According to the flight instructor, the purpose of the flight was to complete recurrent training in the airplane. While on the downwind leg of the traffic pattern, the flight instructor configured the airplane for a simulated engine failure maneuver. The airplane was about a quarter mile from the runway on the base leg of the traffic pattern and the ground proximity warning system announced “500 feet.” As the pilot turned the airplane onto the final leg of the traffic pattern, the airplane overshot the centerline and it began to descend about 200 feet per minute. Then, about 150 feet above ground level, the pilot began to add power, but the airplane continued to descend and subsequently impacted the runway and bounced. The pilot recovered the airplane from the bounce, proceeded to takeoff and flew the airplane around the pattern. The occupants of the airplane noted that the left wing was bent and witness told them that the left main landing gear was bent. During the landing, the airplane veered off the runway and came to rest in a grassy area. During the accident sequence, the airplane incurred substantial damage to the left wing. The flight instructor reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.