Figure 7
From: Tuning load redistribution and damage near heterogeneous interfaces
Average network Green’s functions, \(L=128\). A point perturbation is located in the center, \((x_0,y_0,z_0)=(L,L,L_z)/2\). Green’s functions are averaged over multiple network realizations. Top row: radial Green’s function, computed along the x direction, at three different heights, for non-hierarchical (a) and hierarchical systems (b). Thin solid lines represent the Green’s function of the continuum isotropic problem for \(z=z_0\), obtained evaluating the first \(10^5\) terms of the sum in Eq. (12), and shifted along the logarithmic vertical axis in order to allow for direct comparison with the corresponding discrete Green’s function (thick solid lines). Bottom row: average equipotential surfaces for non-hierarchical (c) and hierarchical (d) systems, with values of \(g\in [10^{-6},10^{-5}]\). Alternating colors are used to distinguish contiguous values of z. Figure generated using matplotlib 3.8, https://matplotlib.org.
