Papadopoulos has primary research and teaching interests in mechanics, including nonlinear structural analysis, computational mechanics, and biomechanics. He is also active in engineering education and engineering ethics, particularly in the subjects of mechanics education and appropriate technology. At UPRM Papadopoulos serves as the coordinator of the Engineering Mechanics Committee in the Department of General Engineering. He also co-coordinates the Social, Ethical, and Global Issues (SEGI) in Engineering Program and Forums on Philosophy, Engineering, and Technology.