i><sub>b</sub> = 0) under uniaxial stretching,\ntotal failure occurred at a certain strain at which multiple bonds\nbroke instantaneously. By contrast, the heterogeneous network (<i>N</i><sub>b</sub> ≃ <i>N</i><sub>s</sub>/2)\nbroke down gradually and locally. Analyses through two-dimensional\nscattering patterns (2DSPs) and local bond statistics revealed the\nfailure behaviors of the network. For the shorter links between cross-links,\nthe bond was broken by the smallest strain. Bond breakage generates\nlarge voids, which can be observed as a characteristic behavior of\n2DSPs. We confirmed that the stress–strain curves for multiple\ncycles showed hysteresis loops that originated from bond breakage.\nSystematic change of bond breakage criteria was confirmed to be important\nin controlling the shape of the hysteresis loop, which is required\nfor comparison with experiments.