To break up :
* to separate, to end a relationship: They couldn't stand each other. They've just broken up.
*to go on a school holiday : When do the schools break up in December?
*that cannot be heard any more (voice when calling someone): Sorry, I can't hear you, you're breaking up!
*breaking into pieces and in this way permanently break: She broke the vase with a baseball bat.
To break down :
* (break down in tears) to suddenly start crying: She couldn't take it anymore so she broke down in tears.
*to reduce to smaller parts in order to analyse: Susan has broken down her favourite doll to see what it is made of.
* to stop working: Sorry I'm late. My car has broken down.
*someone's resistance (to overcome it): Parents should know how to break down their child's barriers.