Normal stresses, contraction, and stiffening in sheared elastic networks

TL;DR

This paper links the Poynting effect in sheared elastic networks to microscopic vibrational properties, showing how network contraction and stiffening depend on vibrational mode shifts and elastic moduli.

Contribution

It introduces a novel relation between the Poynting effect and the Grüneisen parameter, applying it to random spring networks to explain contraction and stiffening behaviors.

Findings

Networks contract or develop tension when stretched due to vibrational mode shifts.

The Poynting effect amplitude depends on the network's elastic moduli.

The Poynting effect can predict the strain scale for material stiffening.

Abstract

When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Gr\"uneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.