At about 1425 Central time, the airplane was substantially damaged while landing. The Private pilot, Flight Instructor and passenger were not injured. Visual conditions prevailed. Upon returning from the practice area, the pilot performed a touch-and-go landing and proceeded around the traffic pattern for a second landing. Prior to touchdown, the pilot and instructor verified the landing gear was extended by performing a visual check via a wing-mounted mirror and also by observing the illuminated green landing gear light. Shortly after touchdown, the right landing gear gave way and the right wing began to descend. The pilot attempted a go-around but the airplane “would not fly” and slid to a stop in the grass near the runway. The airplanes right wing and right aileron sustained structural damage.