Doctor of Philosophy (PhD)
Department of Mathematics
In recent years applied mathematicians have used modern analysis to develop variational phase-field models of fracture based on Griffith's theory. These variational phase-field models of fracture have gained popularity due to their ability to predict the crack path and handle crack nucleation and branching.
In this work, we are interested in coupled problems where a diffusion process drives the crack propagation. We extend the variational phase-field model of fracture to account for diffusion-driving fracture and study the convergence of minimizers using gamma-convergence. We will introduce Newton's method for the constrained optimization problem and present an algorithm to solve the diffusion-driven fracture problem numerically. For the implementation of this method, we use a finite difference scheme.
Dunkel, Friedrich Wilhelm Alexander, "A Phase-Field Approach to Diffusion-Driven Fracture" (2020). LSU Doctoral Dissertations. 5373.