Mathematics – Logic
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1204r&link_type=abstract
American Astronomical Society, DDA meeting #40, #12.04; Bulletin of the American Astronomical Society, Vol. 41, p.906
Mathematics
Logic
Scientific paper
New observations of small asteroids support the idea that many small solar system bodies are gravitational aggregates of loosely bound material. Recent evidence includes a morphological match between radar-derived models of near-Earth asteroid binary 1999 KW4 and theoretical models based on thermal (YORP) spinup of rubble piles (Walsh et al. 2008, Nature 454, 188). Rubble piles are gravitational aggregates with zero cohesion (no tensile strength). The effect of a small amount of cohesion (< 100 Pa, an approximate upper limit based on observations of comets D/Shoemaker Levy 9 and P/Tempel 1) is only just beginning to be explored in numerical simulations. Given that some small solar system bodies have spins in excess of theoretical limits for unconsolidated material, there is motivation to model weak cohesion in these bodies.
We have developed a simple model of weak cohesion based on a Hooke's-law-type restoring force (springs) between adjacent spherical particles in an idealized rubble pile. The "springs" are characterized by the Young's modulus (which determines spring strength) and stress limit (maximum distension before breaking). Once a spring breaks, it remains broken. The particles essentially act as tracers of a continuum solid that deforms under stress until failure.
To explore this model, we have conducted a series of stress tests in which assemblages of particles are subjected to increasing tensile or shear stress until failure. We find that these bodies fail near the center for slowly applied stress, and at multiple locations for rapidly applied stress, reminiscent of real materials. We use these tests to determine an overall bulk strength of the material as a function of packing geometry, "spring" parameters, number of
particles, etc., for comparison with real materials and analytical models. We have begun to include cohesion in simulations of rotational disruption of gravitational aggregates and will report on preliminary results.
Michel Pascal
Richardson Derek C.
Schwartz Stephen R.
Walsh Kevin J.
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