The success of a creative session is tied up to participation. A brainstorming session where only half or less of its members participate actively will not reach its full potential and will create some tensions inside the team.
It is a common problem. It could be personality, personal situation, or trust issues. Whatever the reason is, the problem is always the same: not everyone contributes with ideas when brainstorming. Even when it could sound like a huge issue and some difficult to solve, it's not. You just need to introduce one simple step in your creative sessions: first write, then share.
A classic brainstorming session goes like this: you explain the topic, sit around a table with your team and ask everyone to spit out the ideas that come to their minds.
Well, next time you do this, give your team 5-10 minutes to first note down their thoughts on a piece of paper/post-it. Don't rush it, if you see they need extra time, give it to them. Only when they are done writing the ideas down, ask them to share them.
With this simple trick, you'll encourage everyone in your team to be active, spend some time thinking and push them to contribute with something.