Composite Elastic Shells

Undergraduate Research

As a part of UCLA's Structures-Computer Interaction Lab, I spent three years as an undergraduate researcher investigating applications of elastic composite shells in the field of soft robotics. Although I began by solely doing experimental work in the lab, the COVID-19 pandemic forced me to pivot to simulation-based work. After becoming familiar with programming fundamentals, myself and another undergraduate completed a MATLAB and Abaqus based simulation modeling the deformation of elastic shells, generating the data necessary to fit a shallow neural network. When it became safe to return to in-person work in 2021, I continued my research by fabricating various multi-layered shells, comparing model results to experimental realities. Outlined below are some of the highlights of both my simulation and experimental work.

Computer Modeling

Motivated by the movement of creatures such as jellyfish, I sought to create a bi-layered structure that deformed from a planar 2D shape to a 3D hemisphere following the introduction of energy into the system. Previous works had indicated a 'kirigami' pattern (shown to the right) applied to a stretched substrate layer yields promising results. Working with another undergraduate and under the instruction of Lab PI Professor Khalid Jawed, I spent much of my junior year writing code for simulations to generate energy data for the shell's deformation.

Depiction of overall goal. Image credit: Structures-Computer Interaction Lab

To identify the physical parameters most conducive to the deformation we wished to see, I needed to conduct parameter sweeps in MATLAB and Abaqus. I modified an existing simulation to accommodate the Mooney-Rivlin hyperelastic model, using a Dynamic Mechanical Analyzer to determine empirical material constants. I implemented parallel computing capacity into the program, running it overnight on the lab's virtual machines to generate data. With data in hand, I constructed models relating four key variables: shell stretch, shell element radial coordinate, shell element bend angle, and energy density. Example plots relating radial coordinate, bending angle, and energy density for a given stretch level are shown to the left.

I aimed to use the data to construct an energy model which could be implemented into a newly-written discrete shell model. To do so, I used MATLAB's Deep Learning Toolbox to fit the data to a shallow neural network. Via MATLAB's nftool(), I was able to train the neural network using the Levenberg-Marquardt model and over 55,000 instances of shell element data I had attained in my previous parameter sweeps. The model fitting was successful, with an R-squared value of 0.9978 -- an error histogram comparing training, validating, and testing data sets to the zero-error line is shown below.

Due to challenges with implementing the neural network into the discrete shells model, I also constructed high-order polynomial fits via cftool(). Plots comparing the original data points to the generated polynomial mesh for three individual stress levels is shown below as well.

Six-coefficient energy formulations for (a) 5% Stretch, (b) 14% Stretch, and (c) 23% Stretch.

Experimental Work

Empirically measuring a 3D shell's adherence to a hemisphere is difficult to do. However, visual comparisons and the use of more easily attainable measurements allowed me to initially gauge how well our simulations matched reality. I fabricated both bi-layer and tri-layer composite shells, with both layers made of 3M VHB tapes. While more difficult to model, tri-layered shells had the added benefit of bistability, allowing it to 'snap' from its regular configuration to its inverted form. Material properties not present on data sheets were found through the use of an Instron Machine. This area of work was done in collaboration with postdoctoral researcher Leixin Ma, PhD candidate Mrunmayi Mungekar, and another undergraduate.

Our first fabrication setup stretched the substrate layer radially by pushing it down. While precise, this setup was unable to stretch the substrate to levels needed (beyond 50%). By approximating radial and biaxial stretch to be equal, we were able to use the second fabrication setup, shown in the image gallery to the left. I fabricated a variety of shapes, initially working with the kirigami shape shown earlier and later progressing to more complex shapes provided by computational models. We frequently used a plus shape as an initial approximation, since it was easy to model via beam theory. I included images of bilayer and trilayer shells I fabricated below, along with some Abaqus models of the equivalent shape.

To explore low-power actuation of a trilayer shell from one configuration to another, I made initial attempts at embedding shape-memory alloy (SMA) wire into the specimens. SMA wire can be heat-treated to 'remember' a specific shape, returning to said shape when heated. I've included photos of an SMA-embedded shell below.

SMA-embedded shell

Increasing levels of stretch applied to the same shape

Plus-shaped trilayer shells arranged in order of increasing stretch

Page updated

Google Sites

Report abuse