Discrete particle models have been developed as an alternative to classical continuum mechanics to describe the mechanical behaviour of solids.​ Heretofore, the types of interaction forces considered in discrete particle models have been very limited; consisting mainly of linear pairwise interactions or empirically motivated generalizations thereof. Thus these models have been able to describe a very limited range of macroscopic constitutive behaviour which is also generally strongly dependent on the discretization.​ We present a new paradigm for incorporating multi-body interactions in discrete models using an mesoscale analog of the Cauchy Born rule which relates the deformation of the continuum to that of the underlying atomic lattice.​ Using this, we derive interparticle interactions directly from the continuum constitutive description of the material. We show the efficacy of this approach in describing several interesting problems ranging from brittle crack growth to phase transformations.