A hybrid tabulation-scaling implementation of Thornton and Ningʹs plastic–adhesive particle contact theory

Two novel implementations of the Thornton and Ning (TN) plastic–adhesive particle contact theory for use in numerical simulations using the discrete element method (DEM) are presented. They are both in contrast to the original TN implementation, which is indirect and requires an incremental calculation approach. First, a combined Newton–Raphson bisection (NRB) methodology, which calculates exactly the contact force in a non-incremental manner and, second, a tabulation-scaling (TS) implementation which closely approximates the elastic–adhesive unloading curve for a particle contact, resulting in a significant increase in computational speed, are described. The TS implementation is able to reproduce the total energy transferred during elastic–adhesive unloading force curves to within 3% of the exact NRB result. Since TN theory utilizes real material parameters, such as Youngʹs modulus and adhesion energy, the TS implementation is a physically appealing and relatively fast (only slightly slower than Hertzian elastic spheres) method of performing a DEM simulation to predict the behaviour of plastic–adhesive particles. The subroutines for calculation of TN plastic–adhesive force are compatible with the open source DEM package, LIGGGHTS.