cudgel

cudgel one's brain ( 或 brains)

think hard about a problem

绞尽脑汁；苦苦思索

take up the cudgels

start to defend or support someone or something strongly

奋起维护；捍卫

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

没有其他人去捍卫他们的利益。