Here’s a handful of ways to release your opponent’s grip when you’ve got an armbar on him and he’s defending. They are demonstrated on the Submission Master Grappling Dummy.
The first submission is a basic “elbow crush”. This is demonstrated with one arm hooking through his arm toward his feet.
If that isn’t strong enough, you can increase the pressure by kicking your leg over his arm and figure 4 it with your other leg.
You can also do this technique with your other arm hooked through his arms going towards his head.
The next submission is to hook his leg, fall towards his feet while taking your leg off his head. That causes him to come up, thinking he can escape. Put your leg back over his head and drive downward, opening his grip and letting you complete the armbar.
The next armbar release is too change your grip (see video) to create powerful leverage that allows you to break his grip.
And the last submission technique is a wrist bar, as in the video.
The next technique is when your opponent pushes you away as he puts his knees to your chest in order to spin to guard. Block his head with your knees so he can’t spin, grab his legs, hook one leg, throw the other away, kick over to a knee bar.