Will a body start to deform if it is accelerating very fast? I had a question in my mind that when a body will start accelerating in outer space where there is vacuum and no other object to hit the accelerating one, then will that body start to deform? I mean at lower accelerations we can't feel it nor see it but I think that when the body is very highly accelerated then it should start to deform in some way. I don't know if I am right in thinking so. Your answers would be of much help to me.
 A: Something is applying a force to the object, so yes, there will be distortion.
Either the force is a contact force, and the action of the force has to be transmitted throughout the solid.  Or it's a non-contact force like gravity, in which case every part of the object will experience a different force.  You will point out to me that a constant, uniform force applies to all parts of the object equally.  Then I will point out to you that uniform forces are unphysical.  They don't exist, although you can set things up so that the force is constant to within your equipment's ability to measure the force.
Finally, it doesn't matter whether the acceleration is fast or slow.  I would then ask you what is fast and what is slow.  You would respond "Slow is slow enough that my equipment can't measure the distortion."   Fair enough.  But that's not a distinction made of fundamental physics, that's a distinction made by the quality of your equipment.
A: Yes. Easy evidence is right here on earth, when you shoot a bullet from a gun at a steel plate. The bullet is very strongly (de)cellerated, and squishes into a pancake that then flies to bits.
Less extreme examples abound. For instance, when a piece of sheet metal is bent, the bend zone heats up a bit from what is called internal friction. If you bend the sheet metal very quickly, there is no time for the heat generated by "working" the metal to diffuse out of the metal and that heat then softens the metal, making it easier to deform where it is being bent. In this way, deep-drawn metal shapes can be bent out of sheet metal by a process called high energy-rate forming.
Ever wonder how seamless aluminum beer can bodies are made? Same idea, only the process is called impact extrusion. you place a little pellet of aluminum in the bottom of a hard steel cavity and then smash it with a cylindrical piece of steel that fits into the cavity. The impact acceleration is so great that the solid aluminum flows almost like water up the sides of the cavity and fills the space between the cavity and the impactor.  then you extract the impactor and pull the seamless beer can body out of the cavity.
A: Yes. As shown here a person for example is compressed when stand up, compared to lying down.
The situation is similar in a rocket in space. While the motors are turned off, it is like lying down in earth, there is no compressive force for any body orientation.
If the motors are on, the crew starts to feel an acceleration, that can be for example $g = 9.8m/s$. In this case the body is compressed in the same way of the video for someone 'stand up' in the spaceship.
