# An experimental verification of the one-dimensional static Willis-form equations

## TL;DR

This study experimentally verifies that the one-dimensional static Willis-form equations accurately describe the behavior of inhomogeneous springs under steady circular motion, providing insights into stress effects and material indifference principles.

## Contribution

It provides the first experimental validation of the Willis-form equations for inhomogeneous springs in steady motion, confirming their predictive accuracy.

## Key findings

- The Willis-form equations match experimental results very well.
- They explain stress-stiffening and spin-softening effects.
- The equations offer accurate linear approximations of finite deformations.

## Abstract

This paper investigates the behavior of a heavy soft spring in steady circular motion. Since the spring is inhomogeneous due to centrifugal force, one can rigorously prove that it follows the one-dimensional static Willis-form equations. The theoretical predictions agree very well with experimental results. It further demonstrates that these equations can give a clear understanding of the stress-stiffening and spin-softening effect. These findings reveal that the Willis-form equations can give very accurate linear approximations of finite deformation problems and are also helpful to clarify the classical concept of the principle of material frame indifference.

---
Source: https://tomesphere.com/paper/1702.01678