cudgel one's brain ( 或 brains)

think hard about a problem

絞盡腦汁；苦苦思索

take up the cudgels

start to defend or support someone or something strongly

奮起維護(hù)；捍衛(wèi)

there was no one else to &B{take up the cudgels on their behalf}.

沒有其他人去捍衛(wèi)他們的利益。