I have a question about the typical stress tensor diagrams (shown here).(adsbygoogle = window.adsbygoogle || []).push({});

What assumption is made such that [itex] \sigma_{x,x} = \sigma_{x,-x} [/itex]? In other words, why is the normal stress on one face always equal and opposite to the normal stress on the opposite face?

It seems to me that [itex] \sigma_{x,x} [/itex] and [itex] \sigma_{x,-x} [/itex] do not need to be equal in order for the block of material to be in equilibrium, if the shear forces [itex] \tau_{x,j} [/itex] are allowed to balance it properly.

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# Stresses on opposite faces

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