Scaling behavior of cohesive self-gravitating aggregates

By means of extensive three-dimensional contact dynamics simulations, we analyze the strength properties and microstructure of a granular asteroid, modeled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to diametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behavior can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces. At low inertial numbers, the behavior is ductile with a well-defined stress peak that scales with internal pressure with a prefactor $\simeq 0.9$. As the inertial number increases, both the prefactor and fluctuations around the mean increase, evidencing a dynamical crisis resulting from the destabilizing effect of particle inertia. From a micromechanical description of the contact and force networks, we propose a model that accounts for solid fraction, local stress, particle connectivity, and granular texture. In the limit of small inertial numbers, we find a very good agreement of the theoretical estimate of compressive strength, evidencing the major role of these structural parameters for the modeled aggregates.

Figure 1

Snapshots of a simulated granular asteroid under diametrical compression for (a) ${\varepsilon }_h=0$ and (b) ${\varepsilon }_h=0.1$. Force chains are represented by lines joining the centers of two touching particles. Compressive forces in red, and tensile forces in blue.

Figure 2

Typical curve showing the vertical strength as a function of the cumulative vertical deformation for $\eta =1$ Pa, $D=50$ m, and various values of $I_{\eta }$ (gravitational forces are not activated). The inset show the same curve for $I_c=5\times {10}^{-5}, \eta =\{1,3,10,30,50\}$ Pa for $D=190$ m considering gravitational forces.

Figure 3

Peak stress ${\sigma }_{zz}^{*}$ normalized by the cohesive stress $\eta$ as a function of $I_{\eta }$ (a) without gravitational forces (i.e., $I_{g_0}=0)$, and (b) with gravitational forces (i.e., $I_{g_0}\ne 0$), in which only one or two parameters were varied.

Figure 4

Peak stress ${\sigma }_{zz}^{*}$ normalized by additive stress $p=\eta +\alpha P_0$ as a function of the modified inertial number $I^{\prime }$ for the raw data (color coding as in Fig. 3). Error bars represent the standard deviation around the peak state.

Figure 5

Coordination number $Z^{*}$ and anisotropy descriptors $(a_c^{*},a_n^{*},a_t^{*})$, as a function of $I^{\prime }$ (the same color coding as in Fig. 3). The inset shows the polar diagrams of the angular distributions (black dot) together with harmonic approximations Eq. (2) (solid lines) for the smallest $I^{\prime }$.

Figure 6

Peak stress ${\sigma }_{zz}^{*}$ normalized by additive stress $p=\eta +\alpha P_0$ as a function of $I^{\prime }$ for the raw data (stars) (same as Fig. 4), together with the prediction given by Eq. (5) (color coding as in Fig. 3).