resultant equations can be solved using standard methods such as RungeKutta methods. @ZIV2019mom have adapted such an approach to calculate smooth waves and shocks in semi-infinite compressible Gent media, when subjected to combined transverse and axial impacts. The challenge in solving Eq.$\ $ when the medium is heterogeneous and the initial data is not piecewise-uniform is associated with the interactions between waves that are repeatedly scattered at the interfaces. In this case, the ansatz of simple waves fails and the previous approach is no longer applicable. This brings a need for more sophisticated numerical solvers. The course taken by @ziv2019b was to develop a designated algorithm based on a finite-volume method[^4], by adapting the schemes of @LEVEQUE1997327 [@leveque2002finite] and @bale2002siam, to the type of problem considered here; this adaptation is used in the study described next.

Computational study\[sec:Method-of-solution\]
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*Homogeneous benchmark problem*.—Before we proceed to the study of the main problem, it is advantageous to present the strain relations of the homogeneous benchmark problem. As we will show in the sequel, the reason is that they serve as estimators to the laminated case. Thus, the differential relation between the axial and shear strains in quasi-shear and quasi-pressure waves traversing homogeneous 