Abstract

This talk presents an overview of the Irreversible Phase Field Model for Fracture (Irreversible F-PFM) proposed by the speaker and collaborators, which is based on the concept of irreversible gradient flows. An irreversible gradient flow is a constrained gradient flow in which monotonicity in time is enforced, leading to a natural energy-dissipation identity [Akagi–Kimura, 2019; Kimura–Negri, 2021].

The Irreversible F-PFM applies this framework to the Ambrosio–Tortorelli regularization of the variational fracture model by Francfort and Marigo, ensuring both the irreversibility of crack evolution and monotonic energy decay (i.e., a consistent dissipation structure). This model is compactly formulated using partial differential equations and is readily amenable to standard finite element solvers, enabling crack propagation simulations without a priori knowledge of the crack path.

After reviewing the mathematical structure of the Irreversible F-PFM, the talk will introduce a range of recent extensions and their finite element simulations, each highlighting how the dissipation structure is preserved or adapted. These include: Irreversible F-PFM under unilateral constraints; Thermo-mechanical fracture models; Phase field modeling of fracking in oil and gas reservoirs; Desiccation-induced fracture modeling; Dynamic phase-field fracture models and seismic fault rupture; Through these examples, we aim to highlight the versatility and robustness of the irreversible phase-field approach in simulating complex fracture phenomena across disciplines.

Mathematical Physics and Dynamical Systems Seminar

Seminari di Equazioni Differenziali e Applicazioni