Atomic-to-continuum derivation in Elasticity with interface energy

I will present an atomic-to-continuum derivation in nonlinearelasticity. The atomistic model is based on a two-body interactionenergy, with a potential of the Lennard-Jones type. Performing apointwise Taylor expansion, we obtain a continuum model that predictselastic energy, sharp-interface energy and smooth-interface energy. Thisalso gives a method to describe the configuration of the atoms betweentwo consecutive sharp interfaces, which qualitatively agrees withexperiments in Ni-Mn alloys presenting microstructure.