Afaik, humans never tried to live according to shorter or longer days so the Martian astronauts might be the first humans from Earth that have to follow a different cycle. The Martian day (Sol) is about 40 minutes longer than the Terrestrial day. Martian astronauts might take particular clocks with them that follow the Sols instead of Earth days. Was it ever tested what effects the longer days would have on their health? Perhaps Mars' low gravity would have counter-effects since the astronauts wouldn't have so much effort in the low gravity environment. I think that astronauts in space don't sleep so long as on Earth because they don't get as exhausted in microgravity as in 1 g. So the longer day might not be much of an issue for Martian visitors if they don't get so exhausted in 0.38 g. Or would it be better to land near the Martian poles to follow the Earth's cycle while having permanent day on the Mars pole?
The short answer is: probably nothing significant.
There have been multiple investigations into human circadian rhythms and their variations, especially in the absence of external clues regarding diurnal cycles and timekeeping. The best appears to be the 1974 paper by Mills et al.,"The circadian rhythms of human subjects without timepieces or indication of the alternation of day and night" in the Journal of Physiology. The net result: it varies widely from person to person, but there appears to be a lot of resilience. Many subjects naturally adopted rhythms longer than 24 hours, some significantly so. Two actually would stay awake for 24 hours, then sleep for alternating 8 or 16 hour periods.
I know several of the people who worked with Mars rovers. They had watches built to run on a Martian day! They told me the problem with trying to adopt the Mars diurnal schedule was not that the length of the cycle was troublesome, but instead was the periodic disconnect from Earth's cycle, especially the day/night cycle. Grocery shopping wasn't a problem, but living at home with people on an Earth cycle, and trying to force yourself to sleep during bright daylight hours, made for net sleep deprivation.