The passage from a particle system to a continuum model

A three-dimensional lattice is considered in which each cell contains a number of mass-points. These mass-points undergo displacements under the action of forces. It is shown how, under appropriate smoothness assumptions regarding the forces and displacements, as we move from mass-point to corresponding mass-point in neighboring cells, a continuum model of the director type can be formulated for the mechanical behavior of the system. Particular attention is given to the identification of the “surface” of the system.