Nonlinear finite elements/Homework 6/Solutions/Problem 1/Part 14

Problem 1: Part 14
Apply the plane stress condition and solve for $D_{yy}$.

The plane stress condition requires that $$\sigma_{yy} = 0$$ in the laminar coordinate system. We assume that the rate of $$\sigma_{yy}$$ is also zero. In that case, we get

0 = \cfrac{D}{Dt}(\sigma_{yy}) = C_{13}~D_{xx} + C_{11}~D{yy} $$ or,

D_{yy} = - \cfrac{C_{13}}{C_{11}}~D_{xx} ~. $$

Plugging in the values we get

D_{yy} = - \left(\cfrac{60}{10}\right)~(2.4837) = -14.902 ~. $$