GEOMETRICALLY NONLINEAR STRESS DEFLECTION RELATIONS FOR THIN-FILM SUBSTRATE SYSTEMS

A previously developed geometrically nonlinear stress-curvature relation is expanded in this paper to allow for a less restrictive approximation of the midplane strains in a thin film/substrate system. The previous analysis is based on a minimization of the total strain energy and predicts a bifurcation in shape as the magnitude of intrinsic film stress increases. It is reviewed here and three new cases are presented. Expanding the approximating polynomials for the normal midplane strains epsilon(x)0 and epsilon(y)0, has a small effect on the solution. However, allowing the midplane shear strain, gamma(xy)0, to be nonzero has a pronounced effect on the solution, particularly in the stress region near the bifurcation point.