Substrate curvature due to thin film mismatch strain in the nonlinear deformation range

The physical system considered is a thin film bonded to the surface of an i nitially flat circular substrate, in the case when a residual stress exists due to an incompatible mismatch strain in the film. The magnitude of the m ismatch strain is often inferred from a measurement of the curvature it ind uces in the substrate. This discussion is focused on the limit of the linea r range of the relationship between the mismatch strain and the substrate c urvature, on the degree to which the substrate curvature becomes spatially nonuniform in the range of geometrically nonlinear deformation, and on the bifurcation of deformation mode from axial symmetry to asymmetry with incre asing mismatch strain. Results are obtained on the basis of both simple mod els and more detailed finite element simulations. (C) 2000 Elsevier Science Ltd. All rights reserved.