Modeling coatings under substrate compression

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