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.

Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.

HIGH-PERFORMANCE METHOD OF PRODUCTION OF POWDER FRICTIONAL PRODUCTS ON FE-BASIS WITH HIGH TECHNOLOGICAL AND OPERATIONAL PROPERTIES

Physical and technological bases of DHP-PFM method for production of dry friction powder friction articles on Fe-base with high technological and operational indices for a wide range of practical use have been developed. The DHP-PFM method is that the dynamic hot pressing (DHP) provides production of the new powder frictional materials (PFM) through an underlayer from carbonyl iron between frictional material and a basis (framework) with electroplated nickel coating. Friction lining compaction is made of charge of ФМК-79 type and has high hardness and low porosity. Processes of the choice of composition of furnace charge, formation of structure and properties of new powder frictional materials on Fe-to a basis are investigated. The method is characterized by high productivity, energy saving, simplified technology and provides the possibility to use existing technological equipment for making structural powder products. Method of DHP-PFM manufacturing of dry friction powder friction linings can be used for manufacturing of friction units of transmissions of light track machines with high specific power. The friction material received by this method from furnace charge of FMK-79 type can be used as unified for such frictional units as the main friction clutch, an onboard friction clutch, tape and disk brakes.