🚧 UNDER CONSTRUCTION! 🚧
Project Overview
As part of my Computational Physics and Engineering course, we are to explore a scientific or engineering related computational problem. Previously in my Biophysics course, I gave a presentation on the Fluid Dynamic Behavior of Fire Ant Aggregations, so I thought it would be interesting to code models that demonstrate their viscoelastic behavior! My Biophysics presentation can be found below alongside the research paper which I based my presentation off of! I hope you enjoy following along with my project!
Abstract
This project explores the computational modeling of fire ant aggregations, which dynamically exhibit both solid-like and liquid-like properties. The focus is on simulating their response to mechanical stresses, informed by the research of Dr. David Hu. The models developed here capture the characteristic shear-thinning behavior, creep response, and oscillatory rheology, revealing the ants' collective ability to adapt their properties to environmental stresses. The results underscore the potential for creating adaptive materials inspired by such complex biological systems.
Project Plan
- Setting Up the Environment: Utilizing Python, with libraries like NumPy for numerical computations and Matplotlib for visualization.
- Model Development: Defining stress-strain relationships based on the paper's findings and adapting them for computational modeling.
- Numerical Methods: From simple models to finite difference methods, each iteration brings us closer to capturing the intricate behaviors observed in the aggregations.
- Simulation Runs: Running a series of simulations under varied parameters to reproduce the transitions between solid-like and fluid-like states.
- Visualization: Analyzing and interpreting results through visual representations of the simulations under different conditions.
Phase 0: Trial and Establishment
This phase involved experimenting with the fundamentals of viscoelastic modeling, leading to a focus on three key behaviors: shear thinning, creep response, and oscillatory rheology. While the initial models were simplistic, they were crucial stepping stones for the project.
Early Code Snippets and Plots: [Link to repository or images]
Phase 1: Shear Thinning Behavior
Replicating the shear thinning behavior observed in fire ant aggregations was a significant milestone. This entailed:
- Digitizing data from the paper's graphs to create a baseline for the simulations.
- Creating Python scripts to model the shear thinning, validated against empirical data.
Code and Plots: [Link to repository or images]
Upcoming steps include refining the model to integrate more complex stress-strain relationships and further validation.
Phase 2: Creep Behavior (Outline)
- Modeling the creep response with a focus on time-dependent deformation under constant stress.
- Incorporating a compliance function to simulate the balance between energy storage and dissipation.
- Comparing the model's predictions with experimental creep curves for validation.
Phase 3: Oscillatory Rheology (Outline)
- Applying a Maxwell model for the viscoelastic properties under oscillatory strain.
- Simulating frequency-dependent moduli G′ and G′′, reflecting the material's viscoelastic nature.
- Examining the scaling behavior of the moduli and relating it to the empirical observations from the study.
Abstract
Revise anything in [brackets]
This project investigates the viscoelastic properties of fire ant aggregations using computational modeling techniques. Fire ants form complex structures that exhibit both solid-like and liquid-like behaviors, adapting dynamically to environmental stresses. These behaviors make them an intriguing subject for studies in non-Newtonian fluid dynamics and provide insights into potential applications in materials science and biomimetics.
The primary objective is to [develop a model] or [to model the observed] viscoelastic responses of these aggregations to mechanical stresses as done in the research paper by Dr. David Hu. By modeling the shear-thinning behavior, creep response, and oscillatory rheology, the study seeks to reveal how fire ants collectively adjust their properties to external forces. The simulations are built upon the foundational principles of non-Newtonian fluid mechanics, enriched by empirical observations from the natural world.
[Results from this model could illustrate how fire ant aggregations adjust their mechanical properties in response to external forces, providing a deeper understanding of their collective behavior and potential engineering applications. These include the design of adaptive materials that mimic the dynamic adjustments observed in natural systems, which could be beneficial in developing flexible structures in civil engineering or resilient materials in aerospace industries.]
Project Plan
- Setting Up the Environment:
- We'll use Python for numerical computations and simulations. We'll utilize libraries like NumPy for handling numerical computations, and Matplotlib for visualization of our results.
- Model Development:
- Start with defining the stress and strain relationships and how they change with different ant densities and applied stresses.
- Numerical Methods:
- Implement numerical solutions, starting with simple models and advancing to finite difference methods for more complex behavior.
- Simulation Runs:
- Conduct simulations under varied parameters to observe transitions between solid-like and fluid-like behaviors.
- Visualization:
- Visually represent the model's behavior under different conditions to analyze and interpret the results.
Phase 0: Trial and Establishment
In the initial trial phase, I experimented with various aspects of viscoelastic modeling, which helped narrow the focus to three key behaviors: shear thinning, creep, and oscillatory rheology. Early attempts laid the groundwork for a more structured approach.
First, I created a very simple model where stress is proportional to strain by a constant shear modulus and strain changes over time based on stress divided by a constant viscosity. The information for the initial code was derived from general principles of viscoelastic materials, as referenced in the research paper. Some of the first models are included below.
Code and Output:
As you can see, these trials weren’t particularly successful at accurately modeling the viscoelastic behavior of fire ant aggregations, but they served as a start! From here, I decided that the three areas I would focus on would be the shear thinning behavior, creep behavior, and oscillatory rheology of fire ant aggregations!
Phase 1: Shear Thinning Behavior
A significant discovery in the study was the shear thinning behavior of fire ant aggregations, which maintain a constant stress level across a range of shear rates before transitioning to a shear-independent viscosity characteristic. Key steps taken in this phase included:
- Digitization of experimental data to obtain a function for shear stress versus shear rate. This was done by manually inputting data points from Figure 2 (a) from the research paper.
- Development of a Python script to simulate the shear thinning behavior.
- And finally, validating the model against the digitized data.
Next, we aim to fine-tune the model by incorporating more complex stress-strain relationships and validating against additional empirical data.
Phase 2: Creep Behavior (Outline)
- Develop a model to simulate the time-dependent creep response of fire ant aggregations under constant stress.
- Integrate a compliance function that reflects both the elastic energy storage and viscous energy dissipation.
- Validate the model by comparing simulated creep curves with experimental data.
Phase 3: Oscillatory Rheology (Outline)
- Implement a Maxwell model to describe the viscoelastic properties under oscillatory strain.
- Model the frequency-dependent moduli G′ and G′′, capturing the material's ability to store and dissipate energy.
- Analyze the scaling behavior of the moduli and compare with the empirical power-law relationship observed in the research.