Force chains bias the dynamic response to impacts in rubble-pile asteroids

TL;DR

The paper addresses how internal force-chain networks bias the dynamic response of rubble-pile asteroids to impacts. It develops a 2D proof-of-principle granular-aggregate model with particle-scale stress analysis and force-chain characterization to study post-impact disturbance propagation. The key finding is that velocity fronts and high-stress regions propagate preferentially along pre-existing force chains, a pattern robust to disturbance location, direction, magnitude, and particle-size distributions, and it persists across different cluster compositions. This work provides a mechanistic framework for assessing fragmentation risks and informs strategies for planetary defense by linking internal granular structure to observable propagation patterns.

Abstract

The impact response of rubble-pile asteroids is essential for both elucidating their formation and evolution history and evaluating the efficacy of impact defense strategies. Although state-of-the-art numerical simulations have allowed for the replication of many macroscopic impact characteristics consistent with observations, the understanding of dynamics and response mechanisms within rubble-pile structures remains incomplete and requires further in-depth investigation. Such understanding is critical for assessing the effects and safety of impact defense missions. The loose structure of rubble-pile asteroids affects inhomogeneous internal stress propagation via inherent force chains, which may lead to structural fracturing. We demonstrate this phenomenon here, using a proof-of-principle two-dimensional model of granular aggregates. We find that the velocity response front to impact disturbances preferentially propagates along pre-existing force chains, with particles not in chains responding more slowly. The sites within the response zone where high dynamic stresses manifest are strongly correlated with these initial force chains, and the damages that result are predominantly located within areas enclosed by these chains. The strong correlation between pre-existing force chains and dynamic response is independent of the location, magnitude, direction of the disturbance velocity, or the aggregate's particle size distribution. All evidence suggests that the core reasons for this propagation preference lie in the structural heterogeneity of granular aggregates and the resulting differences in mechanical wave propagation. This investigation provides guidance for future research aimed at quantitatively assessing fragmentation risks based on the statistical properties of force chains.

Figures (10)

• Figure 1: Characterization of the granular aggregate structure and the inter-particle contact interactions. Cells' polygon edges are depicted in red with arrows (clockwise vector group). The black dashed-line quadrilaterals are the quadrons that belong to, and represent the area of, particle $p_i$. $\bm{r}_q$ and $\bm{R}_q$ are the diagonals of a quadron. $\bm{f}_{p_ip_j}$ and $\bm{M}_{p_ip_j}$ respectively denote the force and torque moment that particle $p_j$ applies to particle $p_i$ at their contact position. $\bm{r}_{p_ip_j}$ is the vector extending from the center of mass of $p_i$ to the $p_i$-$p_j$ contact position.
• Figure 2: (a) Pre-impact bi-disperse granular aggregates, colored by the initial stress level Tr($\tilde{\sigma}_0$). Impact disturbances a-d (yellow arrows) are applied at particles I and II (yellow circles, $M=1.78\bar{m}$). (b)-(d) Particle speed propagation at $\tau=2.65\times10^{-4}$, $1.59\times10^{-3}$, $2.92\times10^{-3}$ in the case of Impact "a" with $u_\mathrm{impact}=10$. The particle speed layer in blue-red is superimposed on the layer denoting pre-impact stress Tr($\tilde{\sigma}_0$) in gray scale. In the speed layer, particles with speed $u\lesssim 0.01$ are transparent.
• Figure 3: Propagation of particle stress and microscopic failure events at $\tau=2.92\times10^{-3}$ in the case of Impact "a" with $u_\mathrm{impact}=10$. (a) Dynamic normal stress level Tr($\tilde{\sigma}$). (b) The layer in purple-yellow indicating the absolute value of dynamic shear stress component $\lvert\tilde{\sigma}_{12}\rvert$ is superimposed on the layer denoting pre-impact stress Tr($\tilde{\sigma}_0$) in gray scale. In the shear stress layer, only particles with $\lvert\tilde{\sigma}_{12}\rvert$ values in the top $30\%$ are colored using a gradient from purple to yellow. (c) Dynamic shear stress component $\lvert\tilde{\sigma}_{21}\rvert$, with the same rendering strategy as panel (b). (d) and (e) Contact pairs experiencing sliding and rolling failures are marked in yellow and green respectively, and the underlying layer still represents the Tr($\tilde{\sigma}_0$). (f) Particles with coordinate number=0 are rendered in red.
• Figure 4: (a) A local magnification of the bi-disperse cluster around particle II. The cluster is divided into 8 sectors centered at particle II, labeled by white digits. (b)-(d) Particle speed propagation at $\tau=6.63\times 10^{-4}$ after velocity disturbances ($u_\mathrm{impact}=1$) applied on particle II at $0^\circ$, $60^\circ$ and $90^\circ$ to the local force chain respectively, corresponding to impact "b", "c", and "d" marked in panel (a). The green arrows denote the orientations of particle velocities at the current moment, whose lengths are proportional to the magnitudes of particle velocities. The yellow dashed arrows indicate the directions of perturbation velocity, not scaled according to the velocity magnitude.
• Figure 5: (a) The evolution of $D$ in the 8 sectors around particle II in impact test "c", with $u_\mathrm{impact}=1$ and $u_\mathrm{th}=0.01$. (b) The evolution of the total value of $D$ in impact tests a-d. $u_\mathrm{impact}=1$, and $u_\mathrm{th}=0.01$.