99 years ago Sir Ernest Shackleton’s ship, Endurance, was trapped in an antarctic ice floe; after nearly a year of being icebound like this, it was finally crushed and sank.
A couple of ships have been in the news recently for having been in a similar predicament. It appears they have now broken free of the ice, but supposing that they hadn’t, would they have been in danger of being crushed by the ice like the Endurance was? These are modern vessels made of steel, and one of them is an icebreaker (although that may just mean it’s designed to take substantial dynamic loads on the bow, rather than gigantic sideways crushing forces).
If they do nothing then yes, they are in danger of being damaged (maybe not crushed); that’s one reason they are sending help to free them instead of waiting for a thaw. Anything made by man can be destroyed by nature.
In 1986, the Southern Quest, a North Sea trawler that had been ice strengthened, was crushed by the ice pack and sank off Ross Island. While the Akademik Shokalskiy is twice the size and was built as an oceanographic vessel, it is completely possible that it could have been similarly crushed.
The Chinese icebreaker was probably not in such danger of crushing but may still have been damaged.