# Numerical Investigation of Dynamic Wrinkling Behaviors in Stiff-Film/PDMS-Substrate Structure

## TL;DR

This paper studies how stiff films on flexible substrates behave dynamically, aiming to improve the design of flexible electronics.

## Contribution

A novel numerical approach is introduced to analyze dynamic wrinkling behaviors in stiff-film/PDMS-substrate structures.

## Key findings

- Dynamic equations were derived using energy principles for wrinkled thin film/substrate systems.
- Pre-strain and substrate stiffness significantly affect system stability and energy.
- Numerical simulations reveal the impact on potential energy and chaos critical values.

## Abstract

Thin film/substrate structures based on the principle of buckling mechanics exhibit both excellent stretchability and mechanical stability, and they have been recognized as a critical configuration in the design of flexible electronic devices. During application, flexible electronic devices are usually subjected to complex dynamic environments. Therefore, it is of great significance to investigate the dynamic behavior of thin film/substrate structures for the design of flexible electronic devices. The bending energy, membrane energy, and kinetic energy of the thin film and the elastic energy of the substrate were calculated. On this basis, the dynamic equation of the thin film/substrate structure with a checkerboard wrinkled pattern was derived by applying the principle of minimum energy combined with the Lagrangian function. Numerical simulations were conducted on the system to analyze the effect of pre-strain and the Young’s modulus of substrate on the system’s potential energy function, simulate the temporal response of the system’s dynamic behavior, and investigate the influences of pre-strain and the Young’s modulus of substrate on system stability and the chaos critical value. Theoretical support is expected to be provided for the design of two-dimensional (2D) thin film/substrate structures through this research.