what was the name of the concept which spread this desire for increased militarism and was characterized by the phrade "survival of the fittest"-- evolution being applied to society? Social Darwinism
You're right, again. :-)
The concept you are referring to is Social Darwinism. Social Darwinism is a theory that emerged in the 19th century, which applied the principles of Charles Darwin's theory of natural selection to human societies and social hierarchies. It suggested that societal progress and success were determined by a competitive struggle, leading to the survival of the strongest and most capable individuals or groups.
To find the name of this concept, you could start by recognizing the keywords in your question: "increased militarism," "survival of the fittest," and "evolution applied to society." You could use a search engine to look up these terms together, which would likely lead you to various sources explaining and discussing Social Darwinism.