$(5)$ Consider the bi$-$metallic strip shown $($undeformed$)$ in the figure. A strip of copper and a strip of steel are perfectly bounded together at some temperature.

Figure $1$: Dimetanc strip.

Suppose the bi$-$metallic strip is heated. The copper strip wants to expand more than the steel strip. What can you say about the stress $($in particular ${}_{11},{}_{12},{}_{22})$ at the points A and B$?$ Hint: The copper strip wants to expand more than the steel strip, but the bond holds them together. So the stress tensor can be discontinuous across the interface. Yet, if $n$ is normal to the interface, balance of forces dictate

$t(x,-n)=-t(x,n),=>,{}^{\text{c}\text{o}\text{p}\text{p}\text{e}\text{r}}n={}^{\text{s}\text{t}\text{e}\text{e}\text{l}}n$

Build some intuition: So the copper wants to expand more than the steel strip. After being heated, will the point $A$ be above or below or on the same plane as $B?$ Draw a sketch of what you think the deformation might look like?