# Evolution of instabilities in filament buckling processes

## TL;DR

This paper investigates the dynamic buckling behavior of a filament in a viscous medium through experiments, simulations, and a theoretical model, revealing step-wise evolution of load and wavenumber.

## Contribution

It introduces a combined experimental, numerical, and theoretical approach to understand the dynamical buckling process of filaments in viscous environments, with a novel mechanistic model.

## Key findings

- Load and wavenumber evolve step-wise during buckling
- The theoretical model aligns well with experimental and simulation data
- The model captures key features of the dynamical buckling process

## Abstract

In this work we study the dynamical buckling process of a thin filament immersed in a high viscous medium. We perform an experimental study to track the shape evolution of the filament during a constant velocity compression. Numerical simulations reproduce the dynamical features observed for the experimental data and allow quantifying the filament's load. We observe that both the filament's load and the wavenumber evolve in a step-wise manner. To achieve a physical insight of the process we apply a theoretical model to describe the buckling of a filament in a viscous medium. We solve a hydrodynamic equation in terms of normal modes for clamped-clamped boundary conditions and applied constant load. We find a good agreement with experimental data and simulations, suggesting that the proposed mechanistic model captures the essential features underlying the dynamical buckling process.