## Main Difference – Stress vs. Strain

When deforming forces act on an object, they can change the object’s shape. The **main difference** between stress and strain is that** stress measures the deforming force per unit area of the object**, whereas **strain measures the relative change in length caused by a deforming force**.

## What is Stress

Whenever a force attempts to deform an object, we say that the object is under stress. Stress is **defined as the deforming force per unit area of the object.** Since we can resolve any force on an object into directions parallel and perpendicular to the surface, we define **normal stress** to be equal to the force *perpendicular to the surface* per unit area. Similarly, we define **shear stress** as the force *parallel to the surface * per unit area. If the force acting on a surface is and the area of the surface is , then the stress is given by:

Stress has the same dimensions as pressure, so the units used for measuring stress are also N m^{-2} or Pa (1 Pa=1 N m^{-2}). When forces act to lengthen the material, the stress is referred to as **tensile stress**. When the forces try to compress a material, the stress is referred to as **compressive stress**.

## What is Strain

Strain measures the **amount of relative deformation caused by a force acting on an object**. For simplicity here, we will only consider the **normal strain**, created by normal stress. Suppose the original length of the object is and due to stress, the length changes to . The *change* in length is . The strain is then given by,

Since strain is given by a fraction where the numerator and denominator both have units of length, the strain itself has no units. i.e. it is a “dimensionless quantity”. It is common to see strain expressed in terms of percentages.

## Stress vs. Strain Curve

We can draw a graph of how the strain in a body changes as we vary the stress acting on the object (this can be done, for example, by adding weights). These graphs, called **stress vs. strain curves**, reveal lots of information about the nature of the material that the object is made of. The figure below shows the typical stress-strain curve for a ductile material (“ductile” means that the material can be stretched out well):

The gradient of the elastic region of the curve is called the **Young Modulus**. This is a very important number for materials engineers, as it gives how much strain would be caused by a given stress in a material.

## Difference Between Stress and Strain

### What it Measures

**Stress** gives the force acting per unit area of an object.

**Strain **gives the relative change in length due to deforming forces.

### Units

**Stress** is measured in pascals (Pa).

**Strain** has no units; it is simply a ratio.

**Image Courtesy**

“Typical Stress vs. Strain diagram for a ductile material (e.g. Steel).” by Breakdown (Own work) [], via (Modified)