The pilot was making a wheel landing to a smooth dry grass runway in a tail-wheel equipped airplane. Immediately after touchdown the nose began to pitch down and the pilot's corrective inputs were unsuccessful. The propeller contacted the ground, the tail came up, and the airplane flipped and came to rest inverted. The impact resulted in substantial damage to the left wing, left strut, left aileron, vertical fin and rudder. The pilot reported that he did not react quickly enough to the downward pitching attitude.