Pressure wave vs. Shock wave in solid body

[tricha122]

Hi everyone,

I'm having some difficulty comprehending "normal" transmission of stress/strain through a solid body and "shock" transmission of stress/strain.

Imagine I have two bodies, one rigid - the other elastic.

If the rigid body is fixed in space, and the elastic body is flying at the rigid body with velocity V

At what speed does the pressure wave transmit backward through the elastic body upon impact with the rigid plate? Does this happen at the speed of sound in the medium (i.e. C = sqrt(K/row)). What if V >> C?
or V == C?

Finally, from what I have read, the "shock wave" comes from the increase in speed of sound through the medium with increasing pressure (density?) - and so if the elastic body exhibits plasticity & is crushed as it impacts the rigid plate - do the "normal waves" at initial impact get caught up with by "normal waves" of the compressed region a few milliseconds later, to form a shock?

I could be completely off base, I'm just trying to visualize the transmission of pressure/stress/strain through the solid body under impact.

Any help would be greatly appreciated!

 

[eljose79]

Thank you for your question about the transmission of stress/strain through a solid body and the concept of shock waves. I can provide some information and clarification on these topics.

Firstly, let's define stress and strain. Stress is the force applied to an object per unit area, while strain is the resulting deformation or change in shape of the object. When a force is applied to a solid body, it will experience both stress and strain. In the case of a rigid body, the stress will be evenly distributed throughout the body and the strain will be minimal. However, in an elastic body, the stress will cause a deformation or strain in the body.

Now, let's address the concept of "normal" and "shock" transmission of stress/strain. Normal transmission refers to the gradual and continuous transmission of stress/strain through a solid body, where the stress is evenly distributed and the strain occurs gradually. On the other hand, shock transmission occurs when there is a sudden and rapid increase in stress/strain, resulting in a shock wave.

In your example of a rigid body and an elastic body colliding, the speed at which the pressure wave transmits backward through the elastic body will depend on the material properties of the elastic body. If the elastic body is made of a material with a low speed of sound, then the pressure wave will travel at a slower speed compared to a material with a higher speed of sound. This speed is often referred to as the "elastic wave speed" and is dependent on the material's stiffness and density.

If the velocity of the elastic body (V) is equal to the speed of sound (C) in the medium, then the pressure wave will travel at the speed of sound. However, if V is greater than C, then the pressure wave will travel at a speed faster than the speed of sound, and this is when a shock wave may occur. This is known as supersonic flow and can result in a sudden increase in stress/strain, causing a shock wave.

In the case of an elastic body that exhibits plasticity and is crushed upon impact with the rigid plate, the normal waves at initial impact will indeed get caught up with the normal waves of the compressed region a few milliseconds later, resulting in a shock wave. This is because the sudden increase in pressure and density in the compressed region will cause a rapid increase in the speed of sound, leading to a shock wave.

I hope this helps