Equanimity may not be so different from composure, but from the definitions I've checked it mentions an extra detail of remaining composed in the face of difficulty or hardship, which is not something I've seen for definitions of "composure".
n. composure, esp. under tension or strain; evenness of temper.
Noun 1. equanimity - steadiness of mind under stress;
Calmness and composure, especially in a difficult situation. ‘she
accepted both the good and the bad with equanimity’>br> Oxford Living
a state of psychological stability and composure which
is undisturbed by experience of or exposure to emotions, pain, or
other phenomena that may cause others to lose the balance of their
I'm not sure if this extra semantic detail is commonplace or not.
Also, there is another word I like:
I like it because the prefixes un-, in-, im-, meaning "not" seem to imply a strength in many cases, like impregnable, impermeable, impeccable, impervious, invincible, unconquerable etc.
imperturbable adj. Unshakably calm and collected.
Unable to be upset or excited;
Oxford Living Dictionaries