variational limit of lattice energies of pre-strained elastic materials

MARTA LEWICKA; PABLO OCHOA

Tandil, Buenos Aires

Congreso; V MACI 2015; 2015

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