Christine B. Masters

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 e0x and e0y, has a small effect on the solution. However, allowing the midplane shear strain, γ0xy, to be nonzero has a pronounced effect on the solution, particularly in the stress region near the bifurcation point.

Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

Work in Progress - A Statics Skills Inventory

This paper focuses on assessment of student skills in statics and provides details of development of a statics skills assessment tool. The use of only concept inventories to provide proof of student learning is an incomplete assessment as important engineering knowledge consists of both conceptual knowledge and skill intertwined. A multi-step Delphi process involving a group of engineering educators was used to reach consensus on the important skills of statics. These skills are currently grouped into 10 categories. The Delphi rankings included both the average importance of the skill as judged by the Delphi participants and their judgment of the average proportion of their students whom can perform the skill. Skill-based questions are being developed to probe these areas