Comparative investigations of multi-fidelity modeling on performance of electrostatically-actuated cracked micro-beams

Abstract

Silicon is a commonly used material for the fabrication of beams for use in micro-electrical-mechanical systems (MEMS). Although silicon is a brittle material, it has been shown to accumulate fatigue damage at the micro-scale. Understanding the effect this has on the overall device performance is critical to the design of reliable devices. Analytical methods for modeling damage provide expedient results but are limited by broad modeling assumptions. Numerical models account for more detailed physical phenomena but can be computationally intensive. In this work, two different crack scenarios are modeled using both analytical techniques and 3D computational simulations. First, the effects of a single surface crack on the static deflection and natural frequency of an electrostatically actuated micro-beam are formulated and compared. Then, a new method for approximating damage associated with realistic distributed crack networks is formulated for use in an analytical model and numerical simulations. A method for utilizing experimentally derived crack statistics to inform the analytical and numerical distributed crack models is developed. Good agreement between the analytical and numerical models is obtained for both crack scenarios. Together, these models can be used to effectively simulate a variety of damage and fatigue behaviors in silicon-based MEMS devices.