Impact Forces on a Clamped Rectangular Plate

[makamo66]

I am trying to learn about impact forces on a clamped rectangular plate in order to describe board breaking in the martial arts. I am finding a lot of sources describing Hooke's Law and other theories about elements with elastic properties but I don't seem to find any sources that discuss modulus of rupture in bending in the same level of detail as in the vibrational aspects of impact, the contact phenomena produced by the impact of elastic bodies, and the dynamic processes involving plastic strains. All of these topics show the deformation of bars, membranes, and plates but they only show the vibrations while bending and not the fracture of the element.
3 papers about board breaking:
Jon Chananie uses the coefficient of restitution e for his description of karate strikes which measures the elasticity of the collision but it's not clear to me what e is for collisions that result in fractures. Haywood Blum and Jearl Walker both use Hooke's Law which is valid for elastic materials to analyze the deflection of a beam caused by impact. How can they apply it towards non-elastic brittle elements?

 

[berkeman]

Paging @Doc Al

 

[Baluncore]

How can they apply it towards non-elastic brittle elements?

Everything is elastic, some things fracture with little deformation, so you call them brittle. As a board is bent, there is compression in the concave face, with tension in the convex face. A material will fracture, usually when the tension exceeds a tensile strength limit.

Hook's Law says more force, will cause more deflection, which will cause more tension in the board. To break the board, you must first invest sufficient energy in the elastic deflection of the board, to reach the point where fracture begins. That energy is then lost as the elastic material fails, with the energy going into destroying the internal structure of the material.

https://en.wikipedia.org/wiki/Stress–strain_curve#Classification

 

[makamo66]

thanks, Baluncore

 

[Tom.G]

Many years ago I knew a young woman of somewhat small size. For self defense, she decided to take a course in karate. Towards the end of the course she learned about breaking a board.

It turned out that the board was well aged and well dried. Another trick can be added if the board is being held by someone; they are not just holding the board but also exerting a bending force on it. This pre-tensions the board to split when it is struck by hand.

In other words, it is as much a show as a demonstration!

Cheers,
Tom

(sorry about bursting your bubble )

 

[Doc Al]

I think @Baluncore has nailed it. When breaking a board, you need to deliver enough energy to exceed its tensile strength limit and create a crack that spreads rapidly.

In 1979, there was an article in Scientific American: The Physics of Karate by Feld, McNair, and Wilk. You might find it interesting (and easily findable on the web). (FYI: One of the authors, Ron McNair, was a serious karateka (5th degree) and a physics Ph.D. (MIT). Sadly, he died in the Challenger disaster.)

When I taught a basic physics course (long ago, in grad school), I used to do board-breaking demos. I'd do 'speed breaks': I'd hold 2 or 3 boards in one hand, hanging down, then break them with a chop with the other hand. Good times!

And as @Tom.G states, it helps have the boards dry and brittle. Yes, it's a show.