The student pilot and his flight instructor were on an instructional flight when the airplane suddenly veered to the right upon landing. The flight instructor stated that his student had simply lost control upon touchdown. The flight instructor reported that he took control of the airplane from his student, but he was unable to regain directional control of the airplane before it departed off the right side of the runway and nosed over. The engine mount, left wing strut, left wing main spar, vertical stabilizer, and the rudder were substantially damaged. The flight instructor reported no mechanical malfunctions with the airplane that would have precluded its normal operation. The student pilot reported that they had completed 3 uneventful landings before the accident. The student pilot had observed some stiffness in the rudder system during his preflight inspection, the rudder did not self-center while on the ground at slow speeds, and that the cockpit floor carpet was loose and had to be repositioned several times during the flight. An examination of the airplane wreckage revealed impact-related damage to the rudder that precluded its movement, but there were no additional flight control issues observed. Examination revealed the cockpit floor carpet was loose and bunched-up, but it could not be determined if it had contributed to the loss of directional control or had become unsecured while the pilots made their emergency exit following the accident.