Defective beams in MEMS: a model of non-ideal rods using a Cosserat approach for component level modelling

TL;DR

This paper develops a Cosserat-based model to accurately simulate defective MEMS beams at the component level, demonstrating high agreement with FEA and significantly reduced computation time.

Contribution

It introduces a novel technique for modeling defects in MEMS beams using Cosserat theory, enabling efficient and accurate component-level analysis.

Findings

Maximum 0.5% difference with FEA in ideal case

Under 1% error in defective cases, except one at 2%

Simulation times are greatly reduced

Abstract

We present and derive a technique for the introduction of defects into a beam model based on the Cosserat theory of rods. The technique is designed for the derivation of component models of non-ideal rods for use in MEMS devices. We also present a worked through example of blob/nick defects (where the rod has an area with an excess/lack of material) and a guide for a model with random pits and blobs along the length of the beam. Finally we present a component level model of a beam with a defect and compare it to results from a Finite Element Analysis simulation. We test the Cosserat model for two cases without any defect and four with a defect. Results are in good agreement with a maximum 0.5% difference for the ideal case and under 1% differences for all but one of the defective cases, the exception being a 2% error in an extreme case for which the model is expected to break down. Overall, the Cosserat model with and without defects provides an accurate way of modelling long slender beams. In addition, simulation times are greatly reduced through this approach and further development for both component level models as well as as FEA components is important for practical yet accurate modelling of MEMS both for prediction and comparison.