Method of movable lattice particles

A new simulation technique for modeling elastoplastic deformation and friction processes based on the dynamics of a system of “lattice particles” is proposed. In usual simulation methods like molecular dynamics, only interactions compatible to the symmetries of space (invariant with respect to translations and rotations) are used. In the proposed method, the interaction potentials depend both on the relative position of particles and the orientation of their relative radius vector with respect to prescribed “lattice directions”. We show that in spite of this relation with the “external space”, the system behaves, in linear approximation, as an isotropic elastic medium invariant to both the translations and rotations of the medium as a whole. The coupling with the external space occurs to be a surface effect, which either does not play an important role (if the motions of the boundaries are prescribed) or can be handled properly by introducing fictive compensating surface forces. Introduction of forces depending on the orientation of the local surroundings of a particle makes it possible to describe elastic media with arbitrary elastic properties by using only interactions between the next neighbours. The system of lattice particles shows better stability properties and allows one to describe large plastic deformations, avoiding problems of “packaging” typical for many particle methods.