On the variational limits of lattice energies on prestrained elastic bodies

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\mathrm{\Omega }$. When the mesh size of the discrete lattice in $\mathrm{\Omega }$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\mathrm{\Gamma }$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$.