Reinforced limit of a MEMS model with heterogeneous dielectric properties

TL;DR

This paper derives a limiting model for a MEMS device with an insulating layer as its thickness approaches zero, using Gamma convergence, revealing how dielectric properties influence the limit.

Contribution

It introduces a new Gamma convergence approach to analyze the reinforced limit of MEMS models with heterogeneous dielectric properties.

Findings

The limiting model retains the dielectric characteristics of the insulating layer.

The approach provides a rigorous mathematical framework for thin-layer limits.

The method can be applied to other heterogeneous material models.

Abstract

A MEMS model with an insulating layer is considered and its reinforced limit is derived by means of a Gamma convergence approach when the thickness of the layer tends to zero. The limiting model inherits the dielectric properties of the insulating layer.