While reading Endurance, I am consistently thinking of Maslow's Theory of Needs. I have read the first two parts and it almost seems as though the crew has achieved Self Actualization, which I find absolutely incredible.
With regard to the lowest level, physiological, they have a relative decent supply of food stores and have become adept at hunting seals. As they are stranded on an ice flow, there is a near unlimited supply of water. The crew is also getting a reasonable amount of sleep; given their current conditions. Therefore, the first layer is adequately met.
As for the second level; safety, this is s bit trickier as they are far from safety; and if the slightest thing goes wrong, they could be in mortal danger. However, for the most part of the book to this point; they have seen a relative level of safety. The ice has not caused them any harm, as the Lansing notes when Shackleton wants to make a pass at getting to land, that the crew had become comfortable on the ice floe. Thus, one could argue that the second layer is met.
The next level, Love and Belonging, is easily met. The crew is stranded together and are dependent on each other for survival. They have formed friendships and have become a large family living together; packed into 5 tents. They play pranks on each other, play games, hunt together, sledge together, eat together, sleep together. Their ice floe has become home.
As for Esteem, the crew has been very positive through the entire ordeal (for the most part). They all have mutual respect for each other and have confidence in their own skills and talents, and each others, and know that they will get through this. They have achieved so much up to this point; surviving on a drifting ice floe is not a simple task.
Given this; this expedition has made these men Self Actualized. Although they have a language problem, they are genuinely moral, make judgement based on the facts they have and have accepted their current predicament. But one of the significant parts of Self Actualization is the ability to think critically and problem solve. Therefore, I believe that this adventure took a bunch of random men, brought them together, and developed their self actualization.