The Unbreakable Charm (incantation unknown) was a charm that made an object unbreakable.
Known uses:
It was used by Hermione Granger in 1995 to make a jar unbreakable, in which she placed Rita Skeeter, who was in her Animagus form at the time (a beetle), to prevent her from transforming back into her human form.
After his Nimbus 2000 is turned into kindling by the whomping willow, Harry can't stop thinking about what he could have done to prevent it, and other objects he would hate to see destroyed, like his wand, invisibility cloak, his parents photo album (he shudders to think what Dudley would do to it if he found it), his Weasley jumper, the Marauder's map, his glasses, and few else, really. Sure, he has a few other things, and they are worth protecting, but those are the ones he can't live without or replace.
He asks Hermione, older students, does his own research in the library, and finally learns about and practices the unbreakable charm, and another called the tether charm, which will keep his wand, broom, and anything else close to him until he dispells it. Shrinking and featherweight charms on his trunk and he doesn't have to worry about long fingered housemates. Plus carrying all his stuff with him is oddly convenient.
He puts the unbreakable charm on everything he cares even a little about, it's good practice. He notices it keeps his clothes from wearing out. And then he gets to thinking.
First he tries it on transfigured animals, then on some of Hagrid's chickens. They remain healthy. He puts it on himself with some trepidation. Doesn't hurt or anything, he doesn't feel any different, other than a bit nervous. Later in the day, he notices he can get bumped pretty hard, courtesy of a Slytherin, and it hurts for a second but he doesn't bruise. He tries to stab himself to no avail. His grin is a little bit deranged, and he doesn't bump into anyone else, try as he might, the Slytherins seem to want to avoid him. In Quidditch, he has to keep himself from punching away bludgers.
Next is Hedwig, then Hermione. She's quite confused and more than a little angry, even after he explains. Turns out you are supposed to ask somebody before performing magic on them. She sure didn't when she fixed his glasses on the train while he was wearing them, but wisely he chooses to keep quiet.
Ron calls him barmy and tells him not to do it to him. Harry hits him silently when he has his back turned, and every morning before he wakes up. Then he does himself, and Hermione when they meet in the common room before going to breakfast, even though she has taken to doing it on her own. She does all their books, clothes, and schoolbags once she sees the practicality of it, and she adds the impervious charm to their arsenal. They soon figure out it's better to put it on parchment after you are done writting on it, the charm doesn't differentiate an ink spill from purposefuly writting on the stuff. Ron is miffled he no longer can doodle in his schoolbooks, but knows better than to bring it up.
He pulls the sword out of the basilisk's mouth and cuts the diary in half, perfectly across the spine. The sword must be enchanted to always hit in the right place. Neat. Riddle's departing scream is music to his ears. He puts the tether charm on the sword and the sorting hat, and they drag on the ground behind him. The sorting hat is very rude about it, heh, payback for dropping the sword pommel-first on his head. He makes his way back to Ron with Ginny in his arms, and boy does she weight a lot.
Ron has managed to move away enough rocks to pass through, but the door has closed on its own, and he's been waiting outside. He gladly hands off Ginny, and then starts panicking about how they are going to go back up the pipe.
He's about to picture a snake in his head, not difficult given the circumstances, and ask for a lift, or stairs, when he feels claws sink on his shoulder, and is effortlessly lifted up by Fawkes. He twists around and hits Ron with the 'come along' (tether) charm. Lockhart can rot down there, serves the git right.
Dumbledore is a rotten bastard and takes his cool new sword to decorate his poncy office. That's so not fair! If he wants a cool sword, let HIM fight a sixty foot basilisk.
"Harry, why did you wait for Fawkes to drag you up? And why did you use that spell to drag me up? Don't you carry your broom inside your shrunken trunk with you? i have seen you take it out on the way to class to grab a chocolate frog or a quill."
"Ron, I just fought a sixty foot basilisk and the shade of Voldemort that was possesing your sister, I am allowed to panic and forget things. I am sure I would have remembered after I calmed down... and got hungry. Or needed a quill."
"...Barmy."
On the graveyard. Harry is tied up, and Pettigrew is growing increasinly frustrated as he tries to stab him with a knife.
Harry can't help himself, having spit out the dirty rag a while ago. "Maybe the knife is defective. What about a nice, sharp, jagged rock shard? Just grab one of those round stones in each hand and bash them together... Oh, yeah, sorry, didn't think about that. Grins stupidly, channeling Vincent Crabble. Irate bubbling emerges from the cauldron with increasingly frequency. Maybe the ugly baby thing will drown, after all.
A very confused Pettigrew, bleeding out from his stump, ends up taking blood from Cedric Diggory's cooling body and praying his master doesn't realise the switch, lest his own life be forfeit. He passes out soon after, and Voldemort has to robe himself, after standing dramatically for way too long. He's not best pleased.
When he touches Harry, it burns him, and he passes out from the pain, still a bit weak from the resurrection. A bloody big snake he faintly remembers from his nightmares lunges at and tries to bite Harry, and catches fire for her trouble. Harry swears he hears her hiss something wistfully about rather being a circus freak again before she turns to ashes. Odd.
The conjured ropes fail after a while, helped by vigorous struggling, and Harry grabs Wormtail, his wand and the cup, after divorcing the first from his legs. Let's see him run off now.
When Dolohov's curse hits Hermione in the DoM, she's BLOODY BRASSED OFF; he's ruined her best set of outer robes. She'd forgotten to respell those.
Sirius is not happy Harry tethered him to Moody, or think to call him on the magic mirror. Harry is not happy he left Grimmauld or tried to one on one Bellatrix. It all evens out. Both are angry with Kreacher, and soon there's a new old elf head on the wall, charmed so that Hermione can not see it, a clever reversal of the fidelius.
AN: I was also thinking about aging, cell division and so on. This really can go whichever way the author wants it to, magic is all about intent after all. Spells sometimes wear off on their own in canon, so I expect it would have to be reapplied every so often, so maybe they'd age a bit each day at the end of their sleep.
It would be funniest for them to realise they haven't had any growth spurts in months. Hrry doesn't get sore from Quidditch, but his mucles don't grow either. They talk about it and hermione goes "I read somewhere you grow until you are 30 then you start dying, that's what makes you look older", so they intentionally let themselves age to peak physical form while getting in great shape, and no further. They take to drinking aging potions before reapplying the charms, to make themselves look old enough for their age.
If Dumbledore finds out they are younger than they should be, physically, he might think Harry kept a chip off the philosopher's stone, or that they have recreated it on the sly. He sneakily interrogates Harry about potion brewing in the guise of being interested in his education, and thanks to Prince's book he unwittingly convinces Dumbledore he's a genius alchemist playing dumb.
Crack fics don't need to be that lore consistent (in as much as canon itself is consistent) on how spells work, specially if you go with the theory they are powered and shaped by intent.