The Challenge

My favorite lab in Experimental Techniques involved a deceptively simple challenge: take a standard acrylic dogbone specimen and remove 70% of its material while keeping it as strong as possible. Unlike most labs with step-by-step procedures, this one gave us complete freedom in approach. That's what made it interesting.

Material optimization usually works one way: add density, get more strength. Our professor showed us the classic materials chart - a log plot of strength versus density where materials tend toward the bottom right. He joked that if we found ourselves in the top left, we were either making huge calculation errors or should expect a Nobel prize call.

Finding the Right Approach

I was committed to finding the most optimal material design. My first instinct was to use truss-like structures, as they were well studied. However, standard trusses are optimized for dynamic, not tensile loads, and there are a billion different types to choose from. I could test a few of them, but I could never be sure that I had found the most optimal one.

I realized that I needed to reformulate this challenge not as one of solid mechanics, but instead as one of machine learning. In order to find the best design, I needed to iterate across an entire design space of different material configurations. I had a goal (optimizing stiffness and strength under tensile loads) and a boundary condition (30% weight). I just needed to find an objective function that could efficiently iterate through the combinations.

After some digging, I found a technique called SIMP (Solid Isotropic Material with Penalization) that did exactly what I needed. Instead of guessing at geometries, SIMP:

1. Represents material as a density matrix

2. Calculates stiffness gradient for each element

3. Iteratively moves material to high-stress regions

4. Converges on an optimal distribution

It is relatively simple to build your own SIMP-based optimizer. In fact, a few researchers from the Technical University of Denmark were able to build one in just 99 lines of MATLAB code. Here is an animation of the process in action, courtesy of Numerical tours of continuum mechanics using FEniCS. Note how the density values of the elements tend towards 0 and 1 as the iterations progress.

Material Testing

In order to characterize the acrylic, we conducted tensile tests on 3 samples of a standard dogbone-shaped sample of bulk material. We prepared the material samples by using a water-based paint to create a white background and black spray paint to create a random speckle pattern on the surface of the sample. 

We secured the samples in a tensile testing machine, which was connected to a data acquisition system. Simultaneously, we configured a camera to capture images of the speckle pattern. Digital Image Correlation Engine (DICe) software was used to track the movement of the speckles and produce strain fields. With force data from the Instron and displacement data from DIC, it was possible to generate stress-strain curves and calculate Poisson’s ratio for each sample.

Topology Optimization

Now that we had the material properties, I conducted density-based topology optimization on the middle 2” x 0.75” section of the dogbone. I tried a ton of different software packages, including Fusion 360, SOLIDWORKS, and MATLAB, but found that the built-in modules in ANSYS workbench had the lowest computation time

• Fusion 360: Too slow

• SOLIDWORKS: Limited control

• MATLAB: Complex setup

• ANSYS: Fast and flexible

ANSYS let me experiment quickly so I ran two configurations with different initial density targets:

1. 25% initial density

2. 26% initial density

Both converged to 30% final density but produced completely different geometries. This highlighted a key limitation of gradient-based methods - they can get stuck in local optima. A tiny change in starting conditions led to radically different solutions:

• Design 1: Two parallel bars aligned with load

• Design 2: Complex truss-like pattern

Results & Analysis

I tested three samples of each type under the same conditions as the bulk sample. While these optimized samples exhibited lower ultimate tensile stress and stiffness than the bulk acrylic, they maintained an impressive 66.5-85.45% of the bulk material’s strength-to-density ratio and 74.3-84.1% of its stiffness-to-density ratio. Furthermore, the optimized designs showed increased Poisson’s ratios, indicating a more even redistribution of tensile stresses.

Yes, the first topology-optimized design with two straight bars seems underwhelming at first, but it’s interesting to think about why eacn could provide an effective solution. The bars are positioned far enough from the edges to prevent shearing and all the material aligns directly with the tensile load path. The thickness of the bars is likely dependent on the amount of material available due to the convergence goal. The second design is more visually striking. The geometry is truss-like in that the configuration allows the load to transfer along multiple paths, providing redundancy against localized failures. The symmetry in both designs likely helps mitigate bending moments that could lead to premature fracturing. I can't prove these are the absolute best solutions, but the data shows they're highly optimized.

Why This Mattered

This turned out to be my favorite lab (and class) at UCSD for a few reasons. The open-ended approach forced real engineering thinking, I Had to combine theory with practical constraints, got to use both computational and physical testing, and the results were concrete and measurable.

The research I did sparked my interest in computational design, and I spent much of my free time reading research papers on the theory even after the lab was over. In the future, I’m planning to test more complex structures and load cases and similar techniques that are more likely to converge to a global optimum.