Elastic Materials with Particle Interactions of Finite Range

In this paper a material region is considered to be an aggregate of point particles which move in accordance to Newton's Laws and inter act by means of forces that depend only on the relative distance between the particles and are derivable from a potential U. The follow ing propositions are, then, established: the continuum field equations are obtained by a smoothing assumption that allows the representation of sums by integrals; the classical constitutive equations of elastic materials are obtained when forces between particles are of infini tesimally short range; when the range of interaction between particles is of short but finite range, higher order stresses and strains are neces sary to describe the mechanical state of the material.