burst (up)on (one)
To occur to one suddenly. After that idea burst upon me, I was able to alter the experiment and finally achieve some success.
See also: burst
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
burst (up)on someone
Fig. [for an idea] to strike someone suddenly. (As if an idea had burst forth. Upon is formal and less commonly used than on.) After thinking all morning long, this really tremendous idea burst upon me. It burst on me like a bolt of lightning.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.