The pilot of the experimental light sport airplane was performing touch and go takeoffs and landings in the airport traffic pattern. He stated that the second landing was "hard," but he continued the flight and performed a third takeoff and landing. The third landing was also hard, and the airplane bounced. The nose landing gear separated, and the airplane departed the runway and came to rest in the grass, resulting in substantial damage to the fuselage. The pilot reported there were no mechanical malfunctions or anomalies that would have precluded normal operation of the airplane.