She tried to 'put on a brave face' [=she tried to appear brave or calm] despite the pain of the injury.
You can refuse to talk to her if you like, but you're just 'cutting off your nose to spite your face'.
They made it on time 'in spite of the fact' that they got a flat tire.
(..) E.O.D., Army Delta, Marine Force Recon, Naval intel community, and so on. In spite of your expertise, many of you will not successfully negotiate this program. Those that do will experience an operational tempo... that far exceeds that of any unit (..)1997 G.I. Jane