and @NIEMCZURA2011442, respectively.

The first Piola-Kirchhoff stress tensor derived from Eq.$\ $ is $$\piola=\mu\left(1-\frac{\tr{\defgradT\defgrad}-3}{\jm}\right)^{-1}\defgrad+\left(\kappa-\frac{2\mu}{\jm}-\frac{2\mu}{3}\right)\det{\defgrad}\left(\det{\defgrad}-1\right)\defgradTi-\mu\defgradTi,\label{eq:gentstress}$$ and the corresponding components required for calculating Eq.$\ $ are $$\begin{aligned}\piolacomp{11} & =\mu\left(\pressurestrain+1\right)\left(1-\frac{\pressurestrain^{2}+\shearstrain^{2}+2\pressurestrain}{\jm}\right)^{-1}+\left(\kappa-\frac{2\mu}{\jm}-\frac{2\mu}{3}\right)\pressurestrain-\frac{\mu}{\pressurestrain+1},\\
\piolacomp{21} & =\mu\shearstrain\left(1-\frac{\pressurestrain^{2}+\shearstrain^{2}+2\pressurestrain}{\jm}\right)^{-1}.
\end{aligned}
\label{eq:pexplicit-1}$$ The resultant characteristic velocities are $$c_{\pm}^{2}=\frac{\vc_{3}}{2\refden}+\frac{\mu}{2\refden\vc_{1}^{2}}+\frac{\left(\vc_{1}^{2}+\shearstrain^{2}+\jm\right)\mu\jm}{2\refden\vc_{2}^{2}}\pm\frac{\sqrt{48\vc_{1}^{6}\mu^{2}\shearstrain^{2}J_{m}^{2}+\left(\vc_{1}^{2}\vc_{2}^{2}\vc_{3}+2\vc_{1}^{4}\mu J_{m}-2\vc_{1}^{2}\shearstrain^{2}\mu\jm+\vc_{2}^{2}\mu\right){}^{2}}}{2\sqrt{3}\refden\vc_{2}^{2}\vc_{1}^{2}},\label{eq:cmgent-1}$$ where $$\vc_{1}=\pressurestrain+1,\ \vc_{2}=\pressurestrain^{2}+2\pressurestrain+\shearstrain^{2}-\jm,\ \vc_{3}=\kappa-\frac{2\mu}{3}-\frac{2\mu}{\jm}.\label{eq:cg comp}$$ In the calculations to follow, we use representative moduli of rubber (see [@Marckmann2006yu; @Getz2017gsm], and the references therein), namely, $$\kappa=1\,\mathrm{MPa},\ \mu=200\,\mathrm{kPa},\ \jm=10.\label{eq:paremeters}$$ Numerical solutions of Eqs.$\ $- are shown in Fig.$\ $\[fig:integralCurves\]. We clarify that these solutions are not associated with a concrete problem, and are merely solutions of nonlinear differential equations with compatibility conditions. The resultant curves can be identified with the evolution of $\shearstrain$ and $\pressurestrain$ during the propagation of smooth waves which spread in a uniformly pre-strained homogeneous Gent medium, when subjected to impact [@ZIV2019mom]. Here, we present the shear strain $\shearstrain$ as function of the axial strain $\pressurestrain$, associated with the quasi-pressure (panel a) and quasi-shear (panel b) waves. Each curve is obtained using different values for the compatibility condition , which can be identified by the intersection of a certain curve with the vertical (panel a) and horizontal (panel b) axis. Accordingly, each curve in panel (a) corresponds to one of 