What is the relationship between stress and pressure?

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    Pressure Strain Stress
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Discussion Overview

The discussion revolves around the relationship between stress and pressure, exploring definitions, characteristics, and implications in various contexts such as materials and fluids. Participants examine the nature of internal forces, the concept of restoring forces, and the mathematical representation of stress as a tensor.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that stress is defined as force per unit area, specifically referring to internal forces between particles in materials.
  • There is a question about whether pressure is a kind of stress, with some suggesting that pressure is an isotropic part of the stress tensor.
  • One participant seeks clarification on the use of bulk and shear modulus in practical applications.
  • Another participant questions if internal forces are always restoring forces, suggesting that this may depend on the equilibrium state of the system.
  • Some argue that pressure is force per unit area, countering a claim that it could be defined as force per unit volume.
  • There is a discussion about the tensor nature of stress, with participants noting that stress can be described by six components, which vary with the orientation of the area considered.
  • Examples are provided where stress may or may not act as a restoring force, such as in the case of sound waves in fluids or stresses in a fluid under compression.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of stress and pressure, with no clear consensus reached on the relationship between the two concepts or the nature of internal forces.

Contextual Notes

Some statements rely on specific definitions and contexts that may not be universally accepted, and the discussion includes unresolved questions about the nature of restoring forces and the mathematical representation of stress.

manimaran1605
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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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manimaran1605 said:
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.
 
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Is that internal force is restoring force?If yes, Does that mean all internal forces are restoring forces?
 
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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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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BruceW said:
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.
 
AlephZero said:
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.
 

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