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:

- Stress and Strain are both responses to applied loads on a structure.
- 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. This starts to become a complex topic of discussion, beyond the scope of a simple blog.

If you would like to learn more about Stress Analysis and how it relates to the parts you design, I encourage you to come to our **Engineer 3D!** User Conference in April. While attending, sign up for my presentation called **Understanding Simulation Results.**

*By: Brandon Donnelly, Simulation Applications Engineer*

**Session:**Understanding Simulation Results

**Session Description:**Many people use simulation software, fewer understand how to make the most of what the software is showing them. If you know how to use simulation software, but are less comfortable analyzing the results, this session is for you. Attendees will learn how to analyze simulation results for stress, heat, frequency, and more. Even if you’re thinking about moving to simulation from hand calculations or nothing at all, you will benefit from this session.

**When:**

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