I was wondering if the use of trench warfare was deployed during WW2. If so, please include which countries and why trench warfare did not continue as a major military doctrine after WW1.
Trenches were used during the Second World War but they were never a permanent fixture like they were during the First World War. By the end of the First World War, the tank had begun to emerge as a weapon of breakthrough, one against which trenches were virtually useless. That war ended before tanks could really be utilised independent of other arms.
By the time of the Second World War, tanks had become more reliable, more heavily armed and armoured and perhaps most importantly, far faster. This allowed tanks to be used to quickly advance and overrun entrenched, static positions such as trench lines. Tanks could be countered with anti-tank guns but these could be in turn countered with artillery which had been motorised by that point so could advance closely behind tanks and infantry to be used against enemy strongpoints. Additionally, the use of airpower and tactical bombing severely reduced the effectiveness of trenches as static defensive positions.
War from 1939-1945 was one of mobility with only brief static periods. Defence shifted from the holding of a front line to a doctrine of withdrawal and counterattack to retake lost ground.