Studies of validity of the Cauchy-Born rule by direct comparison of continuum and atomistic modelling

The Cauchy-Born rule is widely used as a standard method in continuum mechanics in order to construct descriptions of material behaviour using atomistic information. The main objective of the present work is to investigate the validity of this kinematic assumption, i.e. to determine the state when a transition to non-affine deformations is possible due to instabilities of the underlying atomic system. To this end, the results of the Cauchy-Born rule are compared with the results of direct molecular dynamics calculations on the one hand and with the results obtained by using the acoustic tensor of continuum mechanics on the other hand.