Are Principal Strains Always Tensile/Compressive or Can They Be Shear?

[kini.Amith]

Are principal strains necessarily tensile/compressive or can they be shear strains also? And are the principal strain planes parallel to principal stress planes at a point?

 

[boneh3ad]

By definition, principle stresses are normal in nature and not shear and are normal to the principal planes.

 

[kini.Amith]

I thought by definition principal strains were just the maximum strains at a point and the fact that they are normal to principal planes is not so obvious. My textbook even has a formal derivation just to prove that the principal strains are orthogonal.

 

[boneh3ad]

The idea is that in any compatible stress/strain field, you can find a coordinate system in which the only stresses are normal. These stresses are the principal stresses and are orthogonal. By definition, then, they are tensile rather than shear in nature.

 

[PJC01]

Principal strains refer to the maximum and minimum normal strains that occur in a material at a specific point. They are not necessarily tensile or compressive strains, as they can also be shear strains. Tensile and compressive strains refer to the stretching and squeezing of a material, while shear strains refer to the distortion of a material in a perpendicular direction.

The principal strain planes are not always parallel to principal stress planes at a point. This is because strain and stress are not always directly related. In some cases, the direction of the principal strain may be different from the direction of the principal stress.

However, in certain materials such as isotropic materials (materials with the same properties in all directions), the principal strain planes will be parallel to the principal stress planes. This is due to the symmetric nature of the material, where any direction can experience the same amount of strain and stress.

In summary, principal strains can be both tensile/compressive and shear strains, and the orientation of the principal strain planes may or may not be parallel to the principal stress planes, depending on the material's properties. It is important for scientists to understand the nature of principal strains in order to accurately analyze and predict the behavior of materials under different loading conditions.