X. Blanc, C. Le Bris, P. L. Lions
ESAIM-Mathematical Modelling and Numerical Analysis, 41, 391–426 (2007).
The present article is an overview of some mathematical results, which provide elements of rigorous basis for some multiscale computations in materials science. The emphasis is laid upon atomistic to continuum limits for crystalline materials. Various mathematical approaches are addressed. The setting is stationary. The relation to existing techniques used in the engineering literature is investigated.