Can I make hard / crunchy food without sugar or fat?
Blah ... this is getting to be a bit long for a comment, so I might as well reformat &amp; expand more, even though it might not be an appropriate answer.  (and I should note that this is mostly from memory as I got an engineering degree ~20 years ago)



Are you asking about the physics of what 'crunchy' is?  It's effectively stiff, brittle things.

When you're dealing with strength of materials, you're looking at how much energy something can absorb before it fails.  Strain is a measure of how much something deforms as it's being loaded.   Items that can take a high load (force applied) without deforming are considered stiff.  (stiffness = force / deformation)

Brittle is a characterization of how it fails -- something that deforms plastically (stretches and won't go back to the original shape once the load is removed) can become weaker as more force is applied, but still keep resisting.  Think of something like taffy.

Brittle failures, however, are almost explosive -- it just breaks suddenly.  Think of a concrete block being crushed -- you load it and it looks like nothing's happening, but suddenly bits of it shoot off and you're left with a pile of rubble.

Why things are crunchy is another issue entirely -- because there's lots of different structures that can result in "crunchy".

Crunchy baked goods are more like a wooden truss bridge.  Wood can handle a lot of force without breaking, but once once member goes, the truss loses strength and is ripped apart, and it suddenly fails.  There's often debris along the breakage because of how the item rips itself apart internally. (although we typically call them 'crumbs' not 'rubble' when talking about this kind of food).

For these foods, water will typically soften the structure making it so they can't support much load -- making them not stiff, and thus not crunchy.

Moist things like apples, lettuce and carrots are often crunchy, but it's a bit different.  It's more like bubble wrap.  Cells are effectively a bunch of tiny water balloons bound tightly together.  As we apply pressure, they pop.  (although they're so tightly packed together that unlike a single water balloon, it doesn't have space to deform).  In this case, we don't see crumbs as much as the moisture from the cells breaking.

If the cells aren't full, then we consider it to be mushy ... maybe even chewy if we dry it far enough ... if the cells don't stay bound together well, then it's mealy -- it crumbles easily, rather than giving us that resistance before it fails explosively.

So anyway ... if you want crunchy without sugar and fat ... have some celery.  If you're okay with a bit of sugar, then carrots.  If a bit of fat, then crackers (but not ritz or really buttery ones).