Line integral approach for fiber-fiber interactions implemented in LAMMPS

Fiber networks are currently modelled using discrete bead-spring type molecular models or cylindrical discrete-element (DEM) models. Bead-spring models often suffer from issues arising from artificial friction originating at the bead-bead contacts, and DEM-type models suffer from high computational demands. Thus, there is a need for better models. Here, the cohesive interaction energy between straight fibers is expressed as a double integral. This double integral can be converted into a single integral that has two terms in its integrand: g(r), which depends on the relative geometrical positioning of the fibers, and V(r), which reflects the interaction energy. Although V(r) is readily available in analytical form, (can be of the lennard-jones type), g(r), which is essentially a distance distribution function of point-pairs located across 2 fibers, requires computation. The method to compute g(r) involves elliptic integrals and is computationally demonstrated in this work. An implementation of the resulting fiber-fiber interaction is demonstrated in LAMMPS, a popular molecular dynamics package, and its computational and scientific performance is evaluated.