Modeling coatings under substrate compression

In an effort to describe the buckling of polymer films under substrate comp ression, we model surface layers as chains of alternating coil and torsion Hooks springs, attached to the bulk via coil springs. We show that an eleme ntary chain unit, which consists of three springs, behaves unstably above a critical value epsilon(c) of the compression. Analyzing a larger system wi th five vertical springs, we find a very rich behavior, which displays loca l and global minima of the energy. In the limit of a very large number of s prings, the equilibrium states turn out to be solutions of an ordinary nonl inear fourth-order differential equation (DE) with nonlinear boundary condi tions. Investigating this DE both analytically and also numerically, we det ermine epsilon(c) and the equilibrium states as a function of the compressi on. [S0163-1829(99)07313-0].