Clarify the interplay among tangential force, tangential displacement, and slip velocity in Mindlin-based DEM contact modeling

Characterize the relationship among the tangential contact force, the tangential displacement, and the slip velocity at the contact point during sphere–wall impact within Mindlin’s tangential contact theory, as used in Hertz–Mindlin and Hertz–Mindlin–Deresiewicz models for Discrete Element Method simulations, to elucidate how these quantities interact during near-normal collisions.

Background

The paper reviews and compares integral and incremental implementations of Hertz–Mindlin and Hertz–Mindlin–Deresiewicz tangential contact models in DEM, focusing on load–displacement behavior and restitution coefficients. The authors find that while all models agree in the gross sliding regime, they diverge in the sticking and sticking–sliding regimes, especially for near-normal impacts.

In analyzing near-normal collisions against experimental data, the authors observe differences in predicted tangential force–displacement curves and slip velocity histories across models. They note that understanding how tangential force, tangential displacement, and slip velocity influence one another is essential for explaining these discrepancies, but this interplay is not yet clearly understood.