# Dynamic Buckling Analysis of Thin Film/Polydimethylsiloxane Substrate Structures in Curved State with Finite Thickness

## TL;DR

This paper studies how thin film sensors on curved substrates behave under stress, aiming to improve their design for use in flexible electronics.

## Contribution

The study introduces a new analysis of dynamic buckling in thin film/substrate structures under curved conditions with finite thickness.

## Key findings

- Dynamic equations considering damping and external excitation were established for curved thin film/substrate structures.
- The effects of excitation frequency, pre-strain, and substrate properties on chaos occurrence were analyzed.
- Findings provide insights for optimizing curved sensor designs in flexible electronics.

## Abstract

Curved sensors hold significant positions in various fields of modern science and technology, such as medical care, soft robotics, and electronic devices. Meanwhile, flexible electronic devices with film/polydimethylsiloxane substrate structures have been widely applied in the configuration design and performance enhancement of sensors. It is essential to consider the dynamic buckling behavior of film/substrate structures under bending conditions for the optimization of sensor functions. In this study, the dynamic behaviors of thin film/substrate structures with finite thickness in the curved state are investigated. Firstly, the dynamic equations considering damping and external excitation are established based on the principle of minimum energy and the Lagrange function. Secondly, the dynamic responses under different parameters are analyzed. Finally, the effects of the frequency of external excitation, pre-strain, the amplitude of external excitation strain, and the Young’s modulus and thickness of the substrate on the critical value of chaos occurrence are discussed respectively. This study is aimed at providing novel insights for the design of curved sensors based on thin film/substrate structures.