It is true that breaking a board or brick or tile is a matter of physics. But the human hand or foot is not the same as a hammer or axe. It is softer and pliable and prone to injury. There are things we can break and those we cannot. Mass X acceleration is the formula. The faster the tool(hand or foot or fingertip) the more force produced.
Psychology also plays a part in the way of belief or confidence.It is not a natural action to hurl a sensitive part of one's anatomy at a hard and unforgiving surface. When the practioner is afraid, they will subconciously hold back at the critical moment thus slowing the attacking tool and lessening the force so mental focus is essential. Also, if the technique is innaccurate then it will also fail. If the wrong part of the tool is produced, then the technique will fail. When the practitioner fails to produce enough force to break the target,they are usually still producing enough force to DAMAGE the tool(hand, foot etc).
Failure can lead to broken appendages which of course hurts enormously. It is possible to be psyched out so there is merit it whatever ritual, practice move, slow breathing etc that the practitioner chooses to use. The traditional shout or KIAI does aid the practitioner in committing heart and soul to the action.In the uk, the very respected TV programme"HORIZON" wanted to explore this very issue. I believe it was during the eighties that they approached various martial artists and settled on the now Grand Master Rhee Ki Ha OCM 9th Dan Taekwon-Do Master. At the time I believe he was a seventh dan.He was chosen because he could CONSISTENTLY perform, time after time, for the camera. I don't know if this archive is accesible, but you shoud try to find it. I seem to remember the title of the article was "MOVING STILLS". High speed photography was used with proper scientific conditions. The program makers discovered that the human body tool use to impact the target actually acted as a liquid at the point of impact, thus avoiding injury even though the target would be destroyed. Further research was inspired. ITF style Taekwon-do teaches breaking to it's students as a matter of course from the outset of the students training. They have never waited till the student reaches a high rank before starting them on breaking. In Taekwon-do, breaking is taught as a test for the power and accurracy of the technique. you can't perform at full power on an opponent , you would break the opponent and end up with no mates.
Search up Grand Master Rhee. He is a veteran of power breaking and even now in his seventies, he still smashes bricks to smithereens.
For my part I am a 4th Dan black belt in the art of Taekwon-do and a former World and European champion (1984). I am now a middle aged lady but I still teach and my students learn to break as soon as they can perform the technique, whether they have trained for an hour, month or year, if they follow my instruction exactly, they succeed.
There is no mystery, but there is definately a special method which needs to be taught correctly. In the case of breaking large amounts of boards, bricks etc, then body conditioning and sheer practice are essential. Please note, that is CORRECT practice.
I can't afford to treat students in a cavalier way. they trust me not to lead them to injury. I've NEVER caused student to damage themselves- EVER. But it can happen.
So after all that, yes it is just physics within the limits of the materials used, ie; human flesh versus really hard strong stuff. BUT it is also psychological conditioning. Make no mistake, you must master youself before you master the target and that just takes as long as it takes--