Patent ID: 7966135

Claim:
A computer-implemented method for determining stresses at a location on a layered structure comprising at least one film formed on a substrate, comprising: computing, by said computer, stresses at a selected location in the layered structure from curvatures at all locations of the layered structure, wherein the layered structure is subject to a spatially varying structural condition which comprises at least one of (1) the film covers only a portion of the substrate, (2) the film has a film thickness that varies from one location to another across the film, and (3) the substrate has a substrate thickness that varies from one location to another; determining in the computation under the spatially varying structural condition a local contribution to stresses at the selected location on the layered structure from curvature changes at the selected location; determining a non-local contribution to the stresses at the selected location from curvature changes at all locations of the layered structure; combining the local contribution and the non-local contribution to estimate the total stresses at the selected location; applying a formula to compute a difference in stresses along a radial direction and an orthogonal circumferential direction that is independent of a thickness of the film when the film thickness varies from one location to another across the film; and using a radial gradient of a sum of curvature changes along the radial direction and the orthogonal circumferential direction to represent an interface shear stress between the film and the substrate.