I.Y. Miranda Valdez: Fractional rheology and data-driven approaches to characterize viscoelastic materials

Abstract: 

Viscoelastic materials are ubiquitous, found in a wide range of applications, from biological tissues to food products. Despite their importance, accurately predicting how these materials flow and deform over time presents a significant challenge for scientists and engineers. This difficulty is largely due to their complex microstructure.

This doctoral thesis improves the modeling and representation of soft materials by integrating two powerful approaches: fractional calculus and machine learning. It demonstrates that the combination of these methods can more accurately capture the complex behavior of viscoelastic materials compared to traditional techniques.

A key finding of this study is the development of an automated modeling approach using Bayesian Optimization. This innovative method simplifies the challenging task of estimating material parameters and identifies the best-fitting models with quantified uncertainty. Additionally, the research introduces a publicly available Python package, making these advanced mathematical tools accessible to the broader scientific community.

The practical applications of this research are demonstrated using bio-based materials, such as cellulose nanofibers and methylcellulose. These materials are essential for developing sustainable alternatives to plastics. By enhancing our ability to predict how these materials respond to mechanical loads over time, this work paves the way for the design of high-performance materials for the bioeconomy.

In conclusion, this dissertation bridges the gap between complex mathematical theory and real-world applications. The results indicate that combining data-driven machine learning with physics-based modeling not only enhances our understanding of soft matter but also provides a faster and more reliable pathway for future material innovation.

Keywords: viscoelasticity, fractional calculus, Bayesian optimization

Opponent: CNRS Research Director Thibaut Divoux, ENS Lyon, France

Custos: Professor Mikko Alava, Aalto University School of Science

Link to electronic thesis: Thesis available for public display 7 days prior to the defence at Aalto University's public display page.