Mechanical and Civil Engineering Special Seminar

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

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 modelling 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-posedness of the image correlation problem with no 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, beyond model discovery, we present an optimal experimental design framework, where future experiments leverage current physics knowledge to maximize information gain, leading to higher-fidelity experiments and inferred models. Together, these approaches create a closed loop between modeling and experimentation for next-generation materials.