Not true about the "solid materials" - much depends on what is the internal structure. If it's a monocrystal, then I guess by "multiplying defects" you mean creating of dislocations that would glide to facilitate creep - but this only happens in several specific orientations of compression. If you have a poly-crystalline solid, then I don't think you multiply defects that much: dislocations are pinned on the domain boundaries and you can't generate too many in each grain. For the more disordered solids (with lots of interstitials/vacancies and eventually - glass) the compression certainly does not increase the number of defects...
The same distinction applies to smectic liquid crystal: if you are talking about aligned monodomain smectic and you compress along the layer normal - then you will eventually generate dislocation loops that would nucleate and spread out to diminish the number of layers to comply with your compression. But if you compress along any other direction - the system would "remember" that it is a liquid after all and the flow along the layers is not inhibited. If you have a polydomain, non-aligned (mosaic) smectic structure - then usually compression causes alignment (which is achieved by shear-flow induced layer rotation in each domain) and I don't think you can identify "defects" in such a process (may be at the latest stages only, but the point is - you eventually reduce the number of dislocations to zero).
To be more accurate, I should say "Does apply strain multiplies instead of reducing defects in smectic liquid crystals?" so compression, dilation, shearing can be all considered.
I agree with you that an in-depth analysis can be quite complex, but let us keep it in a simple (and ideal) situation as people did with metals/alloys, and the general statement is that applying strain multiplies defects. The tricky part is that smectics are only solid in one dimension and fluid in the other two. So I'd like to hypothesis that compression and dilation multiply defects in general, and shearing is inclusive at this moment.