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

Problem 1: Part 14

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

$0=\frac{D}{Dt}({\sigma }_{yy})=C_{13}{D}_{xx}+C_{11}Dyy$

or,

$D_{yy}=-\frac{C_{13}}{C_{11}}{D}_{xx}.$

Plugging in the values we get

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