Do Atomic Nuclei Experience an Analog of Mechanical Fatigue? I'm wondering about the force that holds atomic nuclei together. When I bend a paperclip back and forth, eventually the paperclip weakens and breaks in half.
Is it possible for the nuclear force to experience an analogous weakening from some kind of "wearing away" process?
 A: The reason metal fatigue happens over time is that the material has "memory": solid crystals and their interfaces are deformed and changed, dislocations introduced, and microscopic cracks develop. If you leave the paperclip for some time and then start deforming it again the deformations add up.
This does not happen in liquids like water, where molecules bounce around randomly and localized structures like eddies and flows dissipate rapidly. There is no long-term memory of past deformations that persist since the deformations get spread out across a myriad degrees of freedom (all the different ways the water molecules can freely move and align) and become randomized heat. Gases are even more forgetful.
Atomic nuclei are often modelled as liquid droplets, so it is not too hard to imagine that they are memoryless like liquids.
Nuclear physics issues
If we want to be intellectually careful, though, we need to check this. Perhaps the best way to show it is to note that the Fermi energy of nucleons is about 23 MeV per nucleon and their Coulomb energy about 1.4 MeV: the electrical repulsion is much weaker than the energy they get from being confined in a tiny space by the strong nuclear force. Had they been classical particles one could have said that the ratio between these energies preclude forming a Coulomb crystal and hence the nucleus is at least liquid-like (and in fact more gas-like). 
However, nuclei are quantum systems and hence complicate things a bit. The nucleons can be modelled as belonging to shells a bit like electrons around a nucleus. Their locations are spread out across the nucleus. Typically any disturbance of their state gets corrected on nuclear transition timescales on the order of $10^{-12}$ s, giving very fast forgetting. 
However, there does exist nuclear isomers that can retain some memory over much longer timescales because certain transitions are very hard to do or even forbidden without outside interference. Some of the isomers are differently vulnerable to decay, so in a sense they act like there has been a kind of "metal fatigue". 
The analogy is imperfect since for a given nucleus there are only a finite set of isomer states (rather than the large set of fatigued states of a metal): they are more like different bending configurations. In a very real sense, because of quantum mechanics, there are only a finite number of bits of information storing the entire nuclear state. Even when it does "remember" something it is not much, and usually it gets scrambled by any interactions with the outside world.
A: The forces that bind protons and neutrons together into a nucleus are enormously greater than the forces that bind, for example, iron nuclei into a crystal of metal from which one might form the wire from which a paper clip could be manufactured. Inside an atomic nucleus, there exist none of the crack-generation and propagation mechanisms that are common in macroscopic samples of matter. In this sense, a nucleus is a far more "pure" system than the wire a paper clip is made from. 
This means that the forces required to deform a nucleus into a nonspherical shape are truly huge, and in only specific rare cases (see nuclear shape isomers or spaghettification) can this be done without shattering the nucleus into fragments. 
A: No. A nucleus has a ground state. If a nucleus is in its ground state and you then excite it using a nuclear reaction, it will typically go into an excited state and then decay straight back to the ground state. (Of course there are other possibilities that don't fit this description, such as neutron-induced fission.)
The closest you can come to doing what you're talking about might be in the case of nuclei that have long-lived states. For example, many odd-odd nuclei have multiple states lying very close in energy to the ground state, and these states may have half-lives long enough that they are comparable to the beta-decay half-life of the ground state. So by subjecting such a nucleus to a nuclear reaction, you could change it from one of these states to another. However, this is not really closely analogous to mechanical fatigue. If you pop it from state A into state B, there is no reason for B to be "weaker."
