Data-driven Discovery of Interpretable Constitutive Models

Although a data-driven approach has enjoyed success in various fields, its lack of interpretability often hampers its trustworthiness and therefore prevents its application in real engineering practice. Previous efforts have partially succeeded in improving its interpretability, but they often had to pay accuracy as a price. This work aims to propose a new machine learning framework that not only yields an interpretable model but also does not necessarily compromise predictive accuracy. Furthermore, we aim to develop an interpretable model that is inherently portable so that it can easily be incorporated into a continuum-scale model as a constitutive law that may yield results similar to those from a hierarchical multi-scale model while bypassing the need of running sub-scale simulations at individual Gauss points.

Microthermoporomechanics of Energy Geosystems

A major drawback of classical approach for simulating coupled processes in porous media is that it relies on an assumption that the solid and fluid constituents instantly reach a local thermal equilibrium, which may hinder the accurate prediction of the short-term behavior of the target media. This work aims to present a framework that adopts a dual-temperature concept that can consider the heat exchange between different constituents while coupling Stokes or Navier-Stokes flow inside fractures and macro-pores and Darcy's flow in a porous matrix. This work may not only broaden the spectrum of energy applications but can also be utilized to estimate, for example, the heat extraction performance of a geothermal system. 

Computational Modeling of Ice Lenses in Frozen Porous Media

Goal of this work is to present a computational framework that can overcome the limitations of the phenomenological model for frozen porous media. The formation of ice lens has oftentimes been explained in a one-dimensional setting that lacks the detailed coupling mechanism between elastoplastic response of the solid skeleton and the phase transition of the pore fluid. We aim to fill the knowledge gap by capturing the evolving interface of the ice phase constituent via Allen-Cahn type phase field model coupled with a classical thermo-hydro-mechanical model. We believe that our framework that captures the meso-scale ice lens formation with macroscopic observations can help continuum modelers to gain insights and to investigate and predict the response of geosystem that undergoes freeze-thaw cycles.  

Multi-scale Modeling of Unsaturated Geomaterials

A statistical representative volume composed of thousands of fluid channels and particles may be very different than the field scale domain where billions of grain contacts and pores are collectively reacting to granular responses. This scaling effect is a big challenge in applying insights obtained from nano- or micro-scale laboratory tests to improve predictive capability in the field where applications require predictions at the meter or kilometer scales. The goal of this study is to present a multi-scale model that can preserve the physical insights and length scales without exhausting computational resources. This work not only aims to develop a scheme that efficiently resolves both the global and small-scale responses of the multi-phase material but also to build a foundation for the data-driven approach.

Damage and Fracture in Higher-order Continua

Since many materials exhibit internal length scales while a length scale parameter must be introduced to represent sharp cracks by a regularized function, this work is intended to introduce a unified treatment that captures the size effect of both the elastic deformation and crack growth. By introducing a phase field fracture model for higher-order continuum, we explore the interacting size-dependence of the materials of complex microstructures and its fracture and damage mechanisms. Specifically, we utilize the distinctive degradation functions of the stress-strain and couple-stress-micro-rotation energy conjugated pairs for a given regularization profile such that the size-dependent responses of the material are insensitive to the fictitious length scale parameter of the regularized crack interface.