Solving Stress and Strain: A Guide to Understanding

[aaaa202]

I am so confused about these quantities. For many theoretical setups you assume a linear relation (elastic materials) such that for example if you press on the side of a rectangular box, it makes the box contract in the normal direction to the induced stress. Also the box will expand in the tranverse directions.
But this is a weird setup to me. In reality if the only force acting on the box is the one you induce on the side then it will start to move according to Newtons 2nd law...
So for the above to hold you must have that their is a force balancing the stress you induce, which would the friction with the ground. But doesn't this in turn create a shear stress in the box? And what about the expansion of the box in the direction normal to the ground. How will the ground respond to this?
I am also very confused about the stress tensor. Does it give us the force acting on any surface dS inside a body or does S only refer to the physical surface of the body we are looking at?

 

[mfb]

For the example you gave, you usually press from both sides in a symmetric way.
If you don't do that, the block will accelerate, that gives a similar but not identical situation if there are no other forces acting on it.

 

[Chestermiller]

I am so confused about these quantities. For many theoretical setups you assume a linear relation (elastic materials) such that for example if you press on the side of a rectangular box, it makes the box contract in the normal direction to the induced stress. Also the box will expand in the tranverse directions.
But this is a weird setup to me. In reality if the only force acting on the box is the one you induce on the side then it will start to move according to Newtons 2nd law...

So?

So for the above to hold you must have that their is a force balancing the stress you induce, which would the friction with the ground. But doesn't this in turn create a shear stress in the box?

Yes. So?

And what about the expansion of the box in the direction normal to the ground. How will the ground respond to this?

It doesn't have to respond much. The box can grow by the top surface rising.

I am also very confused about the stress tensor. Does it give us the force acting on any surface dS inside a body or does S only refer to the physical surface of the body we are looking at?

Any surface within the body and the physical surface. And, it can vary with spatial position within the body.

Chet