Stresses and strains at nano/micro scales

This paper is concerned with stress and strain fields at atomic scale. Unlike other formulations of atomistic expression of macroscopic stress fields or ho-mogeneous systems, this paper aims at field descriptions of atomic stresses and strains for multi-element crystalline materials. By decomposing atomic deforma-tion into homogeneous lattice deformation and inhomogeneous relative atomic deformation, a field representation of momentum flux is formulated within the framework of atomic many-body dynamics, and the connection to a macroscopic definition of stress is obtained. The atomic strain measures and the atomic stress-strain relations are derived. Phonon dispersion relations are calculated and pre-sented. 1.