Smooth waves and shocks of finite amplitude in soft materials

Recently developed soft materials exhibit nonlinear wave propagation with potential applications in energy trapping, shock mitigation and wave focusing. We address finitely deformed materials subject to combined transverse and axial impacts, and study the resultant nonlinear waves. We determine the dependency of the induced motion on the impact characteristics, pre-deformation and the employed constitutive models. When using the neo-Hookean constitutive model, we find it cannot capture shear shocks and tensile-induced shocks, in contrast with experimental results on soft materials. Conversely, we find that the Gent 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. These features are in agreement with experimental data. Further, 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.