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Under Hooke's law, we know that sigma stresses are responsible for volumetric strain, while shear stresses are responsible for the formation of form strains. In a lecture at my university it was shown as follows (drawings). However, one thing puzzles me: if our cube were subjected to very high shear stress resulting in large gammas, shouldn't the top wall of the lecture cube move downwards (red arrow)? If so, then we would have a change in volume (shortening height) without a sigma. In that case, does Hooke's law only make sense for very small taus resulting in negligible gamma? Did I make a mistake somewhere in my thinking?

Thank you.

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    $\begingroup$ Could whoever downvoted this provide a comment explaining their problem with it? $\endgroup$ Jun 12 '20 at 6:01
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Think of a stack of playing cards- if you provide a shear load in one direction to slide the top card in the x-z plane, does it reduce the total stack height in the y axis?

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  • $\begingroup$ Thank you for taking your time to respond. This is the best explanation I've read so far :) $\endgroup$ Jun 12 '20 at 15:13

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