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Is the modelling of a beam's bending under stresses a materials science issue or structural mechanic

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The materials science is what is happening 'inside' the beam. The structural mechanics are the effects on the beam as a whole. They both are relevant, but in structural analysis we take all the hard work of the materials guys and bubble it down to a few constants (E, G, nu, etc)
 
I'd tweak drift's explanation a bit.

The answer is, the modeling of the a beam's bending under stress is both material science and mechanics.

Material science describes the effects due to what the beam is made of; mechanics describe the effects due to the geometry of the beam.
 
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