Model Discovery in Mechanics: From Conventional to Data-Driven Methods

Author: Wihardja, Adeline Emily

Year: 2027

Degree: Dissertation (Ph.D.)

Advisor: Bhattacharya, Kaushik

Committee Members: Ravichandran, Guruswami; Ortiz, Michael; Stuart, Andrew M.; Shaikeea, Angkur Jyoti Dipanka; Bhattacharya, Kaushik

Option: Mechanical Engineering

DOI: 10.7907/dx5f-qy46

Abstract

The design of the next generation of multifunctional and structural materials requires an understanding of their complex physics. Materials such as soft active polymers, additively manufactured metals, batteries, and biomaterials are crucial for applications including soft robotics, protection, energy storage, and biomechanical implants. Yet for most emerging functional materials, the governing physics remain only partially understood. We present two approaches to learn and develop high-fidelity models for these complex materials.

We first present a more traditional approach that combines experiments and continuum modeling to study a class of multifunctional materials called Liquid Crystal Elastomers (LCEs). Their behavior at large strains and high strain rate regime was characterized, for the first time, using a novel tensile drop-tower experimental setup. This new insight leads to the development of a complete, high-fidelity engineering model that captures their behavior across multiple orders of strain rates while remaining consistent with their underlying multiscale physics.

We then present a second approach that addresses model discovery for new, emerging materials, where physics knowledge is often sparse or incomplete. Advances in imaging now provide rich, full-field experimental data, but traditional inversion techniques fail to fully exploit this raw information. We introduce an image-to-constitutive model (I2C) method that directly infers models from raw experimental images and data, leveraging all the underlying information in the raw data to obtain high-fidelity models. This method is well-posed (the laws of physics regularize the ill-posed image correlation problem without ad hoc filters) and is amenable to any general form of constitutive relations under large deformations, non-pristine test conditions, and complex loadings. This method has been demonstrated to successfully recover the constitutive relation in rubber materials under large deformations.

Finally, this thesis presents an approach that uses the current model and physics knowledge of the material to design optimal experiments that maximize information gain. This approach couples a Bayesian framework with topology optimization to design sample geometries that produce maximally informative data within a single experiment. Together, these contributions create a closed-loop framework between modeling and experimentation for learning and developing next-generation materials.

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