# Module 2: DIC and planar elasticity

For this module, we will use an image-based technique to determine the deformation fields in solid media. This method is called Digital Image Correlation (DIC). The method's premise is to embed or emboss a random pattern of high-contrast markers that move with the material, and to compare their current states to a reference state. Once the spatial distribution of marker deformations is determined, kinematic quantities of interest such as strain tensors, etc. can be used to answer mechanics questions.

Here, we suggest one of two possible projects. As a first option, you can measure the deformation field ahead of a propagating crack using a high-speed camera. As a second option, you can probe the phenomenon of stress concentration at the tip of a geometric feature with an elliptical geometry at equilibrium. For both of these projects, solutions exist for the deformation field or stress (in the linear-elastic limit) that can be used to compare with the experimental measurements generated in this module. In the spirit of the lab, we encourage you to go deep with the analysis of the data, and to develop rigorous conclusions about the mechanics of the system under study.

As a final option, you can select a problem of your choice in solid mechanics. Candidate options would be a direct probe of the St. Venant's principle, which says that loading conditions that are statically equivalent render the boundary conditions applied as irrelevant. You might attempt to explore the limits of this assumption using direct measurements of the deformation field obtained via DIC.

#### Week 2

On St. Venant's principle: von Mises and Sternberg (2 different papers)

Prepare and submit your drawings, as described in the exercises, below

I strongly encourage you to review the NCORR manual. Section 2.10 will prove particularly useful if you intend to elaborate your analysis, and measure stress fields from the deformation data.

### Exercises

#### Week 1

1. Form new groups.

2. Consider & discuss the problem that you wish to address. Determine what apparatus / testing protocols you should follow. How will you carry out your experiment? Can you think of an interesting scientific component to your question related to mechanics where DIC might provide some insight? Bear in mind that the material we will use is compliant and rubbery - and thus can undergo large deformation.

3. Install NCORR on a PC with one of your group member's accounts. Each account will require a separate install, but once installed, it should always work with that sign in

4. Download and process the image samples from NCORR. Use the hole in the plate dataset to familiarize yourself with the software, the speckle pattern, and calculation of strains. You should work with the documentation in-hand, so you have a clear idea of what each of the software `knobs' does in the experiment.

5. Note: once you have decided your geometry for 3D printing, please send your design files (.stl) to Chenzhuo Li (chenzhuo.li@epfl.ch) before next Monday 7th November.

#### Week 2

Thank you for promptly submitting your .stl files for printing the molds / samples.

For this week, we will carry out the next 3 steps towards a successful DIC measurement.

1. This starts with casting your samples. You'll have to mix the 2-part polymer mixture (green and white materials), in roughly equal amounts. Given that the density of the polymer is 1.2 g / cm^3, try to estimate the total mass you'll need, so you use an amount near what you'll require. If you are casting more than one sample, you can mix it all at once, provided you prepare both of your molds in advance. For those of you with elliptical elements, be sure they are fixed on the appropriate location in the outer portion of the mold.

After mixing the components of the polymer, you'll have to evacuate them with the vacuum chamber to remove any air bubbles. I recommend that you do this after stirring, so any entrained air can be eliminated. Note that once the polymer components are mixed, the clock is running. You have about 20 minutes before it solidifies beyond workability.

Finally, you'll pour polymer into your prepared molds, and wait for the mixture to cure. This should be done one group at a time, in my lab.

2. After your samples are cured, you'll have to apply the pattern that you'll use for DIC. This is done with canned spray paint. For this, I'll ask that you wait until everyone has cast their samples, so the paint application station can be set-up. Again, I'll ask that you go group by group to apply the patterns.

You'll have a 2 MPx camera (1920 x 1080 pixels) to record your images. Given that you'll need about 3 pixels for each speckle in your pattern, decide approximately how your pattern should look to obtain your desired resolution. If you want to, you can practice on a scrap paper, to evaluate the density and size of the pattern you apply, before applying the pattern to your sample. This requires a bit of art, because the resulting pattern will depend on how far away the can is, for how long you spray the paint, etc.

3. Finally, you're nearly ready to test! We'll use the same testing machine as last week, but this time with a camera. You'll have to align the camera at the right distance and focus to resolve your pattern sufficiently. You'll use Micromanager software to operate the camera and record the images. Bear in mind, that you'll want good synchronization between the load values and the images, in case you want to compare your data with theoretical curves. Try to work out a way to do this.

Testing can be carried out one group at a time, as you are ready to test. If you have multiple samples to test, please try to be efficient in gathering your data, so everyone who is ready to test today has a chance to record some data.

### Lecture notes

Groups

 1 Benjamin Colety Dogukan Ustun Kateryn Andrea Leon De la Torre Victor Solelhac 2 Algisi Colleen Cameron Bush Pierre Garrabos Abhijeet Singh 3 Roy Aymeric Mi-Lane Bouchez Filippo Brignolo Alexandre Mehdi Clement 4 Joao Barini Ramos Soury-Lavergne Nathan Syrielle Wicki James Ziadeh 5 Cassandre Pitz Joseph Bernaert Assier de Pompignan Leo Guede Axel 6 Joseph Bejjani Nicolas Avellan Marin Julien Jeandroz Karim Azzouzi

Student Submissions

Group 6 (2022) - 1: How to achieve a good speckle pattern for samples used in DIC.pdf

Group 6 (2022) - 2: How to Model a Hyperelastic Material in Finite Element Analysis.pdf

Group 4 (2022) - 3: Material Model for silicone based on uni-axial traction.pdf

Group 6 (2022) - 4: Data synchronisation for DIC

Group 2 (2022) - 5: A Simplified Guide to Ncorr Installation

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