Elder wand destruction possible?

Question

So I have seen questions that ask Why Did Harry Break the Elder Wand? or Could the Elder Wand be Repaired?

What I am wondering is, according to the history of the Elder Wand is it actually possible to break the Elder Wand? Or to ask that question another way, since the Elder Wand is so drawn to strength and power:

However, the Elder Wand knows no loyalty except to strength. So it’s completely unsentimental. It will only go where the power is. (JKR, PotterCast interview 2007)

Is there evidence that the Elder Wand would act in self defense to prevent someone from breaking it so it could continue to seek out strength?

Answer 1

The reason that it is destructible is because Harry was the owner of the wand. The elder wand simply just had an enchantment of some sort that only allowed it's full power to be realized by somebody who had defeated the previous owner. Also as stated in the link you posted, it was never actually broken in the book. Harry was going to just place it back into Dumbledore's tomb and have the power it held be broken when Harry dies naturally.

http://harrypotter.wikia.com/wiki/Elder_Wand

With Voldemort defeated, and Harry now the true master and possessor of the wand (and in fact all that remained of the Hallows, since he also had the cracked Resurrection Stone and the Cloak of Invisibility), he used it to repair his damaged original wand of holly and phoenix feather, which he said he was "happier with".[1] After the repair, Harry told Dumbledore's portrait that he would place the Elder Wand back in Dumbledore's tomb, and when Harry died a natural death, the wand's power would be broken as Dumbledore had intended. The portrait of Professor Dumbledore approved.

Answer 2

As far as I am aware, there are no quotes relating specifically to the indestructibility of the Elder Wand. However, we have good canon reason to believe it indestructible, or at least very durable.

Consider the other Hallows.

The Invisibility Cloak appears to be resistant to wear, and Ron suggests that spells normally can destroy invisibility cloaks:

“But all the stuff he said about the other cloaks, and they’re not exactly ten a Knut, you know, is true! It’s never occurred to me before, but I’ve heard stuff about charms wearing off cloaks when they get old, or them being ripped apart by spells so they’ve got holes in them. Harry’s was owned by his dad, so it’s not exactly new, is it, but it’s just. . . perfect!”

—Harry Potter and the Deathly Hallows

It seems safe to say that the Cloak of Invisibility has been hit by some spells over the course of its lifetime, yet it survived entirely intact until Harry's day.

Similarly, the magic of the Resurrection Stone proved highly resistant to damage. Dumbledore smashed it with the Sword of Gryffindor, which was impregnated with Basilisk venom, cracking the ring. Basilisk venom is a substance so magically destructive that even the protection and repair spells on a Horcrux do not affect it. Yet the power of the ring survived this highly destructive substance, even after the Horcrux within was destroyed.

The black stone with its jagged crack running down the center sat in the two halves of the Snitch. The Resurrection Stone had cracked down the vertical line representing the Elder Wand. The triangle and circle representing the Cloak and the stone were still discernible.

—Harry Potter and the Deathly Hallows

Given the durability of the other two Hallows, it seems almost certain that the Elder Wand possesses a similar degree of protection; which is to say, even more protection than a Horcrux. Is it indestructible? Perhaps not. But certainly it would take far more than snapping it in half to destroy it.

Answer 3

Here's my take (yes I'm aware that this only happens in the movies but I will use examples from the book).

The Elder wand can be broken but only by its master. The wand itself attracts people seeking its power so, right away, the likelihood of its master snapping it is almost zil. The wand itself chooses strength by whoever takes it for themselves by force from its previous master. Or simply just defeats their previous master without taking the wand from them. Harry disarming Draco caused the wand to switch to him. The wand apparently cares whether Draco was holding it or another wand. So the wand simply let Harry destroy it, because he had the strength to willingly do so.

During the King's Cross scene Dumbledore remarks that he could have never mastered any of the hallows as Harry did. Dumbledore had acquired the wand by accident as with all the other hallows like Harry, but unlike Harry, Dumbledore desired them which made him less of a master than Harry. True, Harry was interested in them but only in his belief that they could help him defeat Voldemort.

In this sense Harry is the true master of the Elder wand and therefore the only one capable of breaking it... This puts rest arguments that Dumbledore himself would have destroyed it if he could.

Also in the book Harry does talk in great deal about the Elder wand in front of hundreds of people so him breaking the wand does make sense more than trying to keep it hidden when many people now know of it.

So in conclusion while speculative the book does support Harry being willing and able to break the wand.