It's possible to destroy some part of the battlefield, the environment in Aftershock.
It is however, not that helpful in creating tactical advantage, since the game is not designed around this feature.
First, we require some good weapon, and pouring fire in one space. Then it can be destroyed. The examples are the gates, the brick walls, some boxes etc. You can not destroy the grounds or the ufo in those maps.
IT's not easy to do so with early stage weapons. After we can use heavy machinegun and sniper rifles that the condition can be satisfied.
Since the environment is pretty sturdy, it's conducive to thinking about attacking straight through a target behind a wall. You just dont know if one full burst on that wall can break the cover and kill target, OR more likely target have enough time to get out of there and attack back during the cool down.
It's also pretty random. If you pour fire into the gate, sometimes it can create a big hole enough for running through, or sometimes it's just some hole bullets can fly through, and you can not change it after that.
Phosphorus (incendiary) grenades can create fires but the fire never seem to destroy environment.