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. Under appropriate smoothness assumptions regarding the forces and displacements, moving from mass-point to corresponding mass-point in neighboring cells, a continuum model of the director type is formulated for the mechanical behavior of the system. Particular attention is given to the identification of the surface of the system.