How would I achieve this realistically?
This is a very complex question due to deformation in itself is a complex subject in physics. Applying this a to 3D game is even harder because you have to think about optimization and implementation.
You could simplify things by just using UE4s collision handling and then use the force to move vertices in opposite direction as of the collision normal. This could be quite easy, but it would not be realistic.
Here is an interesting source to read if you feel like you have the time and guts:
http://www.researchgate.net/publication/220982525_D4MD_deformation_system_for_a_vehicle_simulation_game