# SOLIDWORKS Simulation: What is Stress and Strain?

Stress and Strain are the two building blocks of structural analysis. They are what we use to understand where a component is in relationship to material failure, sharing a close relationship. So close that sometimes their definitions both contain each other making it difficult to understand them individually. What they have in common is:

1. Stress and Strain are both responses to applied loads on a structure.
2. Stress and Strain are both measurements to determine material failure criteria and behavior

Now let’s talk about where they are different. Stress is the measure of internal pressures distributing within the system, while strain is a measure of geometric response and the change in shape due to applied forces. Visually strain is easy to understand. Look at the image below.

If you think of anything you can as being a material spring, strain is simply the distance the spring stretches when pulled, divided by its original length.

Straight-Forward Equation

Strain = Change in Length from Applied Force/Original Length

Mathematical Notation

ε = Δl/l (unitless)

Stress is the pressure a material is seeing in response to a load. The load distributes itself throughout a material based on the stiffness. If you look at the examples below, you will see the first one is a balanced load, evenly distributed accross the end face, resulting in a nearly constant stress across the entire part. In the second case, the load has been shifted entirely to the top edge. This causes the stress (or internal pressure) to redistribute itself in a non-uniform manner to balance out that load.

Straight-Forward Equation

Stress = Force/Area (Units of Pressure)

Mathematical Notation

σ = F/A (Units of Pressure)

Relationship between stress and strain

As I mentioned earlier, stress and strain are linked together. The ratio that binds them together is the Elastic Modulus or Young’s Modulus, which changes by material. Let me illustrate this principle with an image.

In the image above, you can see that in the elastic range, the Modulus is constant, once you go past that, then you start to deal with a modulus that is dependent on the strain level.

By: Brandon Donnelly, Simulation Applications Engineer

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