Ok, Corki has 200 AD
Hextech Shrapnel Shells: Corki's basic attacks are permanently modified to deal 55% AD physical damage and 55% AD magic damage, for a total of 110% AD damage
So 110 Physical damage and 110 Magic damage
Let's assume that the target 100 Bonus Armor because 100 Armor from Thormail. Total armor would be around 150. Let's say 80 MR as well.
Thornmail Unique: Reflects 15% of the physical damage taken (+ 25% bonus armor) from basic attacks and on-hit effects back to its source as magic damage (Calculated before any resistances or reductions are taken into account)
So Corki would receive 16.5 + (25) = 41.5 Damage per AA (before his MR is taken into effect) with the enemy only having 100 bonus armor.
Corki would deal 44 Physical Damage and 49 Magic Damage per AA to a target with 150 Armor and 80 MR.