Why does the tensile strength of a tortilla chips increase then decrease with wetness? A fresh, dry tortilla chip is brittle and has low tensile strength. A wet tortilla chip is soft and has no tensile strength. Yet a tortilla chip left out in moderately humid air becomes hard and relatively strong. What explains this non-monotonic function? Is it related to the specific material composition of tortilla chips (eg fiber, protein), or is there something fundamentally non-monotonic about tensile strength as a function of ductility (since its ductility is a monotonically increasing function of its wetness)?
 A: The opposite trend is a very important aspect of alloy development in metallurgy and may give some insight—subject to experimental verification, of course.
Consider a ductile and soft pure metal such as copper. The mechanism of plasticity (i.e., permanent deformation) is in this case dislocation movement through the atomic lattice. So desirable strengthening relies on interfering with this dislocation movement somehow. (Options include blocking dislocations with more dislocations, single impurity atoms, chunks of impurities, and grain boundaries, for  instance.)
However, the strengthening ultimately comes with a price: if the material becomes so hard that inevitable defects such as crack tips cannot blunt but instead stay sharp enough to provide large stress concentrations, then the material may simply shatter instead of plastically deforming.
Another way to look at this is that Nature says, well, if you make it too difficult to direct loading energy into pushing dislocations through the material, I'll simply redirect that energy into making new surfaces. This is the essence of brittle fracture.
The link to tortilla chips is that they're prepared to present the hard-but-brittle state, with many crack tips that easily propagate and provide an appetizing crunch. I'll conjecture that moisture dissolves some components and weakens others because the hydroxyl bonding that strengthened the dry material has been replaced by water's hydroxyl groups, which easily rearrange. (This is why wet sponges are more compliant than dry sponges, for example.) There may also be some commonality with bread growing stale, where moisture absorption leads to so-called starch retrogradation and crystallization into a robust, hard structure.
Thus, we have an intermediate state where the chip had lost some of its brittleness and is considered stale and hard, followed by soft sogginess as the moisture continues to permeate the material.
The common aspect between the food and the metal is the nonmonotonicity you note: a continuum between a soft state and a hard but brittle state, between which the material is both hard and sturdy—great for metals, not so appealing for some foods.
