Finite Element Analysis of Soft-Pad Moldless Stamping of Bistable Circular Micro Shells

Bistable microstructures are promising for implementation in many mictroelectromechanical system (MEMS)-based applications due to their ability to stay in several equilibrium states, high tunability and unprecedented sensitivity to external stimuli. As opposed to the extensively investigated one-dimensional curved beam-type devices of this kind, microfabrication of non-planar two-dimensional bistable structures, such as plates or shells, represents a remarkable challenge. Recently reported by us, a new moldless stamping procedure, based on pressing a soft stamp over a thin suspended metallic film, was demonstrated to be a feasible direction for the fabrication of initially curved micro plates. However, reliable implementation of this fabrication paradigm and its further development requires better understanding of the role of the process parameters, and of the effect of both the plate and the stamp material properties on the shape of the formed shell and on the postfabrication residual stresses, and therefore on the shell behavior. The need for an appropriate choice of these parameters requires the development of a systematic modeling approach to the stamping process. Here, we report on a finite element (FE)-based methodology for modeling the processing sequences of a successfully fabricated aluminum (Al) micro shell of realistic geometry. The model accounts for the elasto-plastic behavior of the plate material, the nonlinear material behavior of the foam and the contact between them. It was found that the stamping pressure and the plate material parameters are the key parameters affecting the residual shell curvature as well as its shape. Consistently with previously presented experimental results, we show that the fabrication procedure partially relieves the prestresses emerging during preceding fabrication steps, leaving a nontrivial distribution of residual stresses in the formed shell. The presented analysis approach and results provide tools for designers and manufacturers of systems including micro structural elements of shell type.