# Stress, strain, pressure

## Main Question or Discussion Point

I studied that Stress is defined as Force per unit area. Force here referred to internal force between the particles in the materials per unit area. am i right?

Is pressure a kind of stress? (Internal force per unit volume) for fluids but i have studied that pressure is external force per unit volume

Give me some example what is the use of finding Bulk and Shear modulus

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Chestermiller
Mentor
I studied that Stress is defined as Force per unit area. Force here referred to internal force between the particles in the materials per unit area. am i right?
Yes.
Is pressure a kind of stress? (Internal force per unit volume) for fluids but i have studied that pressure is external force per unit volume
Pressure is an isotropic part of the stress tensor.
Give me some example what is the use of finding Bulk and Shear modulus
Look up the general tensorial equation for a Newtonian fluid in a fluid mechanics book. This equation describes the rheological behavior of gases and most liquids.

• 1 person
Is that internal force is restoring force?If yes, Does that mean all internal forces are restoring forces?

sophiecentaur
Gold Member
This is just a matter of definition, surely. A force would only be described as a 'restoring force' if you were dealing with an equilibrium situation i.e. when there are no external applied forces or when your system consists of balancing stress and applied forces.

Pressure is not force per unit volume. It is force per unit AREA.

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• 1 person
BruceW
Homework Helper
yeah. and (I think) the stress IS the entire internal force per area at some given point. (i.e. not including 'body forces' like gravity). So it is quite general, and in a general case, it will not be a restoring force. But for an example, if you have a (linear) sound wave moving through some fluid, then I guess this is an example of when stress can be a restoring force.

edit: an example of when an internal force is not a restoring force: uh... let's say we have some fluid inside a closed cylinder, if we push one wall inward, there will be stresses inside the fluid, which propagate through the fluid (starting from the moving wall). These stresses act to change the system, so that it goes from lower density to higher density throughout the fluid.

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AlephZero
Homework Helper
yeah. and (I think) the stress IS the entire internal force per area at some given point.
In general (as chestermiller implied) stress is a tensor, described by 6 components (3 for direct stress and 3 for shear stress). These 6 components describe the "force per unit area" on an "area" that is in any orientation through a point in the body, and in general the force will be different depending on the orientation of the area. (I'm not sure if that's what you meant by the "entire internal force").

The idea of "stress = force per unit area" is often used as an explanation of the concept of stress for beginners, in simple situations like the tension in a string or rod, when 5 of the 6 stress components are zero, and the "area" is perpendicular to the non-zero stress component.

"Internal pressure" is the special case where the 3 direct stress components are equal, and the 3 shear components are all zero. In that case, the "force per unit area" is independent of the orientation of the "area" in the body.

BruceW
Homework Helper
These 6 components describe the "force per unit area" on an "area" that is in any orientation through a point in the body, and in general the force will be different depending on the orientation of the area. (I'm not sure if that's what you meant by the "entire internal force").
yeah, I didn't mention the tensor aspect, since I'm guessing the OP is not on to that stuff yet.