The pilot reported that the airplane's engine lost power and began shaking violently as the airplane was approximately mid-field downwind for landing. He stated that he had insufficient altitude to execute a power-off landing to the runway and elected to land the airplane in a farm field. He said that he flared the airplane and as the airplane settled into the corn, he applied full aft elevator but the airplane pitched nose down and flipped onto its back. He stated that he had performed a pre-flight engine run-up before the accident. He made no mention of any discrepancies noted during the run-up, takeoff, or initial climb out.