Implementation and Validation of an Anisotropic Influence Function in PDLAMMPS

Abstract: Technological advancements into the nanoscale have made it necessary to perform solid mechanical calculations on devices being produced on this scale. Traditionally, the field of continuum mechanics has been used to perform calculations in the field of solid mechanics, but the ubiquity of faster computers have opened up the field of peridynamics as an alternative. Peridynamic theory models materials on a per-particle basis, making it an attractive alternative when it comes to the nanoscale where objects are often only a few thousand atoms in volume. Furthermore, peridynamics can handle discontinuities which classical continuum mechanics cannot. To perform these calculations, the department of mechanics at the engineering faculty of Lund University uses a software called LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator, developed at Sandia laboratory in the United States. LAMMPS performs peridynamic simulations but can by default only perform simulations on materials that are expected to deform uniformly regardless of the direction of the forces the material is being subjected to, known as isotropic materials. Unfortunately, many materials are instead anisotropic - they do not behave uniformly when subjected to forces or stresses in different directions. In this thesis, a mathematical model is implemented into LAMMPS and tested as a proof of concept for a method of simulating anisotropic materials. The model is introduced into source files of LAMMPS itself, extending the program in a straightforward manner. The implemented model is tested through simulating nano-beams in LAMMPS with and without the model. The model is found to severely alter the behaviour of the simulations. Clear qualitative dierences in behaviour is shown independently of pre-existing simulation parameters. The model is shown to be internally consistent.