Fundamentals of Enriched Finite Element Methods

Alejandro M. Aragón is an Associate Professor in the Department of Precision and Microsystems Engineering at Delft University of Technology in the Netherlands. His research stands at the intersection of engineering and computer science, with a primary focus on pioneering novel enriched finite element methods. This cutting-edge technology, seamlessly integrated in widely applicable software, is leveraged to address complex engineering challenges. Specifically, Dr. Aragón’s innovations have been employed in the analysis and design of a diverse spectrum of (meta)materials and structures, including biomimetic and composite materials, as well as acoustic/elastic metamaterials, photonic/phononic crystals, and even edible fracture metamaterials. Since 2015 he has also been teaching advanced courses on finite element analysis at TU Delft. Dr. Aragón boasts a strong industrial network and holds two patents for the inventive use of acoustic/elastic metamaterials and phononic crystals for noise attenuation. C. Armando Duarte is a Professor in the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign. Prior to joining the UIUC, he 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 Sao Paulo, Brazil. He has five years of industrial experience and has made fundamental and sustained contributions to the fields of computational mechanics and methods, in particular to development of Meshfree, Partition of Unity, and Generalized/eXtended Finite Element Methods. He proposed the first partition of unity method to solve fracture problems and pioneered the use of asymptotic solutions of elasticity equations of cracks as enrichment functions for this class of methods. His group has developed a 3D GFEM for the simulation of hydraulic fracture propagation, interaction, and coalescence, and he has published more than 95 scientific articles and book chapters, and also coedited 2 books on computational methods. He has papers featured on the ScienceDirect top 25 Hottest Articles of Computer Methods in Applied Mechanics and Engineering and Engineering Fracture Mechanics.

• 1. Introduction2. The Finite Element Method.3. The p-version of the Finite Element Method4. The Generalized Finite Element Method5. Discontinuity-enriched Finite Element Formulations6. GFEM approximations for fractures7. Approximations for Weak Discontinuities8. Immerse boundary (fictitious domain) problems9. Nonconforming mesh coupling and contact10. Interface-enriched topology optimization11. Stability of approximations12. Computational aspects13. Approximation theory for partition of unity methodsAppendix. Recollections of the origins of the GFEM