Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?

When we push the rock and fail to move it. Some of our energy is absorbed by the rock in the form of potential energy and the rest of our energy is goes to environment through our muscles and the surface between the rock and out hand. 

When we push a huge rock, there is no transfer of muscular energy to the stationary rock. Also, there is no loss of energy because muscular energy is transferred into heat energy, which causes our body to become hot.

When we push a huge rock, then the rock also exerts a huge force on us according to Newton’s third law of motion. The muscular energy spent by us in the process is used to oppose the huge force acting on us due to the rock.