Mechanical Properties of Dust, Pebbles, and Planetesimals Based on Johnson–Kendall–Roberts, Griffith, and Weibull Theories

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Mechanical properties of small bodies such as dust, pebbles, and planetesimals are key to better understanding the formation of planetary systems against their collisional destruction. We present a simple mathematical formulation to determine the static tensile strength, elastic modulus, fracture energy, fracture toughness, and sound velocity for solid particles of any composition, size, structure, and porosity. This formulation is based on the Johnson–Kendall–Roberts theory of contact mechanics, the Griffith theory of fracture mechanics, and the Weibull theory of flaw statistics, in which both aggregate particles and monolithic particles are treated as agglomerates of small constituent grains and molecules, respectively. We show that our formulae are consistent with the results of laboratory experiments and molecular dynamics simulations for porous and nonporous particles of silica or ice, irrespective of the sintering process and the internal heterogeneity. This provides us with a great opportunity to infer the internal structure of asteroids and comets from observational data on their tensile strengths.