From Molecular Theories to Continuum Elasticity: a Possible Track

Claude Le Bris
Ecole Nationale des Ponts et Chaussees

Abstract: I will discuss our common series of works (first with I. Catto and PL Lions, next with X. Blanc and PL Lions) that describe a possible passage from atomistic models to some elasticity models using simplifying assumptions. First, our thermodynamic limit results on molecular models to obtain models for microscopic (periodic and non periodic) crystals. Second, how the scale is changed, yielding models of stored mechanical energies. And third, the relation of such discrete to continuum passages with more traditional homogenization theories for elliptic pdes.