Welcome to the first post in our three part series featuring all of the Brain Teasers that were posted weekly on the Fidelis LinkedIn page between 2020 and 2022!

This week’s collection of Brain Teasers focuses on material-related questions, further sorted by subject. The answers to these questions, as well as the explanations, are shown after all the questions. These Brain Teasers make for excellent practice for exams, technical interviews, or for anyone looking to reinforce their FEA knowledge. Let us know how many you get right! Also, stay tuned for Part 2!

Part 2: **Mechanics**

Part 3: **Analysis**

## Questions

### Stress-Strain Curves:

1.

2.

3.

### Defining materials in Abaqus:

4.

5.

6.

7.

### Poisson’s Ratio:

8.

9.

10.

### Rubber:

11.

12.

### Hardening:

13.

14.

15.

### Other:

16.

17.

18.

## Materials Answer Key:

1.

In reality, the proportional limit is the point in the loading curve where the material begins to deform plastically, but it is extremely difficult to measure with any confidence. Hence, engineers decided to come up with more consistent methods to measure ‘yield stress’ (such as 0.2% offset), which is represented by point B here.

2.

Technically, the area underneath the stress-strain curve is called the Modulus of Toughness, which can be used to express a material’s ability to absorb energy. Similarly, Modulus of Resilience is the area underneath the elastic region of the stress-strain curve.

3.

The low stiffness of rubber and its nonlinear hyperelastic behavior give this one away. As polymer chains begin to align in tension at very high strains, stiffness increases significantly, giving the curve that unmistakable shape.

4.

Of course, when we test a material in the lab, we obtain engineering stress-strain, which is really more of an approximation of material behavior. In reality, the assumption that initial cross-sectional area is maintained is false – as the material is stretched (or compressed) its cross-section changes. Therefore, we need to calculate the ‘true’ stress and strain post-test. Additionally, in FEA we’ve already defined the elastic modulus of the material, so in order to avoid double counting of elastic strain, we define plastic strain only, hence why it begins at the elastic limit stress with a zero value of strain. The result of all of this data juggling is the true stress-true plastic strain curve.

5.

Not much explanation needed for this one… since we’re removing all of our elastic strain from the full stress-strain curve, the plastic strain at our yield point is 0.

6.

As you can see from the image above, we ran a steady-state thermal analysis with just thermal conductivity. If we were to be running a transient analysis, we would also need density and specific heat.

7.

Nitinol is a fascinating material with very unique properties – it can reversibly deform to a high strain in response to high stress. This is known as superelasticity.

8.

The Poisson’s ratio of a stable, isotropic, linear elastic material must be between -1.0 and +0.5 because Young’s modulus, shear modulus, and bulk modulus must retain positive values. Most materials have Poisson’s ratio values ranging between 0.0 and 0.5. A perfectly incompressible isotropic material deformed elastically at small strains would have a Poisson’s ratio of exactly 0.5.

9.

An incompressible material is a material that does not change in volume under deformation. This can be represented by a constant known as the bulk modulus (K). The bulk modulus is the ratio of direct stress to volumetric strain, so if there is no change in volume, the bulk modulus should be infinite. It relates to Young’s Modulus by the formula K = E/(3(1-2v). When Poisson’s Ratio is 0.5, this makes the bulk modulus infinite; therefore, the material is incompressible.

10.

Although often considered pseudo-materials, auxetics have a negative Poisson’s ratio, meaning that their volume increases under tensile load. They can be really useful in applications such as footwear, body armor and shock absorbers.

11.

Lattice Boltzmann actually relates to CFD, being a state-of-the-art methodology in which fluid density on a lattice is simulated with streaming and collision processes, rather than via the typical Navier-Stokes equations. This advanced method is seen in SIMULIA products such as XFlow and PowerFLOW. Reach out to our sales team if you’re interested in learning more about these solutions!

12.

The Mullins effect is typically seen in filled rubbers, where the stress–strain curve depends on the maximum loading previously encountered. More specifically, instantaneous and irreversible softening of the stress–strain curve occurs whenever the load increases beyond its prior all-time maximum value. This can make characterization tricky and knowledge of the history of the part/sample critical!

13.

The key difference between isotropic and kinematic hardening is that flow grows the yield surface and shifts it, respectively. For one-off loading scenarios, both models will provide essentially the same behavior, but upon unloading and subsequent reloading, the expanded yield surface generated in an isotropic hardening model results in unrealistic yielding characteristics. As a tidbit, a combined isotropic-kinematic model is often most appropriate for modeling true cyclic material response.

14.

While the main goal of surface hardening is to improve durability, it can also possibly improve fracture toughness and wear resistance.

15.

Fast cooling of carbon steel typically results in a martensitic microstructure, as can be seen in the cooling diagram above. The fast cooling from the FCC austenite phase, which steel assumes at high temperature, results in a solid state phase change to FCT martensite because of the lack time for full diffusion to BCC ferrite. This metastable phase is extremely hard and is often beneficial for durability and wear resistance (often tempered with some ferrite by reheating).

16.

The Neuber correction allows us to estimate the effect of plasticity on the stress and strain of the material in a notch or other stress concentrator. However, we must ensure that the region is bounded by elastic material because the theory falls down if global plasticity begins to affect the stress state.

17.

Creep occurs when an object is under constant stress and is allowed to deform due to atomic and vacancy diffusion along grain boundaries. Stress relaxation is a similar mechanism, just under constant strain.

18.

The yield strength of concrete is higher in hydrostatic compression than tension (and increases as hydrostatic compression increases), hence the yield surface looks like a cone. This contrasts with metals and other materials we’re more familiar with, where hydrostatic stress does not affect yield strength, so the surface is cylindrical.

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