On the interface between Continuum Mechanics analysis and Discrete Element Method simulations

Rubble pile objects are small Solar System bodies with diameters in the range 0.2 < d < 10 km and described as loosely bound boulder aggregates (Walsh, 2018). Over the past few years, several in-situ missions to these objects, e.g., Hayabusa2 (Watanabe et al., 2017), OSIRIS-REx (Lauretta et al., 2017), and DART (Daly et al., 2023), have provided a substantial advance in the understanding of them. In general, the missions’ achievements confirmed some expected characteristics while also finding unexpected properties. It is well known that the dynamics of rubble piles are strongly influenced by their shapes, sizes, and composition. This fact makes the investigation of these bodies challenging, since it seems that each object can keep its own dynamical characteristics. For all the objects visited by probes, their surfaces were described as covered by boulders of different sizes and cohesionless. However, one of the main goals in the characterisation of these objects is the understanding of their internal structure, since there is still a lack of physical description. In the past decades, different approaches were developed in order to describe their interior. Some of them used semi-analytical approaches from continuum mechanics (Holsapple, 2001, 2004) to impose the stress limit condition for cohesionless bodies. In these works, material properties of solid bodies were assumed to describe the behaviour in the interior of these minor objects. The bodies were handled as elastic-plastic ellipsoids and it was possible to describe the friction angle changes when varying different values of spin velocity and object size. On the other hand, other techniques simulated the structure of rubble piles using DEM (Discrete Element Method) N-body codes (Richardson et al., 2009; Schwartz et al., 2012; Ferrari et al., 2017), treating the interaction between the aggregates of boulders through self-gravity and contact/collisions. The DEM codes are, in general, able to reproduce physical effects due to the geometry of contact interactions between the boulders without taking into account cohesion strength interactions such as those described by continuum mechanics. Both approaches are able to investigate the evolution and stability of the internal structure of small bodies, but there is no direct relation between the physical parameters that describe each technique. In this work, we present an approach about how to connect results from solid bodies described by continuum mechanics with DEM simulations using the GRAINS (Ferrari et al., 2017; Ferrari and Tanga, 2020) code. Despite the different natures of analysis of each technique, it is possible to track the results from each approach if we restrict their physical properties and create similar scenarios of simulation. In order to reach this connection, we investigate the stress behaviour (Zhang et al., 2017) in both methods, considering ellipsoidal bodies under the effects of constant spinning rotation and self-gravity. We explore the connections between the physical parameters that describe both methods, investigating their influence on each approach and creating a relation between them. Since the cost and efforts to develop a mission to study these minor bodies in-situ are high, one possible way to validate the characterisation of these objects and find out similar features of the internal structure of these bodies can be to assemble computational techniques. We therefore expect the results obtained from both approaches to be mutually consistent.

Acknowledgements: This study was financed in part by the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) - Finance Code 001, Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) – Proc. 2022/01678-0, Proc. 2022/11783-5, Proc. 2025/19962-4, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) – Proc. 316991/2023-6, 405349/2025-4, and 307400/2025-5. E.F. and F.F. acknowledge funding of the European Union’s Horizon Europe research and innovation programme under grant agreements No. 101264707 (Marie Skłodowska-Curie Actions Postdoctoral Fellowship, SEISMOR: E.F.) and No. 101077758 (ERC, TRACES: F.F.).

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