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 ε⁰_x and ε⁰_y, has a small effect on the solution. However, allowing the midplane shear strain, γ⁰_xy, to be nonzero has a pronounced effect on the solution, particularly in the stress region near the bifurcation point.