The pilot reported that during the takeoff roll on a rough turf runway the airplane bounced and swerved to the right. The pilot corrected for the swerve when the airplane bounced a second time and despite his inputs, the airplane departed the left side of the runway. The right wheel encountered a depression and collapsed; subsequently the right wing struck the ground and sustained substantial damage. The pilot reported no preimpact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.