The guy on the Action Lab, who has a doctorate in chemical engineering, explained solid-state fan terminology well. He said that, although piezoelectric fans do have moving
parts, they still are considered solid-state devices because they don't have any wearing
parts. Nothing is moving against anythign else and since everything is vibrating under the elastic limit of the material, there is no chance of work hardening either. Recall that it's plastic deformation that's necessary for work hardening to occur. Essentially, the devices never mechanically wear out.
Note that if the moving part is made of cheap plastic, eventually the plasticizer will volatilize out, which will change its elastic properties thus rendering it brittle. UV damage or oxidation would eventually do the same thing. However, these susceptibilities are not inherent to the devices themselves, nor would they be much of a concern with a high-quality plastic such as Teflon.
I'll let the Wiki author explain this:
Work hardening is a consequence of plastic deformation, a permanent change in shape. This is distinct from elastic deformation, which is reversible. Elastic deformation stretches the bonds between atoms away from their equilibrium radius of separation, without applying enough energy to break the inter-atomic bonds. Plastic deformation, on the other hand, breaks inter-atomic bonds, and therefore involves the rearrangement of atoms in a solid material.