Atomistic Elasticity: Linking Atoms and Continuum

This chapter is dedicated to provide a link between the atomistic models and continuum theoretical concepts of stress and strain. We review the basic thermodynamical concepts that enable a rigorous link between atomistic systems and corresponding continuum theoretical concepts. The discussion includes a review of entropic and energetic contributions to elasticity, free energy models, entropic effects in rubber-like materials as well as the Cauchy-Born rule. We discuss elastic properties of a variety of crystal structures for different interatomic potentials.