Date of Award

2024

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)

Administrative Home Department

Department of Mechanical Engineering-Engineering Mechanics

Advisor 1

Susanta Ghosh

Committee Member 1

Ramin Bostanabad

Committee Member 2

Shiva Rudraraju

Committee Member 3

Siva Nadimpalli

Abstract

Phase field modeling is a crucial tool in scientific and engineering disciplines due to its ability to simulate complex phenomena like phase transitions, interface dynamics, and pattern formation. It plays a vital role in understanding material behavior during processes such as solidification, phase separation, and fracture mechanics. Particularly in fracture mechanics, phase field modeling can be utilized to predict the crack path in complex materials. Understanding the failure behavior is vital for applications of any material. The specific contributions to the field of phase field fracture mechanics, are, Firstly, we propose a novel phase field fracture model to simulate the fracture in glass with residual stress generated through an ion-exchange process. This work demonstrates that ion-exchanged glass exhibits increased fracture toughness. Secondly, we introduce a phase field fracture model to simulate the failure of 3D printed thermoplastics and fiber-reinforced composites. Our focus is on understanding the variation of fracture toughness with printing parameters.

In a second line of work, we explore the application of artificial intelligence (AI) and machine learning (ML) techniques for solving partial differential equations and enhance phase field modeling. Physics-informed neural networks or physics-informed machine learning is a recently developed approach where scientific problems involving differential equations are solved using neural networks. This approach shows tremendous promise in various fields of science and engineering. In the realm of scientific machine learning for solving phase field problems, we propose a novel backward-compatible physics-informed neural network approach to solve complex nonlinear partial differential equations. While this method can predict complex phase evolution in two-dimensional and three-dimensional systems, it lacks the efficiency of standard numerical methods. To improve efficiency, we propose a novel separable neural network-based approach to solve the gradient flow of Ginzburg-Landau free energy using a minimizing movement scheme. This work successfully demonstrates that the proposed method is much faster than conventional numerical methods such as finite element analysis.

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