Problem $3$: Slip in Single Crystals

Write a script $($I prefer Matlab $)$ to calculate the Schmid

factors for the $12$ slip systems in a FCC crystal for an arbitrary applied stress tensor, ${}_{ij}$

a$.)$ Turn in your code

b$.)$ Demonstrate that the $[123]$ loading of a single crystal has approximately the highest

Schmid factor and only one active slip system and demonstrate that the $[111]$ loading

direction has the lowest Schmid factor and $6$ slip systems simultaneously active.

c$.)$ Demonstrate your code works for ${}_{ij}=[120,15,-30$;$15,90,28$;$-30,28,-100]MPa.$