Understanding Stress and Strain: The Relationship Between Two Variables

  • #1
tellmesomething
65
9
I was going through the stress-strain curve and I realized that strain is taken as the independent variable and stress as the dependent variable. In reality is this true or is it the other way around?I saw a lot of answers on Quora that say that strain is the cause and stress is the effect. But I found answers on PSE that cite the exact opposite.

Intuitively I would think that more change in dimensions (strain ) on attaching some load would mean more restoring force per unit area(stress) but I might be wrong as I must admit my fundamental understanding of stress & strain is still very dusty.

Can someone help me out?
 
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  • #2
In the analysis it actually doesn't matter. If you 'apply a strain' (mathematically) a stress will follow, and vice versa. However, in reality you can only interact with any body by surface forces (two bodies interacting, or a body and a fluid/gas) or volume forces (magnetic force, gravity force, inertial forces if you're analyzing in a non-inertial frame of reference, etc.). The surface forces apply a stress resulting in a strain. The volume forces apply... well... now it's semantics, I wouldn't say a volume force applies a stress (different units), but rather a force per volume... It does result in both a stress and a strain however (also depending on the boundary conditions applied...). In reality you cannot 'apply a strain'.

[edit]
I actually notice the semantics discussion when applying a 'volume force'. But a 'surface force' is actually a stress, in continuum mechanics you cannot apply a force directly, it is always a stress.
[/edit]
 
Last edited:
  • #3
Arjan82 said:
In the analysis it actually doesn't matter. If you 'apply a strain' (mathematically) a stress will follow, and vice versa. However, in reality you can only interact with any body by surface forces (two bodies interacting, or a body and a fluid/gas) or volume forces (magnetic force, gravity force, inertial forces if you're analyzing in a non-inertial frame of reference, etc.). The surface forces apply a stress resulting in a strain. The volume forces apply... well... now it's semantics, I wouldn't say a volume force applies a stress (different units), but rather a force per volume... It does result in both a stress and a strain however (also depending on the boundary conditions applied...). In reality you cannot 'apply a strain'.
But you can apply a displacement, which results in both strain and stress.
Arjan82 said:
[edit]
I actually notice the semantics discussion when applying a 'volume force'. But a 'surface force' is actually a stress, in continuum mechanics you cannot apply a force directly, it is always a stress.
[/edit]
 
  • #4
In reality, you can apply stresses and displacement at the boundaries of a body. The displacement variations internal to the body determine the stresses, and the stresses have to satisfy the stress-equilibrium equations. So in most complicated situations, you will be solving for the displacements as a function of spatial position with a body.
 
  • #5
Arjan82 said:
In the analysis it actually doesn't matter. If you 'apply a strain' (mathematically) a stress will follow, and vice versa. However, in reality you can only interact with any body by surface forces (two bodies interacting, or a body and a fluid/gas) or volume forces (magnetic force, gravity force, inertial forces if you're analyzing in a non-inertial frame of reference, etc.). The surface forces apply a stress resulting in a strain. The volume forces apply... well... now it's semantics, I wouldn't say a volume force applies a stress (different units), but rather a force per volume... It does result in both a stress and a strain however (also depending on the boundary conditions applied...). In reality you cannot 'apply a strain'.

[edit]
I actually notice the semantics discussion when applying a 'volume force'. But a 'surface force' is actually a stress, in continuum mechanics you cannot apply a force directly, it is always a stress.
[/edit]
Sorry for the late reply. I was just thinking for the tensile test from which we get the
stress vs strain grapph there we measure the stress according to the elongation hence the graph where strain is the independent variable and stress the dependent one. Also how can we apply stress? Isnt it a reaction developed inside the body in response to the external applied force.
 
  • #6

Chestermiller said:
In reality, you can apply stresses and displacement at the boundaries of a body. The displacement variations internal to the body determine the stresses, and the stresses have to satisfy the stress-equilibrium equations. So in most complicated situations, you will be solving for the displacements as a function of spatial position with a body.
how can we apply stress? isnt it a response developed inside the body to the applied force
 
  • #7
tellmesomething said:
how can we apply stress? isnt it a response developed inside the body to the applied force
We can apply it at the surface only, as a distributed force.
 
  • #8
tellmesomething said:
Intuitively I would think that more change in dimensions (strain ) on attaching some load would mean more restoring force per unit area(stress) but I might be wrong as I must admit my fundamental understanding of stress & strain is still very dusty.
Please, see:
https://en.wikipedia.org/wiki/Stress–strain_analysis

https://en.wikipedia.org/wiki/Stress_(mechanics)

https://en.wikipedia.org/wiki/Strain_(mechanics)

External load ⇒ Deformation ⇒ Internal forces ⇒ Internal stress
 
  • #9
"Quora that say that strain is the cause and stress is the effect. But I found answers on PSE that cite the exact opposite."Stress and strain appear at the same time not one after another. How can there be a causality relation between them? You can plot whichever you want on the horizontal axis, causality has nthing to do with it.
 
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  • #10
tellmesomething said:
how can we apply stress? isnt it a response developed inside the body to the applied force
We can apply it at the surface. It is the force per unit area applied at the surface. Do you think that only point force can be applied at a surface?
 

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