C172 flight instructor reported an engine failure in flight and a subsequent off field landing resulted in no injuries or damage to the aircraft.

Narrative

At approximately XA30 zulu I conducted a flight that resulted in a loss of engine power in flight. The flight was a training lesson with a pre-solo student. We took off around XB30 local time and proceeded from ZZZ to the northeast to our practice area. Upon departing to the northeast we received flight following with ZZZ Approach for our VFR maneuvers in the local area. We proceeded approximately 8-12 miles northeast of ZZZ where we did a series of ground reference maneuvers at 2500 ft. MSL. After performing ground reference maneuvers we started a constant airspeed climb at 75 kts. to an altitude of 4000 ft. MSL. At 4000 ft. MSL we set up for slow flight and a power off stall. We then did an unusual attitude recovery. After unusual attitude recovery practice we then did a series of power on stalls at 4000 ft. MSL. We performed 4 power off stalls and activated the carburetor heat anytime the power was outside of the green arc. We then turned the carburetor heat on and reduced power to 1800 RPM where we descended at 500 FPM for approximately 1 minute.Once at 3500 ft. MSL I reached over and retarded the throttle to idle to simulate an engine failure. Upon reducing the throttle to idle the carburetor heat was still on. I then asked my student 'what do we do if we have an inflight engine failure?' they stated that we start with the checklist; I then corrected them and stated that we pitch for maximum lift/drag speed which is 65 kts. We then chose the best field to hypothetically land in. I then noticed that I could see the shape of the propeller turning instead of the typical blur of a turning prop. I immediately looked at the tachometer and we had less than 400 RPM. I immediately advanced the throttle forward and there was no increase in RPM. I then verbally announced to my student that 'I have flight controls'. As I took over flight controls we were already trimmed for 65 kts. and had a field selected. At this point we are at approximately 3000 ft. MSL and I start the engine restart procedure and confirm with the checklist. I checked the fuel selector valve to both (it was already on both); mixture rich (already rich); carb heat on (still on); fuel primer locked (still locked in place); and then I turned the key form both to start. The propeller was windmilling and I tried the starter 3 times.I then let ZZZ Approach know that we had lost engine power and we were circling a field. Approach asked how many souls and fuel. I stated that we have 2 souls and 30-35 gallons of fuel. We were at approximately 2500 ft. MSL (approximately 1000 ft. AGL) on a downwind for the selected field. I then asked ZZZ Approach what the winds were at ZZZ. Approach stated the winds were 150 degrees and I cannot recall the velocity. I determined that the engine would not be able to be restarted in flight. I then focused on securing the cabin. I turned the fuel selector valve off; pulled the mixture to cut off; turned the ignition key to off and removed the key; and unlatched my door and told my student to unlatch their door. I then turned base and added flaps as necessary. Upon turning final we had the field made and I made a call to ZZZ Approach and told them that we will be landing in a field and this would be our last call. I then turned the master switch off. I landed on a grass field that was approximately 2500 ft. long and used a soft field landing technique. Once we safely rolled to a stop we evacuated the airplane. There was no damage to the airplane and no injuries.