Tensile Strength of Dust, Pebbles, and Planetesimals: A Simple Mathematical Formula from Aggregates to Monoliths Based on an Extension of an Elastic Theory for Particle Assemblies to Molecular Networks

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Abstract
The tensile strength of solid particles is the key parameter that controls not only the formation of planetesimals in protoplanetary disks but also outburst and splitting of comets and rotational bursting of asteroids in planetary systems. It is, therefore, highly desirable to find a mathematical model that properly provides the tensile strength of porous and nonporous solid particles as functions of their known material and structural properties. We demonstrate the applicability of a rigorous theory for the tensile strength of particle assemblies to both porous and nonporous solid particles, by treating the particles as solid media with cross-linked networks of molecules. The practicability of the analytical function for the tensile strength of solid particles provided in this paper is proven to a large extent by the reproduction of laboratory experiments and molecular dynamics simulations of water ice, silica, and carbon specimens, irrespective of their crystallinities. While there is still room for improvement, specifically, on the choice of material-dependent parameters, we may conclude that our formulation is a major step forward in the inference of small-bodies’ material and structural properties from observational data on their tensile strengths.

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