Hydrogel sphere impact cratering, spreading and bouncing on granular media

The impact of a hydrogel sphere onto a granular target results in both the deformation of the sphere and the formation of a prominent topographic feature known as an impact crater on the granular surface. We investigate the crater formation and scaling, together with the spreading diameter and post-impact dynamics of spheres by performing a series of experiments, varying the Young's modulus $Y$ and impact speed $U_{0}$ of the hydrogel spheres, and the packing fraction and grain size of the granular target. We determine how the crater diameter and depth depend on $Y$ and show the data to be consistent with those from earlier experiments using droplets and hard spheres. Most specifically, we find that the crater diameter data are consistent with a power law, where the power exponent changes more sharply when $Y$ becomes less than 200 Pa. Next, we introduce an estimate for the portion of the impact kinetic energy that is stored as elastic energy during impact, and thus correct the energy that remains available for crater formation. Subsequently, we determine the deformation of the hydrogel spheres and find that the normalized spreading diameter data are well collapsed introducing an equivalent velocity from an energy balance of the initial kinetic energy against surface and elastic energy. Finally, we observe that under certain intermediate values for the Young's modulus and impact velocities, the particles rebound from the impact crater. We determine the phase diagram and explain our findings from a comparison of the elastocapillary spreading time and the impact duration.

Numerical modelling of recent impacts on Mars and contribution to InSight mission science

<p>The crust on Mars has been structurally affected by various geologic processes such as impacts, volcanism, mantle flow and erosion. Previous observations and modelling point to a dynamically active interior in early Martian history, that for some reason was followed by a rapid drop in heat transport. Such a change has significantly influenced the geological, geophysical and geochemical evolution of the planet, including the history of water and climate. Impact-induced seismic signature is dependent on the target properties (conditions in the planetary crust and interior) at the time of crater formation; Thus, we can use simulations of impact cratering mechanics as a tool to probe the interior properties of a planet.</p><p>Contrary to large impacts happening in Mars’ early geologic history, the present-day impact bombardment is limited to small meter-size crater-forming impacts (in the atmosphere and on the ground), which are also natural seismic sources (Daubar et al., 2018, 2020; Neidhart et al., 2020). Impact simulations, in tandem with NASA InSight seismic observations (Benerdt et al., 2020, Giardini et al., 2020), can help understand the crustal properties over the course of Mars’ evolution, including the state of Mars’ crust today. Our most recent numerical investigations include: estimating the seismic efficiency and moment from small meter-size impact events, tracking pressure propagation from the impact point into far field, transfer of impact energy into seismic energy, etc (Rajsic et al., 2020, Wojcicka et al., 2020). Understanding coupling between impact crater formation process with the generation and progression of seismic energy can help identify small impact everts in seismic data on Mars. We also looked at the same process on the Earth (Neidhart et al., 2020) and the Moon (Rajsic, et al., this issue).</p><p>Since the landing of the NASA InSight mission on Mars, there was a dozen known new impacts (Miljkovic et al., 2021). However, all but one impact occurred much too far away (3000 to 8400 km distance from the InSight lander) to be within the detectability threshold estimates (Teanby et al., 2015; Wojcicka et al., 2020). About 50% of the observed craters were likely single impacts and the other 50% were evidently cluster craters with less than 40 individual craters in the largest cluster. The largest single crater was ~14 m in diameter, and the largest crater in a cluster was ~13 m (Neidhart et al., this issue), consistent with crater cluster observations (Daubar et al., 2013). The one impact that had a possibility of being detected by SEIS was 1.5 m in diameter at 37 km distance (Daubar et al. 2020).</p><p>Considering that orbital imaging is limited in space and time, these known new impacts represent only a fraction of the total number of impacts that have occurred on Mars in the last ~2 years. According to impact flux calculations (Teanby and Wookey, 2011), there should have been ~3000 detectable craters, larger than 1 m in diameter, formed on Mars since InSight landed. If any of these unobserved impacts have been large enough and close enough to InSight to detect seismically, we have not yet discerned them in the seismic data.</p><p>References:</p><p>Banerdt, W.B. et al. (2020) <em>Nature Geosci. </em>13, 183-189.</p><p>Giardini, D. et al. (2020) <em>Nature Geosci. </em>13, 205-212.</p><p>Daubar, I.J. et al. (2020) <em>J. Geophys. Res. Planets</em>, 125: e2020JE006382.</p><p>Wójcicka, N. et al. (2020) <em>J. Geophys. Res. Planets</em>, 125, e2020JE006540.</p><p>Rajšić et al. (2021) <em>J. Geophys. Res. Planets</em>, 126, e2020JE006662.</p><p>Daubar et al. (2013) <em>Icarus</em> 225, 506-516.</p><p>Teanby, N.A. & Wookey, J. (2011) <em>PEPI</em> 186, 70-80.</p><p>Neidhart, T. et al. (2020) <em>PASA</em>, 38, E016.</p><p>Teanby, N.A. et al. (2015) <em>Icarus</em> 256, 46-62.</p><p>Miljkovic, K. et al. (2021) <em>LPSC</em>, LPI Contribution No. 1758.</p>

Discrete Element Modelling of Pit Crater Formation on Mars

Pit craters are now recognised as being an important part of the surface morphology and structure of many planetary bodies, and are particularly remarkable on Mars. They are thought to arise from the drainage or collapse of a relatively weak surficial material into an open (or widening) void in a much stronger material below. These craters have a very distinctive expression, often presenting funnel-, cone-, or bowl-shaped geometries. Analogue models of pit crater formation produce pits that typically have steep, nearly conical cross sections, but only show the surface expression of their initiation and evolution. Numerical modelling studies of pit crater formation are limited and have produced some interesting, but nonetheless puzzling, results. Presented here is a high-resolution, 2D discrete element model of weak cover (regolith) collapse into either a static or a widening underlying void. Frictional and frictional-cohesive discrete elements are used to represent a range of probable cover rheologies. Under Martian gravitational conditions, frictional-cohesive and frictional materials both produce cone- and bowl-shaped pit craters. For a given cover thickness, the specific crater shape depends on the amount of underlying void space created for drainage. When the void space is small relative to the cover thickness, craters have bowl-shaped geometries. In contrast, when the void space is large relative to the cover thickness, craters have cone-shaped geometries with essentially planar (nearing the angle of repose) slope profiles. Frictional-cohesive materials exhibit more distinct rims than simple frictional materials and, thus, may reveal some stratigraphic layering on the pit crater walls. In an extreme case, when drainage from the overlying cover is insufficient to fill an underlying void, skylights into the deeper structure are created. This study demonstrated that pit crater walls can exhibit both angle of repose slopes and stable, gentler, collapse slopes. In addition, the simulations highlighted that pit crater depth only provides a very approximate estimate of regolith thickness. Cone-shaped pit craters gave a reasonable estimate (proxy) of regolith thickness, whereas bowl-shaped pit craters provided only a minimum estimate. Finally, it appears that fresh craters with distinct, sharp rims like those seen on Mars are only formed when the regolith had some cohesive strength. Such a weakly cohesive regolith also produced open fissures, cliffs, and faults, and exposed regolith “stratigraphy” in the uppermost part of the crater walls.

Discrete Element Modelling of Pit Crater Formation on Mars

Pit craters, and pit crater chains, are now recognised as being an important part of the surface morphology and structure of many planetary bodies, and are particularly remarkable on Mars. Pit craters do not possess the elevated rims, ejecta deposits, or other features that are typically associated with impact craters. They are thought to arise from the drainage/collapse of a relatively weak surficial material into an open (or widening) void in a much stronger material below. The creation of such voids has been suggested to be due to extensional fracturing/dilational faulting, shallow dike intrusion, lava tube collapse amongst other hypotheses. These craters have a very distinctive expression, often presenting funnel, cone, or bowl-shaped geometries. Analogue models of pit crater formation provide a map-view picture of their initiation and evolution but give little insight into their internal structure or geometry, but produce pits that typically have steep, nearly conical cross sections. Numerical modelling studies of their formation have been limited and have produced some quite interesting, but nonetheless puzzling, results whereby the simulated pit craters had generally convex (steepening downward) slope profiles with no distinct rim; quite unlike many of those observed on Earth or on Mars. To address these issues, I present here a high-resolution, 2D discrete element model of weak cover (regolith) collapse into either a static or a widening underlying void. I use frictional and frictional-cohesive discrete elements to represent a range of probable cover rheologies. Under Martian gravitational conditions, frictional-cohesive and frictional materials produce cone, bowl and scoop-shaped pit craters. For a given cover thickness, the specific crater shape depends on the amount of underlying void space created for drainage. When void space is small relative to cover thickness, craters have bowl or scoop-shaped geometries. In contrast, when void space is large relative to cover thickness, craters have cone-shaped geometries with essentially planar (nearing angle of repose) slope profiles. Frictional-cohesive materials exhibit more distinct rims than simple frictional materials and thus may reveal some stratigraphic layering on the pit crater walls. In the limit, when drainage from the overlying cover is insufficient to fill the underlying void, ´skylights´ into the deeper structure are created. Implications of these results for the interpretation of pit craters on Earth, Mars, other planets and moons are discussed.