Fig. 3: Mechanical cooperation and non-affinity.

a The relaxation modulus E_r as a function of time for a network loaded to held stretch λ_m = 2.1 with decay force f₀ = 0.0004. Networks relax from the short-term modulus \({E}_{r}^{0}\) characterized by contributions of both networks, to long-term modulus \({E}_{r}^{\infty }\) governed solely by the permanent network. Three snapshots of the network at (I.) λ = 1, (II.) λ = 2.1 just after loading, and (III.) λ = 2.1 after elapsed time 5τ_r are shown above. b Evolution of the chain end-to-end distribution ϕ(r) for the permanent (red) and dynamic (blue) networks for (I.) the initial configuration, (II.) immediately after loading and (III.) after relaxation for 5τ_r. c Probability distribution of force within the permanent network. d The non-affinity Δr² versus time for varying held stretch λ_m. This is normalized by the stretched mesh distance \({(\xi {\lambda }_{m})}^{2}\). e Normalized non-affinity at time τ_r = 5 as a function of the held stretch for decay forces f_o = [0.004; 0.0004; 0.0001] shown with circles, squares, and triangles circles respectively.