Cauchy-Born Rule, Generalized Cauchy-Born Rule and Applications to Nanomechanics

Tuesday, April 12, 2005 - 2:30pm - 3:30pm
EE/CS 3-180
Weinan E (Princeton University)
The focus of this talk is to develop continuum mechanics type of models for studying the deformation of nano-scale objects such as nano-tubes, nano-rods and DNA. The basic tool we will use is various generalizations of the classical Cauchy-Born rule. For this purpose, we will first review the classical Cauchy-Born rule for bulk crystals.
We will discuss the validity of the Cauchy-Born rule and give a precise
characterization of its boundary of invalidity. We then discuss the generalization of the Cauchy-Born rule to curved low dimensional objects, including the local Cauchy-Born rule and
the exponential Cauchy-Born rule. Finally we turn our attention to nano-tubes and nano-rods, and examine whether their deformation can be described by these continuum theories.