# Plane stress plane strain

In summary, 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. plane strain applies to a solid in which one of the principal strains is zero (typically as a result of the imposed boundary conditions).

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 ?

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 ?

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.

## 1. What is the difference between plane stress and plane strain?

Plane stress and plane strain are two conditions used to describe the deformation of a material under stress. In plane stress, the material experiences stress in two dimensions, while in plane strain, the material experiences stress in all three dimensions. Essentially, plane stress occurs when the stress is restricted to one plane, while plane strain occurs when the stress is distributed throughout the entire material.

## 2. What types of materials experience plane stress and plane strain?

Plane stress and plane strain can occur in any material, but they are most commonly observed in thin materials, such as sheets, plates, and shells. These materials are more susceptible to bending and deformation in two dimensions, leading to the conditions of plane stress and plane strain.

## 3. How do engineers account for plane stress and plane strain in their designs?

Engineers use mathematical models, such as the theory of elasticity, to analyze and predict the behavior of materials under plane stress and plane strain conditions. They also consider the material properties, loading conditions, and geometry of the structure to determine how it will respond to these types of stress.

## 4. Can plane stress and plane strain occur simultaneously in a material?

Yes, it is possible for a material to experience both plane stress and plane strain at the same time. This can happen when the material is subjected to a combination of loads and constraints that result in stress in multiple directions.

## 5. What are some real-world applications of plane stress and plane strain?

Plane stress and plane strain have many practical applications in engineering, including the design of aircraft structures, bridges, and pressure vessels. They are also important in the analysis of geological formations and the behavior of materials in manufacturing processes.