How to kill a Brute effectively

Your initial thoughts are correct about the armor. This link describes how to kill a brute and offers a brief video with some general info.

http://www.ign.com/wikis/mass-effect-3/Brute

Brute's defenses consist entirely of a yellow Armor bar. To deplete this you can use fire-based attacks and Powers meant to reduce armor. The most important thing to remember is to keep your distance. Stay behind cover and roll out of the way when it nears you. If it hits you, your shields will evaporate. Hit it with Grenades and other explosives. Armor Piercing Rounds and Disrupter Ammo are good to help reduce the armor, but explosives can momentarily pause the creature, giving you valuable time to get away.

The other thing I've been doing a lot is saving my grenades for large enemies and bosses only. I've really only had to deal with brutes and atlases so far, but having grenades while your other abilities are in cooldown makes a big difference.

As with most creatures, Aim for the Head!

Specifically, you'll want to aim for that Turian head grafted onto the front of the Brute. Nail it right between the eyes, and it won't last long.

As a Sentinel, I've found that the Lob Grenade power is extremely useful, particularly when you're being surrounded by multiple brutes. 3-4 grenades should drop them to almost 1/4 of their armor strength.

Couple of shots of Warp interspersed with Lob Grenades should make mincemeat of the brutes. Also, do run away from brutes - climb the ladders, brutes can't climb them. Close/melee encounters with the brute will leave you in jelly in no time