The flight instructor reported that, while returning to the departure airport after an instruction flight, she noticed that the weather was deteriorating and decided that she would perform the landing. She added that she felt windshear during the approach and she flew the airplane about 5 to 10 knots faster than normal. During the landing, she "felt a strong push from behind that accelerated the plane tremendously." She applied full brakes, the airplane continued moving forward, approaching and leaving the end of the runway. Concerned the airplane would impact a deep ditch, the flight instructor turned the airplane to the left, collapsing the right main landing gear and coming to rest on the grass. The airplane sustained substantial damage to the left and right wing. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. An automated weather observation station, located 4 miles north, reported that, about 11 minutes after the accident, the wind was calm with light thunderstorm rain. The airplane was landing on runway 18. Additionally, at 45 past the hour, thunderstorms and cumulonimbus clouds were reported in the area with peak wind gusts from 240° at 29 knots.