How to derive plane strain bulk modulus?

[lou_skywalker]

This is a homework problem and I thought about putting it in the homework section bu since its very materials science specific I decided to put it here:

For a transversely isotropic material, the “plane strain bulk modulus”, K23, is an
engineering constant that is defined by the stress condition (sigma)2 =(sigma)3=(sigma)
and the strain conditions (epsilon)1=0, (epsilon)2=(epsilon)3=(epsilon)
Show that these conditions lead to the stress-strain relationship (sigma)=2*(epsilon)*K23, and find the relationship among K23, E1, E2, G23, Mu12 (poisson's ratio).

I tried using the relationship Epsilon= stiffness matrix x stress, plugging in all the given relationships (and sigma1 is zero because epsilon1 is zero) but just got stuck at
sigma=(epsilon)*E2/(1-Mu23)

 

[Rafa]

if epsilon 1 =0 then sigma 1 won't be 0 because if you limit the deformation you will hava a stress