Figure 3:

Simulations on inclusion-matrix models relate fiber buckling to matrix softening. (a, b) Enlarged views of the dipoles of Fig. 2c and d, respectively, along with nearby matrix fibers before (I) and after (II) the contraction of the inclusions. Fibers are color coded by normalized excess length ξ/L_f. After contraction of the inclusions, the fibers are highly buckled, as indicated by the large excess lengths. The fibers constituting the microenvironment of the dipole were defined using circles of radius r = 0.25L_f at the end points of the dipole. (c) Scatter plot of normalized stiffness (k_s/k_s,ref) sensed by each dipole against average excess length (ξ/L_f) in the vicinity of that dipole. The values of k_s/k_s,ref were always less than one, indicating that the matrix softened at the scale of the dipoles. The correlation between the reduction in matrix stiffness and excess lengths was statistically significant (p = 0.0076, Pearson). Each marker type indicates a dipole from an independent model.