Interpreting the results

Force–extension curve: The green squares (quasi-static loading) follow the stable branch up to the fold at ||(F_{\max} = 2.55||), where the LAMMPS minimiser crashes — an atom is lost. The blue line (arclength continuation) traces smoothly through the fold onto the unstable branch (decreasing force). Bond lengths: Under increasing applied force, all bonds stretch, but the weakest bond (||(D=0.85||)) stretches the most. At the fold, it passes the inflection point ||(r^*||) and begins to snap — its length increases rapidly while the other bonds contract (since the total force is now decreasing). This confirms that disorder determines which bond breaks: the weakest link in the chain.