Events

Recent Developments in the Generalized Finite Element Method for 3-D Fracture Propagation

The Generalized or eXtended Finite Element Method (GFEM) offers several advantages over the classical Finite Element Method (FEM) in modeling problems involving crack propagation, material discontinuities, and multi-scale phenomena. The first part of this talk focuses on fundamental aspects of the method such as GFEM approximations and their conditioning control. We will present a quadratic GFEM approximation for fractures that is optimally convergent and with a conditioning of the same order as the standard FEM. This allows the method to adopt coarser meshes than the FEM while delivering accurate quantities of interest such as stress intensity factors.

Applications of this method to 3-D fracture propagation are presented in the second part of the talk. The first application is the simulation of a fatigue crack propagation problem involving crack front splitting. This problem is also used for a blind verification of the method. The second application is the simulation of non-planar 3-D hydraulic fracture (HF) propagation. This process is widely used in the oil and gas industry to increase reservoir permeability and involves the injection of pressurized fluid in the fracture cavity. Hydraulic fractures are often created in fracture clusters, and this can lead to complex fracture geometries due to fracture interactions and fracture realignment with the preferential propagation direction. A precise estimate of the fracture geometry created during hydraulic stimulation operations is believed to be key to maximizing the extraction of hydrocarbons from unconventional resource plays.

Professor C. Armando Duarte

C. Armando Duarte is the Nathan Newmark Professor in the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign (UIUC). Before joining the University of Illinois in 2004, Professor Duarte was an Assistant Professor in the Department of Mechanical Engineering at the University of Alberta, Canada, and a Visiting Professor in the Department of Structural Engineering at the University of São Paulo, Brazil. He has five years of industrial experience (Altair Engineering). Professor Duarte is a Fellow of the United States Association for Computational Mechanics, and a Fellow of the National Center for Supercomputing Applications (NCSA). Dr. Duarte has made fundamental and sustained contributions to the fields of Computational Mechanics and Methods, particularly to the development of Meshfree, Partition of Unity, and Generalized/Extended Finite Element Methods (G/XFEM). He proposed the first partition of unity method to solve fracture problems (1997) and pioneered the use of asymptotic solutions of elasticity equations in the neighborhood of cracks as enrichment functions for this class of methods. Dr. Duarte has published more than 130 scientific articles and book chapters, co-edited two books on computational methods, and co-authored a book on enriched FEMs (Fundamentals of Enriched Finite Element Methods). Dr. Duarte’s group has a history of collaborative research with industry (Boeing, ExxonMobil, GE) and U.S. government agencies such as the Department of Defense (AFOSR and AFRL) and the Federal Aviation Administration (FAA).