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<p>The objective of this article is to critically review four of the widely used methods for the implementation of Mindlin’s no-slip and partial slip model under constant normal loading and Mindlin Deresiewicz's micro-slip model under varying normal loading, for simulations of granular flow. Two of the chosen methods determine the tangential forces based on the incremental tangential displacement, while the other two estimate the tangential forces based on the instantaneous position of the particles and are known as the "integral" method. The tangential load–displacement behaviour during the contact between a spherical particle and a flat surface is investigated using these models. In addition, the rotational coefficient of restitution (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation>) is determined and compared with the experimental values reported in literature for the gross sliding, slip-stick–slip, and stick–slip regimes of contact. In the gross sliding regime, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation> obtained from all the models, shows an excellent agreement with the experimental results; however, in the stick–slip and slip-stick–slip regimes, the agreement is only qualitative.</p> Graphical Abstract <p></p>

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Revisiting the implementation of Hertz-Mindlin and Hertz-Mindlin -Deresiewicz models for application in the discrete element method

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • Sourav Ganguli,
  • Partha Sarathi Goswami,
  • Manaswita Bose

摘要

The objective of this article is to critically review four of the widely used methods for the implementation of Mindlin’s no-slip and partial slip model under constant normal loading and Mindlin Deresiewicz's micro-slip model under varying normal loading, for simulations of granular flow. Two of the chosen methods determine the tangential forces based on the incremental tangential displacement, while the other two estimate the tangential forces based on the instantaneous position of the particles and are known as the "integral" method. The tangential load–displacement behaviour during the contact between a spherical particle and a flat surface is investigated using these models. In addition, the rotational coefficient of restitution ( \(\beta \) ) is determined and compared with the experimental values reported in literature for the gross sliding, slip-stick–slip, and stick–slip regimes of contact. In the gross sliding regime, \(\beta \) obtained from all the models, shows an excellent agreement with the experimental results; however, in the stick–slip and slip-stick–slip regimes, the agreement is only qualitative.

Graphical Abstract