B777-200 First Officer reported tow bar jackknifed and snapped flattening a nose tire during push back. Flight was towed back to the gate.

Narrative

My memory of the event; which was normal ops right up until the tow bar snapped is as follows: We were having a normal day; no weather or maintenance issues to speak of in ZZZ; we readied the aircraft for pushback in accordance with flight manual. Captain contacted ground crew and did his normal coordination. I called and got us clearance from ZZZ ground control to do pushback at Gate XX in ZZZ per the Jeppesen charts. Captain passed to the ground crew we were cleared to pushback onto Taxiway 1; then as we were pushing back and starting to angle from Gate XX onto Taxiway 1we heard a soft clunking noise which is not unusual as the tow bar and nose gear maneuver the aircraft. However; quickly following that initial noise that caused us to look at each other but not immediately react; we felt the aircraft start to move slowly again. I initially assumed we were continuing pushback; we had not received any communication from ground crew regarding any problem. Then rather quickly more noises were heard; we felt a jolt and heard a yell over the interphone; it was just a yell; no one said 'set brakes'. But it was now abnormal enough that the Captain did feel something was wrong and set them. That part all happened within about five seconds. The Captain then called them multiple times asking what was going on; with no response. I estimate within 10-30 seconds we got the EICAS message TIRE PRESSURE; which made the situation obviously abnormal; I looked around outside the aircraft to see multiple ramp members/marshallers standing in normal wing walker positions and looking at the aircraft; but as I told the Captain no one appeared to be panicked or running in to provide assistance or acting overtly like there are an accident or continuing circumstance that needed us to do anything else. No one was really looking to us in the cockpit at all as we waited for an answer; the Captain made multiple solicitations for information from our pushback crew or guidance over interphone. We had the APU running; but had not started engines at this time. From upstairs we could tell the aircraft had settled slightly due to the zero tire pressure indicated on the GEAR display on EICAS. After a short while someone came back on the interphone and asked to confirm the brakes were set. The parking brake was set and we confirmed this with the individual. We were informed the right nose tire was flat; the tow bar had snapped and broken away from the tug tractor. The Captain inquired if anyone had been hurt and they said the tow crew was very shaken up and the driver had perhaps hurt her hand but was overall okay; no severe injuries. The ground crew then informed us they'd start working to bring over the tug tractor that could lift the nose tire off the ground and tow us back to the parking place. Once that different tug arrived; they discovered its sensors would not allow it to connect to our aircraft due to the damage done.From here the Captain and ground crew discussed our options of getting off the aircraft or waiting upstairs as they'd need to bring out supervisors and change the tire on Taxiway 1 also. The Captain confirmed with them that they could handle the situation without us onboard and stairs were brought up to the right side of the aircraft to allow us to exit and look. Once we got downstairs we could see the right nose tire was popped and the right nose gear door had contacted something. When I asked the crew downstairs they said it had run into the tug tractor cab; I never saw this part as the original tug tractor was removed and the new one brought in before we were able to exit the aircraft. The tow bar that was involved had also been removed by the time we were downstairs via a forklift.Later talking to the ground crew inside ops; it sounded like the instructor/supervisor in the tug cab at the time it happened felt it was as they made the turn from gate XX to Taxiway 1 AND proceeded to push slightly up hill the bar became jackknifed. That is why it snapped and took away part of the tug tractor as well. It also sounded like they were lucky the tug tractor had a cab with a window structure; because something struck the cab of the tow tractor and shattered the window. Cause: Ground crew training or experience Suggestions: Better training.