$\times$ $1$ mm, i.e. the maximal contact radius is limited to $0.5$ mm. The indentation simulations are carried out over a set of deformable asperities located on a deformable half-space; very small indentation depths are used. Naturally, no periodic boundary conditions are used. The sphere is approached in 100 load steps from the separation[^5] $u_z = 4\sigma$ down to $u_z = \sigma$ in 100 load steps. In order to accelerate the simulations, only those asperities are considered which (1) “penetrate” into the sphere in the undeformed state, i.e. $z_i > u_z + R-\sqrt{R^2 - (X_0-x_i)^2 - (Y_0-y_i)^2}$, and (2) which are located in the circle $\sqrt{(x-X_0)^2 + (y-Y_0)^2} < r_0$, where $r_0 = 1.5\sqrt{2(4\sigma - u_z)R}$, which is 1.5 times bigger than the radius of geometrical overlap of a sphere, whose tip is penetrated under a plane by distance $(4\sigma-u_z)$.

After convergence, at every step we record the total contact force $N$ and total contact area $A$. Moreover, at every load step, a coarse grained map of the contact pressure and the contact area is saved. The map represents a regular grid $N\times N$ created over the indentation area $L\times L$ with cells of size $\Delta x \times \Delta x$. 