Modelling complex particles in LAMMPS using spherical harmonics

A novel contact algorithm is presented that allows for contact between arbitrarily shaped particles using DEM, presently in the form of a user package. The surface of these particles is captured through a spherical harmonic analysis [1], where their radii can then be reproduced at discrete spherical coordinates. This is achieved through the creation of a new atom style, which stores the coefficients of all particles in the simulation in one array. Any instance of this atom style simply accesses the appropriate coefficients. The repulsive force between particles depends on the volume of overlap and follows an energy-conserving contact theory [2], which is implemented in a pair style. These particles are represented by their bounding spheres when building neighbour lists and checking for potential contacts. Calculation of the volume of overlap, in addition to other properties required by the contact theory, is handled through numerical integration over the spherical caps [3] formed by the overlap of these bounding spheres. This is managed through the addition of standalone routines for spherical harmonic and quadrature functions, defined in a similar way to those in MathExtra. Lastly, the resolution of these particles and consequently the computational requirement, can be varied by changing the number of terms in the spherical harmonic expansion. The development of a contact algorithm for particles described using spherical harmonics allows for an accurate description of the motion of complex particles.

References

1. E. J. Garboczi, Three-dimensional mathematical analysis of particle shape using x-ray tomography and spherical harmonics: Application to aggregates used in concrete, Cement and Concrete Research 32 (10) (2002) 1621–1638.
2. Y. T. Feng, An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues, Computer Methods in Applied Mechanics and Engineering 373 (2021) 113493.
3. K. Hesse, R. S. Womersley, Numerical integration with polynomial exactness over a spherical cap, Advances in Computational Mathematics 36 (3) (2012) 451–483.