A micromechanics-based notion of stress for use in the determination of continuum-level mechanical properties via molecular dynamics

By formulating a continuum homogenization problem that includes inertia effects, a link is established between continuum homogenization and the estimation of effective mechanical properties for particle ensembles whose interactions are governed by potentials (e.g., as is seen in molecular dynamics). The focus of this chapter is on showing that there is a fundamental consistency of ideas between continuum mechanics and the study of discrete particle systems, and that it is possible to define a notion of effective stress applicable to discrete systems that can be claimed to have the same meaning as it has in continuum mechanics.