Grumman AA5 Instructor pilot reported a runway excursion during a training flight at a non-towered airport due to improper flight control rudder inputs by the student during landing. The aircraft struck a concrete barrier damaging the aircraft. The Instructor and student evacuated safely.

Narrative

On Day 0 I was conducting Flight training as a CFI in my personal airplane a Grumman AA5. The student and I departed ZZZ to conduct some basic flight maneuvers then returned to the airport to do some takeoff and landings. When entering the downwind there was a Piper Comanche taking the runway that called an aborted takeoff. As we were turning onto our base turn the pilot of the Comanche said he 'needed some time' and then stated he would exit onto the closed runway. We briefed a touch and go. After a normal landing my student applied full power and stomped on the left rudder pedal as I was calling for right rudder. I attempted to override his inputs which was very difficult as we started to veer off the runway he froze up on the controls. I was able to apply brake pressure but we had exited the runway on the grass and I realized the aircraft was heading directly towards the parked aircraft on the closed runway and we were not stopping. I had gained control of the aircraft from the student and was faced with two choices; hitting the other aircraft or a concrete barrier that had been erected on the closed runway. I chose the barrier as the better of the two because I knew we could not maneuver back to the right onto the runway. We hit the barrier and damaged the aircraft. Neither of us were hurt and exited the aircraft without assistance.