A force–displacement relation based on the JKR theory for DEM simulations of adhesive particles

Studying the collective behavior of adhesive particles with the discrete element method (DEM) requires well-founded force–displacement relations (force models). While the Johnson–Kendall–Roberts (JKR) theory reliably predicts the dependence of the contact radius a on the force F, it has remained a challenge in this framework to obtain a straightforward force–displacement relation F(δ) with physically meaningful parameters to calculate the force F from the displacement δ. We derive a novel force–displacement relation from the JKR theory as a composition of functions F(δ)=(F∘a∘λ)(δ), with the intermediate functions contact radius a(λ) and effective adhesive contact radius λ(δ). We also analyze contact geometry errors in the Hertz and JKR models, derive the exact contact centroid to accurately calculate contact torques and relative tangential velocities, and propose a smoothed JKR model to avoid discontinuities in force and energy. We find that incorrect torques and relative tangential velocities are obtained when the stiffness quotient is neglected because it affects the exact location of the contact centroid. We also find that contact geometry errors can become non-negligible for nanoparticles due to their large relative contact size. In addition, we show from bouncing ball simulations that the JKR models with a nominal coefficient of restitution derived for the Hertz model result in higher damping and thus reduced actual coefficients of restitution. Our analysis serves as a foundation for contact-mechanics-based force models for DEM simulations of adhesive particles to investigate their collective behavior in the future.