Fig. 4: Role of percolation on bond energy distribution and non-affinity.
a The change in permanent bonds energy ΔUb within a small subdomain for a network undergoing relaxation. We show snapshots at three intervals in time: (I) immediately after loading, (II) after 2.5τr, and (III) at 5τr. Dynamic bonds are colored in gray. b The average bond energy for permanent (dotted) and dynamic (dashed) bonds over time. c The fraction of energy \({U}_{b}^{i}/{U}_{b}^{tot}\) stored in network i for permanent (dotted) and dynamic bonds. During loading the relative fraction in bond energy remains roughly unchanged. Following relaxation  ~80% of the energy is carried by the permanent network. Inset shows schematic illustration of load transfer from dynamic to permanent bonds during dissociation events. d The relative size of the largest cluster (see Supplementary Note 1) increases sharply at a permanent bond fraction of p ~ 0.4 indicating the threshold for percolation pc. Above this, the permanent network spans nearly the entire width of the domain. Insets show corresponding change in bond energy from the loaded to relaxed states. Note that voids remain constrained as the giant cluster size approaches unity. e The non-affinity for networks with three permanent bond fractions as a function of the held stretch λm.
