Engineering topics
Publications and source records attributed to Asphaug, E..
We describe a possible international multiple-rendezvous mission to probe the interiors representative near-Earth objects. Features include SEP, autonomous navigation, stereo imaging, radio tomography, anchored seismology stations and explosive signal sources. Additional information is contained in the original extended abstract.
Past collisions determine the current mechanical properties of asteroids, and hence their response to future collisions. To understand the evolution of their diverse shapes, structures and spin states, we model hypervelocity impacts into small asteroids using a modern 3D smooth-particle hydrocode (SPH3D) that takes material strength and fracture into account.
Numerical simulations have been used to study high velocity two-body impacts. In this paper, a two-dimensional Largrangian finite difference hydro-code and a three-dimensional smooth particle hydro-code (SPH) are described and initial results reported. These codes can be, and have been, used to make specific predictions about particular objects in our solar system. But more significantly, they allow us to explore a broad range of collisional events. Certain parameters (size, time) can be studied only over a very restricted range within the laboratory; other parameters (initial spin, low gravity, exotic structure or composition) are difficult to study at all experimentally. The outcomes of numerical simulations lead to a more general and accurate understanding of impacts in their many forms.
The asteroid 4 Vesta, with its unique basaltic crust, remains a key mystery of planetary evolution. A localized olivine feature suggests excavation of subcrustal material in a crater or impact basin comparable in size to the planetary radius (R(sub vesta) is approximately = 280 km). Furthermore, a 'clan' of small asteroids associated with Vesta (by spectral and orbital similarities) may be ejecta from this impact 151 and direct parents of the basaltic achondrites. To escape, these smaller (about 4-7 km) asteroids had to be ejected at speeds greater than the escape velocity, v(sub esc) is approximately = 350 m/s. This evidence that large fragments were ejected at high speed from Vesta has not been reconciled with the present understanding of impact physics. Analytical spallation models predict that an impactor capable of ejecting these 'chips off Vesta' would be almost the size of Vesta! Such an impact would lead to the catastrophic disruption of both bodies. A simpler analysis is outlined, based on comparison with cratering on Mars, and it is shown that Vesta could survive an impact capable of ejecting kilometer-scale fragments at sufficient speed. To what extent does Vesta survive the formation of such a large crater? This is best addressed using a hydrocode such as SALE 2D with centroidal gravity to predict velocities subsequent to impact. The fragmentation outcome and velocity subsequent to the impact described to demonstrate that Vesta survives without large-scale disassembly or overturning of the crust. Vesta and its clan represent a valuable dataset for testing fragmentation hydrocodes such as SALE 2D and SPH 3D at planetary scales. Resolution required to directly model spallation 'chips' on a body 100 times as large is now marginally possible on modern workstations. These boundaries are important in near-surface ejection processes and in large-scale disruption leading to asteroid families and stripped cores.
The impact crater Stickney dominates one hemisphere of the Martian moon Phobos; its diameter (11 km) is about half the size of the body (19 x 22 x 27 km). Besides demarking a threshold between cratering and catastrophic disruption, this impact reveals a great deal about the target's interior. Because Phobos has an unusually low density yet exhibits no direct evidence for volatiles such as water ice, it has been supposed that it sequesters volatiles in the deep interior, or that it is made of some exotic substance, or that it is a loosely-aggregated rubble pile. The network of fracture grooves created by the Stickney impact constrain which, if any, of these models accord with observation.
The break-up of Periodic Comet Shoemaker-Levy 9 into multiple pieces following its grazing encounter with Jupiter in July 1992 can be used to study tidally-induced fracture in comets. This spectacular event allows us not only to set limits on the size, strength and density of Shoemaker-Levy 9 itself, but provides invaluable guidance to numerical modeling of such encounters. In an extensive treatment of tidal breakup which assumed self-gravitating, homogeneous, perfectly elastic bodies, Dobrovolskis derived simple analytical expressions for the tidally-induced surface and central stresses. Both can be cast in such a way that Poisson's ratio is the only material dependent constant entering these expressions. Whether both surface and central failure must be initiated as a criterion for breakup, or either one of them is sufficient, remains a subject of disagreement. To resolve this debate, we model the details of cometary breakup using a three-dimensional Smooth Particle Hydrodynamics (SPH) code modified to simulate fracture in small solid objects. At lower stresses associated with brittle failure, we use a rate-dependent strength based on the nucleation of incipient flaws whose number density is given by a Weibull distribution.
The hypervelocity impact that excavated the Stickney crater on Phobos is numerically modeled in order to understand the effects this collision had on the interior and surface of Phobos. The model assumes homogeneity prior to impact based on Fujiwara's (1991) results. Constitutive relations for water ice and basalt are applied in tandem models. Fracture energetics is used to show that the impact itself is sufficient to cause the cracks observed on Phobos. It is further shown that the Stickney impact itself could not have created large voids; thus, the low density of Phobos must either be compositional in nature or else the result of porosity at a scale sufficiently small to avoid scattering the impact energy substantially.
Vesta is a large asteroid whose crust is mostly basaltic. Spectral heterogeneity suggests a sizable olivine feature which may be explained as impact excavation. The spectral data probably show a localized feature approximately 200 km in diameter or a diffuse feature approximately 400 km in diameter. Lightcurve irregularities suggest heterogeneity on a similar scale. This heterogeneity may represent the crater bowl, the extent of its ejecta deposit, or indeed something unrelated to cratering. In any case, drawing direct inferences about the state of Vesta's surface on the basis of these observations involves substantial speculation. We are still far from understanding the boundary between cratering and catastrophic disruption, particularly on targets for which strength and self-gravity both matter. But we are now able to model the underlying physical process -- dynamic fragmentation -- accurately with fragmentation hydrocodes such as SALE 2D and SPH3D. We present several impact scenarios for Vesta; our study is similar to a previous impact model for the formation of Stickney crater on Phobos. We illustrate the effects of impactors of different sizes and velocities, and the effect of gravity and structural inhomogeneity.
Impact phenomena shaped our solar system. As usual for most solar system processes, the scales are far different than we can address directly in the laboratory. Impact velocities are often much higher than we can achieve, sizes are often vastly larger, and most impacts take place in an environment where the only gravitational force is the mutual pull of the impactors. The Smooth Particle Hydrodynamics (SPH) technique has been applied in the past to the simulations of giant impacts. In these simulations, the colliding objects were so massive (at least a sizeable fraction of the Earth's mass) that material strength was negligible compared to gravity. This assumption can no longer be made when the bodies are much smaller. To this end, we have developed a 3D SPH code that includes a strength model to which we have added a von Mises yielding relation for stresses beyond the Hugoniot Elastic Limit. At the lower stresses associated with brittle failure, we use a rate-dependent strength based on the nucleation of incipient flaws whose number density is given by a Weibull distribution. Following Grady and Kipp and Melosh et al., we introduce a state variable D ('damage'), 0 less than D less than 1, which expresses the local reduction in strength due to crack growth under tensile loading. Unfortunately for the hydrodynamics, Grady and Kipp's model predicts which fragments are the most probable ones and not the ones that are really formed. This means, for example, that if a given laboratory experiment is modeled, the fragment distribution obtained from the Grady-Kipp theory would be equivalent to a ensemble average over many realizations of the experiment. On the other hand, the hydrodynamics itself is explicit and evolves not an ensemble average but very specific fragments. Hence, there is a clear incompatibility with the deterministic nature of the hydrodynamics equations and the statistical approach of the Grady-Kipp dynamical fracture model. We remedy these shortcomings by making the incipient flaw distribution explicit, i.e., particles carry activation strains which are distributed at random with a probability of occurrence given by the Weibull distribution. If the local principal axis strain exceeds this limit, damage starts to grow. By growing explicit cracks together with statistical cracks (damage) at the sub-particle scale, we ensure that material strength and fragmentation is independent of model resolution. We tested our scheme by simulating laboratory impact experiments on basalt spheres.
The dynamic fragmentation in impacts into solids is examined using a physical model for the formation and growth of cracks in rocks. The physical model is then inserted into a numerical model (hydrocode) of stress wave propagation and interaction, from which the outcome of a given impact event can be computed. The hydrocode model predicts fragment sizes due to impact in terms of shock waves propagating in a homogeneous elastic medium containing a distribution of crack nucleation centers known as Weibull flaws.
A collision of two rocky objects circling the sun in space, each roughly the size and mass of a large mountain range, was modeled. A fragmentation hydrocode was developed to perform dynamical computations of collisional outcomes. Explosive framentation and fluid dynamics were used and drawn together into a single application. To model a solid, certain material parameters, such as density, elasticity, rigidity, and energies of melting and vaporization were input. These parameters are well-known for a variety of important materials, such as ice, iron, granite, and basalt. Another important parameter used is the distribution of initial flaws within the material.