Exam.pdf

A $10cm10cm2cm$ tin sample is processed by pressing a block of metal into a mold as shown below:

Determine the force required to yield the sample by pressing it into the mold. Note that the material properties of tin include a yield strength of $14$ MPa $,$ an elastic modulus of $47$ GPa $,$ and a Poisson's ratio of $0\mathrm{.}24.$

Hint: This is a multi$-$axial stress analysis problem. Understand that the fixed walls apply a stress on the tin in the $y-$direction, while the free sides of the mold allow strain in the $x-$direction without any resulting stress.