# The ABC’s of FEA as simple as 1-2-3

What do you need to know about engineering material science to use Simulation to drive innovative designs? The answer might come as a surprise. There are no engineering or analysis prerequisites successfully leveraging the power of Finite Element Analysis (FEA) with SolidWorks Simulation. It certainly wouldn’t hurt to know a few of the basics; what I call the Material Science Essentials for SolidWorks Professionals.These are the three essential properties of any engineering material used in Simulation:

1. Poisson’s Ratio
2. Young’s Modulus
3. Shear Modulus

These three properties are not independent of one another; they are in fact related to one another through Hooke’s Law. This is the most basic principle of FEA which says that Poisson’s Ratio, Young’s Modulus, and Shear Modulus are all related because stress and strain are related. This principle is something you already use in your everyday life and can easily apply to Simulation. Here’s how this is applied in the real world as well as in Simulation.

Fundamentally, these are the same two processes even though they may seem different on the surface. Whether it is out in the real world or inside of Simulation you observe and then make a conclusion.

• Step 1 Measure strain. Strain is quantitative in that it is a quantity that you can physically measure.
• Step 2 Calculate stress. Stress is qualitative in that it is not something you can directly measure but it is what you use to qualify designs as good or bad, safe or unsafe.

In the real world and in Simulation you observe or measure your model’s change of shape and then conclude if it’s a good or bad design. This is all possible because of the relationship between stress and strain.

• Strain is a quantity that describes the ratio of the change in shape of an object. When you stretch something you might say it’s now 25% larger than it was before. That 25% is really just strain.
• Stress is a quantity that describes the intensity of a load applied to an object. That 25% stretching is fine if it’s Silly Putty, but bad news if it is made of steel because the Silly Putty will be under less stress while the steel will be under much more stress.

For linear static simulations, every material that is used whether it is aluminum, steel, or any other type of material will have a linear stress-strain relationship like the one shown in the stress-strain curve. A stress-strain curve is really the road map for a simulation. It defines the exact path a particular material will always follow whenever it is loaded. If it has stretched “X” you know it is under “Y” stress.

However, for linear static studies, you don’t actually define the full stress-strain curve like you can in more advanced study types. It is much easier than that. It only takes two numbers to completely define the behavior of a material used in Linear Static Simulation.

1. Poisson’s Ratio describes the way a material will change shape.
2. Young’s Modulus describes the relative strength of a material.

Young’s Modulus, or sometimes called the Elastic Modulus, is the ratio of axial stress to axial strain. This number tells you the slope of the line in the stress – strain curve. A stronger metal like steel will have a much higher Young’s Modulus than a weaker metal like aluminum. Poisson’s Ratio tells you how a model’s geometry will change when it is loaded. Take the bar for example. If you pull on it (tension), it will stretch in that direction but it will shrink in the other two; or if you push on it (compression), it will shrink in that direction but expand in the other two. This is a concept we are all familiar with– Poisson’s Ratio just tells us this mathematically.

Last but not least is the Shear Modulus. This is interesting because it is not a property that is defined by the user even though it is listed in the Material Database of SolidWorks. That’s why it was excluded from the list above. Simulation calculates the Shear Modulus internally from the defined Young’s Modulus and the Poisson’s Ratio using the equation below where G is the Shear Modulus, E is the Young’s Modulus, and v is Poisson’s Ratio.

The Shear Modulus is similar to the Young’s Modulus in that they both define the ratio of stress to strain, except the Shear Modulus deals only with shear stress and shear strain. In this FEA world, there are two types of stresses and strains—normal and shear. Normal stress and normal strain are the ones with which we are most familiar. These quantities come from loads that are normal to the cross section like pulling on a steel bar. Shear stresses and shear strains are produced by loads that are parallel to the cross section– think of sliding something across a table or desk. An object under a shearing strain looks like this:

At the end of the day, it is just these three properties– the Young’s Modulus, Poisson’s Ratio, the Shear Modulus- that Simulation uses to paint the picture of your CAD model’s performance and guide you through the design process. With FEA, just like pretty much every subject, there can always be more to learn and more to discuss. People devote entire careers to learning and studying these topics but to me that is not the point of Simulation.

Instead, it’s a tool meant to be put FEA in the hands of every designer. By taking their famous mantra of simplicity and applying it to engineering analysis, SolidWorks shows us that behind all the complexity of the applied numerical methods, matrix algebra, and differential equations of FEA lies the elegance and intuitiveness of Simulation. It’s FEA made easy as ABC, simple as 1-2-3.

Written by Stephen Petrock. Stephen is an Elite Application Engineer and Simulation Specialist with ModernTech working out of their South Florida office in Fort Lauderdale.

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#### Stephen Petrock

Since 1998, TriMech has helped our clients design better products by partnering with them and offering, not only CAD, CAE, PDM, FEA, CAM software products, but also by engineering solutions involving full-time and temporary staffing, contract design, analysis and drafting services, rapid prototyping, custom programming and implementation services. TriMech is a value-added reseller of SOLIDWORKS and Stratasys 3D Printers in the Mid-Atlantic and South-East including New Jersey, Pennsylvania, Delaware, Maryland, West Virginia, Virginia, North Carolina, South Carolina, Tennessee, South Carolina, Georgia, Florida, Alabama, Mississippi, Oklahoma, Arkansas and Louisiana.