Deformable Thin Films: From Macroscale to Microscale and
from Nanoscale to Microscale
ABSTRACT: We begin with some background on the physical behavior of
thin films: how films are synthesized and patterned, how
stress is measured in films (e.g. the wafer curvature measurement).
Some background information on the behavior of active films is given.
We present the basic intuition that underlies
plate and shell theories: this concerns the relation between
thinness and the geometry of SO(3) and a discussion of the
scales at which "membrane" and "bending" theories emerge.
We then launch into a discussion of the direct passage
from 3-D elasticity to thin film theory with and without interfacial
energy (macroscale to microscale). We discuss first the membrane theory.
In the case that the membrane theory is trivial, we discuss the
derivation of the bending energy. This relies on a new quantitative
Reshetnyak-Liouville theorem (joint work with Friesecke and Muller)
We then highlight some predictions that are unique to
thin films of active materials, in particular, the presence of
interfaces that are possible in films but not in the corresponding
bulk material. We suggest some applications to microactuators:
tents, tunnels, wedges, pacmen.
We then present a new idea for the passage from atomic to
continuum theory for films (joint work with Friesecke). Its
implementation for carbon sheets is presented.
Finally, we present an idea for an active cantilever,
which, however, does not seem to covered by any of the theories
previously described. This motivates a new theory: piecewise rigid
body mechanics. We summarize by highlighting the many open problems
in this area.
Univ of Minnesota
Dept of Aero. Eng. and Mechanics
110 Union St. SE
Minneapolis, MN 55455
Tel: (612) 625-0706
FAX: (612) 626-1558