Atomistic to continuum limits for computational materials science
X. Blanc, C. Le Bris, P. L. Lions
ESAIM-Mathematical Modelling and Numerical Analysis, 41, 391-426 (2007).
ABSTRACT
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.