Fundamentals of Enriched Finite Element Methods

   1st Edition - November 9, 2023


Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and their real-world applications, recommending in what situations they are best implemented. It starts with a concise background on the theory required to understand the underlying principles behind the methods before outlining detailed instruction on implementation of the techniques in standard displacement-based finite element codes. The strengths and weaknesses of each are discussed, as are computer implementation details, including a standalone generalized finite element package, written in Python. The applications of the methods to a range of scenarios, including multiphase, fracture, multiscale, and immersed boundary (fictitious domain) problems are covered, and readers can find ready-to-use code, simulation videos, and other useful resources on the companion website of the book.


Researchers working on numerical procedures in sold mechanics, Graduate students in a broad range of engineering disciplines, Professional engineers looking for new FEM techniques.

Key features

  • Reviews various enriched finite element methods, providing pros, cons, and scenarios for best use;
  • Provides step-by-step instruction on implementing these methods;
  • Covers the theory of general and enriched finite element methods.

About the authors

Team Member Alejandro M. Aragón

Delft Univ. of Technology

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.

  • Discontinuity-enriched finite element methods
  • Material interfaces and fracture
  • Topology optimization

Team Member Armando C. Duarte

Univ. of Illinois at Urbana-Champaign

C. Armando Duarte is a Professor in the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign. He 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.

  • Generalized/eXtended finite element methods
  • Fracture
  • Stabilization