An explicit solver may well be best suited for your objectives. Just so you know, we often do use implicit structural elements to simulate wave propagation in solids - for example, in SAW and BAW (surface and bulk acoustic wave) filters.
We cannot attach files to forum posts, but the image below is a single frame of an animation of stress waves propagating from left to right (in the +x direction) in the piezoelectric material beneath a pair of output electrodes.
In these devices, the wavelength of the frequency of the wave that is not to be filtered (passed) equals the electrode spacing.
In the image above, the stress waves are absorbed without reflection in the "PML" (perfectly matched layers) region to the right of the output electrodes.
Nonlinear material laws can be used to account for material yield and damage in full transient analyses, which would of course affect stress wave propagation.
But explicit dynamics is almost certainly more often used for simulations such as what you described.
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