Stress in cylindrical nanowires, equations 12-13

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StellenboschS
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Hi,

I came across a piece of maths with which I am struggling to find info on. It has to do with the stress induces in a cylindrical shaped wire (nanowire to be precise).
The article where the maths appear is attached. The specific problem is in equations 12 through 13.

Thanks
 

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Can you be more specific about what you are not understanding in those equations?
 
I don't know how they derived it. Is it standard equations?
 
Great, thanks for that. Seeing as I am an electrical engineer, I know nothing of these things!