GA instructor pilot reported while training in the VFR pattern they noticed an aircraft on the EFB in the pattern not transmitting on the CTAF. The other aircraft remained in the pattern and made an opposite direction approach that resulted with the crew taking evasive action to avoid a NMAC between the aircraft. Both aircraft landed safely at the airport.

Narrative

I was the instructor pilot in Aircraft X in a formulated instructional flight with routing to 5r4 for touch and goes. Upon arrival; another aircraft was in the pattern; established runway 36. After one landing; winds did note to favor 18 slightly; but still a crosswind.After 3 touch and goes; I noticed on the EFB; Aircraft Y has appeared behind me on the left downwind for 36; as I was on base. I have never heard any radio calls from this airplane; and called it out to the crew. We continued on final and made more advisory calls. The airplane then descends from its established downwind; to cross midfield for runway 36; below traffic pattern altitude. On short final; I note the aircraft low and crossing shortly above. Upon touch and go; I make additional radio calls about the take off due to the confusion of the situation.Aircraft Y; makes for a immediate turn to right downwind runway 18; approx 500 MSL; near approach end. Without radio calls; it then makes a left 180 for the opposite; non active runway. Due to the timing of the situation; I was 300 ft MSL for the upwind 36; and opposing aircraft was established for its short approach; base to final runway 18. I take evasive action of greater than 30 degrees AOB (Angle of Bank); and start an early crosswind to avoid midair.I state on the radio during the evasive maneuver; that the aircraft not making radio calls; is turning into me and to watch out. No response was ever made from Aircraft Y. I stayed in the downwind circling until opposite traffic had decided to back taxi on the runway; and clear the opposite direction runway.After inspection of Aircraft Y; has ferried from a nearby airport; never got above 850 ft its entire flight of 8 minutes. Issue seemed to be complacency of that local aircraft in familiarity; over comfort with the area; lack of proper pattern entries; CTAF calls; and non standard; improper traffic pattern procedures. As well as lacking hazard avoidance with negligence.