Impact of two elastic bodies

[Mrx1]

Hello
Can someone please tell me what is the use of poisson's ration in determinig stress cos what I know in this case we should have stress=E*strain and so now use for poison

 

[feynman1]

when stretching sth, it's elongated in the stretch direction and shrunk in the 2 orthogonal directions. the poisson's ratio effect is just the shrinking in the 2 orthogonal directions.

 

[Mrx1]

Thank you so much for your answer I'm a student and trying to implement the material point method so I have the following problem as a benchmark
Did I get the stiffness matrix right? Cos that's the only thing I can think of for getting the same results

 

[feynman1]

no worries. for plane stress and plane strain, the stress strain formulae are different

 

[Mrx1]

Does that mean I got that stiffness matrix right?