# Smooth waves and shocks of finite amplitude in soft materials

## TL;DR

This paper investigates nonlinear wave propagation in soft materials under impact, highlighting how different constitutive models predict shock formation and how pre-shear influences shock thresholds.

## Contribution

It compares neo-Hookean and Gent models in predicting shocks, revealing Gent's superior alignment with experimental observations and analyzing impact and pre-deformation effects.

## Key findings

- Neo-Hookean model cannot capture shear and tensile shocks.
- Gent model predicts impact-induced shear and pressure shocks.
- Pre-shear lowers the impact threshold for shock formation.

## Abstract

Recently developed soft materials exhibit nonlinear wave propagation with potential applications for energy trapping, shock mitigation and wave focusing. We address finitely deformed materials subjected to combined transverse and axial impacts, and study the resultant nonlinear waves. We determine the dependency of the induced motion on the impact, pre-deformation and the employed constitutive models. We analyze the neo-Hookean constitutive model and show it cannot capture shear shocks and tensile-induced shocks, in contrast with experimental results on soft materials. We find that the Gent constitutive model predicts that compressive impact may not be sufficient to induce a quasi-pressure shock---yet it may induce a quasi-shear shock, where tensile impact can trigger quasi-pressure shock ---and may simultaneously trigger a quasi-shear shock, in agreement with experimental data. We show that the tensile impact must be greater than a calculated threshold value to induce shock, and demonstrate that this threshold is lowered by application of pre-shear.