Abstract
In this work, we explore the underlying structure of most common bond models used in particle dynamics and discrete element methods, to derive simple equilibrium conditions and stability requirements that must be fulfilled for a model to stand effective and reliable. We then propose a simple model taking into account such considerations, with which we are able to capture inter-particle bonding very straightforwardly once a given bonding criterion is met. The model can be particularized to work with different contact models, such as Hertzian contact, as well as with different adhesion models, such as the classical Johnson, Kendal and Roberts (JKR) model. The derived requirements yield guidelines that may help the selection of proper parameter values (such as, but not only, the stiffness of the bond) for most common bond models, thereby guiding (or even avoiding) burdensome problem-dependent calibration. Numerical examples are provided for illustration.
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Notes
We will restrict ourselves to the central (or normal) direction of the interaction in this work.
A similar expression may be written to represent the motion of \(j\).
For bonding criterion here we mean, e.g., the temperatures of the particles reaching a certain critical temperature, like their melting temperature, or the concentration of chemical substances reaching a certain critical concentration, for significant sticking or gluing effects to develop.
A similar expression may be derived for damped contacts.
A stick–slip friction scheme (with a Coulomb-type static friction limit) is adopted, as described in details in Campello [11].
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Acknowledgements
First author acknowledges support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, under the Grant 307368/2018-1. Second author acknowledges scholarship funding from Itaipú Binacional, Brazil-Paraguay, through BECAL (Programa Nacional de Becas de Postgrado en el Exterior “Don Carlos Antonio López”), under the grant 590/2016.
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Campello, E.M.B., Quintana-Ruiz, O.D. On a simple, stable and efficient bond model for inter-particle adhesion. Comp. Part. Mech. 9, 29–44 (2022). https://doi.org/10.1007/s40571-021-00388-z
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DOI: https://doi.org/10.1007/s40571-021-00388-z