Canceling the elastic Poynting effect with geometry

TL;DR

This paper demonstrates that the classical Poynting effect in soft solids can be reversed by adjusting the geometry, specifically the aspect ratio of the cuboid, enabling control over vertical displacements.

Contribution

It introduces a simple geometric method to cancel the Poynting effect in hyperelastic solids, supported by theoretical, experimental, and simulation results.

Findings

Reducing the aspect ratio reverses the Poynting effect.

Cubes always exhibit a reverse Poynting effect regardless of material properties.

Finite Element simulations confirm the geometric control of the effect.

Abstract

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using Finite Element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).