Something tossed through window

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Pengwuino

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Something I've been wondering lately is how much energy (or well, speed really) an object loses if it smashes through something (like glass). I was thinking if you knew the Young's modulus and the dimensions of the "something", you could use the integral of the F * dx. Then i realized Young's modulus is a pressure value so then i became lost. How exactly would you determine what kinda energy you would lose?
 

Tide

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Young's modulus won't do it since it is the proportionality constant in the linear regime of the stress-strain relationship. You'll need something called the "yield strength" or "ultimate strength."
 

PerennialII

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Young's modulus is part of it (but only the associated deformation), but if we assume that the window is completely brittle (does not experience anything else than Hookean deformation) one can account for the crack initiation (for multiple cracks), propagation, and possible arrest energies in the 'total' energy balance using fracture mechanics (note the initiation used here refers to fracture mechanical treatment of initiation). So you use a material property called 'fracture toughness' to describe cracking occurring during the smashing, which can again be linked to the energy the 'smashing' takes. Essentially your typical impact analysis is added an another energy term affiliated with material failure, recently been having fun with similar stuff & same principles with aircraft impacts.

Easy to do in 'simple' cases, but for example analysis of 'realistic' smashing of something through a window can take 'some' work (well, there are published results that apply pretty good).

edit -- yeah, if what you'd be smashing through would exhibit 'limit failure', like plastic yielding and collapse, then you could do a yield & tensile strength based evaluation. Typically "hard" to find glass behaving in that manner.
 
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