# Plane stress plane strain

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.

## Answers and Replies

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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 dont get the difference between plane stress and plane strain.

Chestermiller
Mentor
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 ?

Chestermiller
Mentor
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.