What is the Difference Between Plane Stress and Plane Strain?

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Discussion Overview

The discussion centers on the differences between plane stress and plane strain, exploring their definitions, implications, and relationships. Participants seek clarification on whether one condition implies the other and under what circumstances.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant requests clarification on the difference between plane stress and plane strain, indicating a lack of understanding of the terms.
  • Another participant provides basic definitions of stress and strain, including relevant equations for axial forces, but does not directly address the question about plane conditions.
  • A participant explains that plane stress applies to a material where the stress in the thickness direction is negligible, while plane strain applies to a solid where one principal strain is zero due to boundary conditions.
  • Some participants suggest that plane stress can imply plane strain in specific situations, but this is not universally applicable.
  • Further clarification is provided that in plane stress, one principal stress is zero, while in plane strain, one principal strain is zero, emphasizing the dimensional aspects of each condition.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the implications of plane stress and plane strain on one another, with some suggesting conditional relationships while others highlight the lack of a universal implication.

Contextual Notes

Participants have not fully resolved the conditions under which plane stress may imply plane strain, nor have they agreed on the definitions' implications in all scenarios.

akhadima
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Hello everybody,

Can you please tell me what's the difference between plane stress and plane strain ? Does one imply the other ? For example, does plane stress imply the plane strain ?

Thank you in advance.
 
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sigma = E * epsilon

stress (sigma) = F / A

strain (epsilon) = delta L / L

E = Young's modulus

The equations above are for bars with axial forces applied.

stress is force per unit area

strain is the amount an object deforms under stress

There are similar analogies for bending and shearing
 
Thank you Steamking,
Actually my question is about "plane". I know the definitions of strain and stress, but I don't get the difference between plane stress and plane strain.
 
Plane stress applies to a sheet of material in which the stress in the thickness direction is much much lower than the stresses within the plane. The stress in the thickness direction is taken as zero.

Plane strain applies to a solid in which one of the principal strains is zero (typically as a result of the imposed boundary conditions). For example, if you had a sheet of material that could not strain in the thickness direction (constrained by boundaries above and below), and if the shear stresses imposed by these boundaries were also zero (slippery interface), you have a plane stress situation.
 
So plane stress can imply plane strain in particular situations but not always. right ?
 
akhadima said:
So plane stress can imply plane strain in particular situations but not always. right ?

Well, if there is no deformation, then the stresses and strains are all zero. So I guess this counts as one of those situations.

Let me say it a different way. In plane stress, one of the principal stresses is equal to zero throughout the deforming body, and in plane strain, one of the principal strains is equal to zero throughout the body. Plane strain is basically a 2 dimensional deformation, in which the displacements and strains in the third dimension are zero (although the stress in the third dimension is not). Plane stress is for the most part a 2 dimensional deformation, although, in this case, the strain in the third dimension is such that it causes the stress in the third dimension to be zero.
 

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