CNA 2001 Summer School




Deformable Thin Films: From Macroscale to Microscale and from Nanoscale to Microscale

Richard James

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.

Richard James
Univ of Minnesota
Dept of Aero. Eng. and Mechanics
110 Union St. SE
Minneapolis, MN 55455
Tel: (612) 625-0706
FAX: (612) 626-1558