Dissertation Title: Energy Barrier in Crack Nucleation via the Phase Field Approach to Fracture
Date: 2026/05/15 – 2026/05/15
Dissertation Title: Energy Barrier in Crack Nucleation via the Phase Field Approach to Fracture
Speaker: Yihao Chen (陈义豪)
Time: May 15, 2:00 p.m.-3:30 p.m., 2026 (Beijing Time)
Location: Room 403, Long Bin Building
Abstract
The classical Griffith theory provides a foundational energy criterion for crack propagation: a crack will grow when the released elastic strain energy is sufficient to overcome the surface energy required to create new crack faces. Although this criterion is successful in describing the behavior of solids with pre-existing cracks, when considering crack nucleation in an initially crackless solid, even if the energy criterion is satisfied, a crack will not instantaneously nucleate. The reason is that a typical energy landscape of crack nucleation has two minima, or two wells, corresponding to a crackless state and a cracked state, separated by an energy barrier. This energy barrier (1) leads to overestimation of material toughness with normal numerical approaches and (2) it is significant in determining the nucleation kinetics under the framework of transition state theory (TST).
The first part of this work proposes a computational framework, the “parallel universe” scheme to correctly predict the critical load for crack nucleation. This framework captures the energy competition between crack surface energy and strain potential energy in the energy landscape of the crack nucleation, by tracking two universes corresponding to the crackless state and the cracked state, respectively. The universe with a currently lower energy is the true universe.
This scheme has two key ingredients: (a) a necessary condition for cracking solely based on the current crackless solution, and (b) beginning from when this condition is met, Newton iteration with two initial guesses, a crackless one and a cracked one, will both be performed and the converged candidate solution with lower energy is accepted as the solution at that load step. Once the cracked candidate solution is accepted, the crackless one is discarded, i.e., only one universe is retained. This cracked initial guess is obtained only once for all load steps by solving a series of similar minimization problems with a progressively reduced critical crack energy release rate. Numerical examples with isotropic and anisotropic critical crack energy release rates indicate that the proposed algorithm is more reliable (as there is no need to retrace) and more efficient than the standard Newton iteration and a well-known backtracking algorithm.
The second part of this work constructs a framework for formulating the energy barrier in crack nucleation within TST. This framework considers all possible paths connecting the crackless state and the cracked state. The path with the lowest peak energy is the minimum energy path (MEP), and the energy barrier is then the difference between that peak energy and the energy of the crackless state.
This framework is constructed with the phase field approach to fracture and Nudged Elastic Band method. As the phase field is an internal variable, the configurations are expressed solely in terms of the set of discretized phase field values. The analytical formula is derived by approximating the realistic phase field configuration through two typical configurations in the phase field approach to fracture, thereby calculating the energy barrier.
For the numerical formulation, the reaction path is optimized with Nudged Elastic Band method.
The reaction path is subjected to two forces: one is a pseudo-spring force, derived from the difference between neighboring configurations, which keeps intermediate configurations even spaced; the other is a potential force, which drives the configurations toward the minimum energy path. Once the reaction path is optimized, the energy barrier is readily available. Numerical examples demonstrate that this scheme can robustly capture energy barriers across a range of typical material geometries.
Biography
Yihao Chen is a is a Ph.D. candidate at the Global College, Shanghai Jiao Tong University. His research centers on the phase field approach to fracture and crack nucleation. To date, he has published 2 academic papers as first author.