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N. Sukumar
Professor, Computational Mechanics
Department of Civil & Environmental Engg
University of California
One Shields Avenue
Davis, CA 95616
Phone: +1 (530) 754-6415
Fax: +1 (530) 752-7872
E-mail: nsukumar-at-ucdavis.edu

RESEARCH INTERESTS

My research interests lie in the areas of computational solid mechanics and applied mathematics, with recent emphasis on new methods development for failure modeling in materials and in ab initio electronic-structure (Kohn-Sham equations of DFT) calculations. I have been involved in the development of meshfree (natural neighbor) and partition of unity finite element methods. Other areas of interest and current research emphasis include computational geometry, level set and fast marching methods, information theory, Bayesian theory of probability, maximum entropy methods in mechanics, bone fracture, constrained optimization and variational analysis, and parallel computing.

EDUCATION
1998 Ph.D., Theoretical and Applied Mechanics, Northwestern University, Thesis: "The Natural Element Method in Solid Mechanics." Thesis Committee: Brian Moran, Ted Belytschko, and Vladimir Volpert
1992 M.S., Materials Science and Engineering, Oregon Graduate Institute of Science & Technology, Thesis: "Finite Element Analysis of Mixed Mode Fracture and Failure in Composite Iosipescu Specimens." Advisor: Maciej Kumosa.
1989 B. Tech., Metallurgical Engineering, Indian Institute of Technology, Bombay. Senior Project: "A Microprocessor-Based Temperature Controller for an Electrical Resistance Furnace." Advisor: Nirdosh Khosla

ACADEMIC RESEARCH EXPERIENCE
07/10–present

Professor, Department of Civil and Environmental Engineering, University of California, Davis
01/11–08/11

Visiting Professor, PULSE Institute, Photon Science, SLAC National Accelerator Laboratory
07/07–06/10

Associate Professor, Department of Civil and Environmental Engineering, University of California, Davis
09/07–12/07

Visiting Associate Professor, Sibley School of Mechanical and Aerospace Engineering, Cornell University
07/00–06/07

Assistant Professor, Department of Civil and Environmental Engineering, University of California, Davis
07/00–12/00

Research Associate, Department of Mechanical and Aerospace Engineering, Princeton University
01/99–06/00

Post-Doc, Theoretical and Applied Mechanics, Northwestern University
01/94–06/98 Research Assistant, Theoretical and Applied Mechanics, Northwestern University
09/90–10/92 Research Assistant, Department of Materials Science and Engineering, Oregon Graduate Institute

INDUSTRIAL EXPERIENCE
1992–1993 Consultant, Endochronics Inc., WA
Numerical implementation of a gradient plasticity theory (proposed by Dr. K. C. Valanis) to describe the motion of particles in granular media.
1989–1990 Systems Engineer, Tata Steel, India.
Developed and implemented software modules in Oracle for management information systems.

TEACHING EXPERIENCE
2001–present

Assistant/Associate Professor/Professor, University of California, Davis

  • Advanced Structural Mechanics (Spring 10)
  • Elasticity (Fall 11)
  • Finite Element Procedures in Applied Mechanics (Winter 01-10, 12; Fall 05)
  • Finite Elements: Applications to Linear and Nonlinear Structural Mechanics Problems (Spring 03-04, 07)
  • Matrix Structural Analysis and the Finite Element Method (Fall 03/05)
  • Mechanics of Materials (Fall 01/02/06/08/10, Winter 02)
  • Meshfree Methods and Partition of Unity FEM (Spring 06, Fall 08, Spring 10)
  • Statics (Fall 04, Spring 05)
1997–1998 Teaching Assistant, Northwestern University .
Assisted in teaching, held office hours, and conducted MATLAB tutorials
  • Statics (Winter 1997)
  • Dynamic systems modeling (Spring 1998)

PRESENTATIONS
  1. "Maximum-Entropy Approximants: Applications in Solid Mechanics and Structural Engineering," Invited Lecture, Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, February 2012.

  2. "Efficient Numerical Integration Schemes for Singularities, Sharp gradients and Cusps: Applications in Fracture and Quantum Mechanics (with J. E. Pask and S. E. Mousavi)," Symposium on Meshfree and Extended/Generalized Finite Element Methods, PACAM XII, Port of Spain, Trinidad, January 2012.

  3. "Maximum-Entropy Approximation Schemes," Symposium on Meshfree and Extended/Generalized Finite Element Methods, PACAM XII, Port of Spain, Trinidad, January 2012.

  4. "Maximum-Entropy Approximations in Computational Mechanics," Invited Lecture, Department of Applied Mechanics, IIT Madras, Chennai, India, December 2011.

  5. "Partition-of-Unity Enriched Finite Elements to Solve the Hartree-Fock Equations (with T. J. Martínez)," Symposium on Current Multiscale Computations and Algorithms, 48th Annual Technical Conference of Society of Engineering Sciences, Evanston, IL, October 2011.

  6. "Enriched Finite Element Solution for the All-Electron Coulomb Problem in Solids (with J. E. Pask and S. E. Mousavi)," Poster Presentation, CECAM - Jülich Summer School 2011 on Fast Methods for Long-Range Interactions in Complex Systems, Jülich, Germany, September 2011.

  7. "A New Real-Space Formulation for the All-Electron Coulomb Problem in Crystalline Solids (with J. E. Pask and S. E. Mousavi)," Symposium on Recent Developments in Nanoscale Modeling of Materials, 11th U.S. National Congress on Computational Mechanics, Minneapolis, MN, July 2011.

  8. "Partition-of-Unity Finite Elements for Large, Accurate Quantum-Mechanical Materials Calculations," Plenary Lecture, ECCOMAS Thematic Conference on the Extended Finite Element Method (XFEM 2011), Cardiff, UK, July 1, 2011.

  9. Invited Participant, Mini-Workshop: Mathematical Models, Analysis, and Numerical Methods for Dynamic Fracture, Mathematische Forschungsinstitut Oberwolfach, Germany, April 24-30, 2011.

  10. "Extended Finite Elements for Crack Modeling: Numerical Integration Issues and Harmonic Enrichment Functions," Invited Lecture, Seminar in Computational Mechanics Organized by Laboratori de Calcul Numeric, Universitat Politecnica De Catalunya, Barcelona, Spain, July 2010.

  11. "Maximum-Entropy Meshfree Method in Computational Mechanics," Invited Lecture, Universidad Politecnica de Valencia, Spain, July 2010.

  12. "Extended Finite Elements using Harmonic Enrichment Functions for Crack Modeling," Invited Lecture, Universidad Politecnica de Valencia, Spain, July 2010.

  13. "Extended Finite Element Method for Crack Modeling: Formulation and Recent Developments," Invited Seminar, Dpto. Mecanica de Estructuras, Universidad de Granada, Spain, June 2010.

  14. "Extended Finite Element Method for Crack Modeling: Formulation and Recent Developments," Invited Seminar, Universidad de Sevilla, Spain, June 2010.

  15. "Maximum-Entropy Meshfree Method," Invited Lecture, Student-Run Applied & Math Seminar, Department of Mathematics, University of California, Davis, CA, April 2010.

  16. "Partition of Unity Finite Elements for Quantum-Mechanical Calculations in Condensed Matter: Have Planewaves Finally Met Their Match," Invited Lecture, Department of Mechanical Engineering, Mechanics of Computation Seminar, Stanford University, January 2010.

  17. "Maximum-Entropy Approximation in Computational Mechanics," Invited Lecture, Department of Civil and Environmental Engineering, Structural Engineering Seminar Series, University of Illinois at Urbana-Champaign, October 2009.

  18. "Efficient Numerical Integration for Discontinuities and Vertex Singularities in the Extended Finite Element Method," Invited Lecture, Institute of Continuum Mechanics, Leibniz University Hannover, Hannover, Germany, October 6, 2009.

  19. "Linear Scaling Finite Element Solution for the All-Electron Coulomb Problem in Solids," Invited Lecture, Institute for Numerical Simulation, University of Bonn, Bonn, Germany, October 1, 2009.

  20. "Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (with S. E. Mousavi)," ECCOMAS Thematic Conference - XFEM 2009 The extended finite element method: Recent developments and applications, Aachen, Germany, September 28-30, 2009.

  21. "Maximum Entropy Coordinates for Arbitrary Polytopes (with Kai Hormann)," 10th US National Congress on Computational Mechanics, Symposium on Synergies in Computational Mechanics and Geometry, Columbus, OH, July 2009.

  22. "Partition of Unity Finite Element Method to Solve the Kohn-Sham Equations of Density Functional Theory (with J. E. Pask)," Keynote Lecture, Symposium on Advances in Multiscale and Multiphysics Methods: From Quantum to Continuum, 8th World Congress on Computational Mechanics WCCM8, Venice, Italy, July 2008.

  23. "A New Finite Element Method for Three-Dimensional Non-Planar Crack Growth Simulations," Invited Lecture, Department of Mechanical and Aeronautical Engineering, University of California at Davis, CA, June 2008.

  24. "Linear Scaling Enriched Finite Element Solution of the Coulomb Problem in Solids," Invited Lecture, Structural Mechanics Seminar, Georgia Institute of Technology, Atlanta, GA, March 2008.

  25. "Partition of Unity Finite Elements for Electronic-Structure Calculations in Molecules and Crystalline Solids," Invited Lecture, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, December 7, 2007.

  26. "X-FEM and FMM: A Paradigm for Planar and Non-Planar Crack Growth Simulations," Invited Presentation, Global Engineering and Materials, Inc., Baltimore, MD, December 5, 2007.

  27. "A New Real-Space Finite Element Method to Solve the Kohn-Sham Equations of Density Functional Theory," Invited Lecture, Numerical Analysis and Scientific Computing Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY, November 16, 2007.

  28. "Partition of Unity Finite Elements for Electronic-Structure Calculations in Molecules and Crystalline Solids," Invited Lecture, Joint Mechanical Engineering/Civil Engineering Seminar, Columbia University, New York, NY, November 9, 2007. [PDF]

  29. "Barycentric Finite Element Methods," Invited Lecture, Symposium on Barycentric Coordinates and Transfinite Interpolation, Tenth SIAM Conference on Geometric Design & Computing, San Antonio, TX, November 5, 2007.

  30. "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method," Invited Lecture, Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY, October 29, 2007.

  31. "Mesh-Independent Crack Modeling using the Extended Finite Element Method," Invited Presentation, Cornell Fracture Group, Cornell University, Ithaca, September 27, 2007.

  32. "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method (with D. L. Chopp, N. Moës, E. Bechet)," 9th U.S. National Congress on Computational Mechanics, San Francisco, CA, July 25, 2007.

  33. "Finite Element and Meshfree Methods in Mechanics," Invited Lecture, GGAM Mini-Conference, Department of Mathematics, University of California, Davis, CA, March 31, 2007.

  34. "Linking Geometry and Approximation for Computational Mechanics," Invited Lecture, Mechanics Colloquium, Technical University of Kaiserslautern, Germany, September 18, 2006.

  35. "Partition of Unity Finite Elements in Quantum Mechanical Materials Calculations," Invited Lecture, Seminar in Computational Mechanics Organized by Laboratori de Calcul Numeric and CIMNE, Universitat Politecnica De Catalunya, Barcelona, Spain, September 15, 2006.

  36. "Meshfree Methods and Partition of Unity Finite Elements," Short Course at Universidad Politecnica De Valencia, Valencia, Spain, September 5-11, 2006.

  37. "Partition of Unity Finite Element Method for Large-Scale Electronic Structure Calculations (with J. E. Pask)," Seventh World Congress on Computational Mechanics, Symposium on Enriched Finite Element Methods for Evolving Discontinuities and Interfaces, Los Angeles, CA, July 2006.

  38. "Continuity of Maximum-Entropy Basis Functions via Variational Analysis (with R. J-B Wets)," Seventh World Congress on Computational Mechanics, Symposium on Computational Geometry and Analysis, Los Angeles, CA, July 2006.

  39. "Recent Advances in Polygonal Finite Element Methods," Invited Lecture, Mathematical Modeling and Analysis Group, Los Alamos National Laboratory, Los Alamos, New Mexico, April 2006.

  40. "Natural Neighbors and Voronoi Tessellations in Computational Solid Mechanics," Keynote Lecture, The World a Jigsaw: Tessellations in the Sciences, Lorent Center, Leiden University, The Netherlands, March 6-10, 2006 [PDF] [HTML] [PDF]

  41. "Scattered Data Approximation and Meshfree Methods," Invited Lecture, Applied Math Seminar, Department of Mathematics, University of California, Davis, CA, October 2005 [PDF]

  42. "Adaptive Computations using Conforming Quadtree Meshes," (with A. Tabarraei), Invited Lecture, Mechanics Colloquium, Technical University of Kaiserslautern, Germany, September 2005

  43. "Construction of Meshfree Approximation Schemes: Use of Information- Theoretic Variational Principles," Invited Lecture, Technical University of Kaiserslautern, Germany, September 2005

  44. "Meshfree Methods and Partition of Unity Finite Elements: Basic Principles and Applications," Invited Lecture, Technical University of Kaiserslautern, Germany, September 2005

  45. "Adaptive Computations using Residual-Based Error Estimators on Conforming Quadtree Meshes," (with A. Tabarraei), Third International Workshop on Meshfree Methods for Partial Differential Equations, Bonn, Germany, September 2005

  46. "Maximum Entropy Approximation," 25th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, San Jose State University, CA, August 2005

  47. "Maximum Entropy Approximation," Symposium on Meshfree and Particle Methods, Keynote Lecture, Eight U.S. National Congress on Computational Mechanics, Austin, TX, July 2005 [PDF]

  48. "Scattered Data Approximation using the Maximum Entropy Principle," Invited Lecture, Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY, May 2005.

  49. "Scattered Data Approximation using the Maximum Entropy Principle," Invited Lecture, Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA, December 2004.

  50. "Modeling Arbitrary Crack Discontinuities in Finite Elements," Invited Lecture, Rockwell Scientific Company, Thousand Oaks, CA, November 2004

  51. "Recent Advances in Polygonal Finite Elements: Construction and Applications to PDEs,", Keynote Lecture, International Workshops on Advances in Computational Mechanics (Meshfree/Particle Methods), Hosei University, Tokyo, Japan, November 2004.

  52. "Construction and Application of Polygonal Finite Element Approximations," (with A. Tabarraei), Sixth World Congress on Computational Mechanics, Symposium on Meshfree and Extended/Fictitious FEM, Beijing, China, September 2004.

  53. "Polygonal Interpolants: Construction and Adaptive Computations on Quadtree Meshes," (with A. Tabarraei), European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Symposium on Computational Fracture Mechanics, Jyvskyla, Finland, July 2004.

  54. "Polygonal Finite Elements: Construction and Applications to PDEs," Invited Lecture, Ecole Centrale de Nantes, Nantes, France, July 2004

  55. "Partition of Unity and Polygonal Finite Element Methods," Invited Lecture, Universidad Politecnica de Valencia, Spain, April 2004

  56. "Numerical Formulation and Application of Polygonal Finite Elements" (with A. Tabarraei), 7th International ESAFORM Conference on Material Forming, Trondheim, Norway, April 2004

  57. "Conforming Polygonal Finite Elements," Invited Lecture, Laboratoire de Mecanique des Systemes et des Procedes, ENSAM, Paris, France, April 2004

  58. "Modeling Strong and Weak Discontinuities within Displacement Based Finite Elements," Invited Lecture, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India, March 2004

  59. "Modeling Arbitrary Discontinuities in Finite Elements," Invited Lecture, Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, India, March 2004

  60. "Partition of Unity Enrichment for Bimaterial Interface Cracks," (with J. H. Prévost, Z. Suo, and Z. Y. Huang) Seventh U.S. National Congress on Computational Mechanics, Albuquerque, NM, July 2003 [PDF]

  61. "Irregular Lattice Models for Diffusion Processes and Crack Propagation," (with J. E. Bolander) Invited Presentation, Mimetic Discretizations of Continuum Mechanics, San Diego, CA, July 2003

  62. "Meshless Methods and Partition of Unity Finite Elements" Keynote Lecture, 6th International ESAFORM Conference on Material Forming, Salerno, Italy, April 28-30, 2003

  63. "Finite Element-Based Model for Crack Propagation in Polycrystalline Materials" Invited Lecture, 2nd Symposium on Computational Modeling of Multi-Scale Phenomena, Petropolis, Brazil, August 2002 [PDF]

  64. "Modeling Discontinuities and their Evolution within Finite Elements: Application to Material Interfaces, 3-D Cracks, and Microstructures," Invited Lecture, Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ, September 2001

  65. "Enriched Natural Neighbor Interpolants for Two-Dimensional Crack Modeling," Sixth U.S. National Congress on Computational Mechanics, Dearborn, MI (August 2001) [PDF]

  66. "Microstructural Effects in Brittle Fracture with the Extended Finite Element Method," (with D. J. Srolovitz, J. H. Prévost, and T. J. Baker) Sixth U.S. National Congress on Computational Mechanics, Dearborn, MI, August 2001 [PDF]

  67. "Sibson and Non-Sibsonian Interpolants for Elliptic Partial Differential Equations," First MIT Conference on Fluid and Solid Mechanics, Cambridge, MA, June 2001

  68. "Extended Finite Element Method: Introduction and Applications," MAE Material Group Seminar, Princeton University, NJ, December 2000

  69. "Natural Neighbor Galerkin Methods," (with Brian Moran) ICTAM 2000, Chicago, IL, October 2000

  70. "Modeling Holes and Inclusions by Level Sets in the Extended Finite Element Method," Mechanics Club Seminar, Northwestern University, Evanston, IL, February 2000

  71. "The Natural Element Method," Number Crunch Seminar, Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, October 1999

  72. "Galerkin Methods for Elliptic Partial Differential Equations," Number Crunch Seminar, Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, October 1999

  73. "An Element-Free Galerkin Method for 3D Crack Growth," (with T. Belytschko, B. Moran, and T. Black) Joint ASME, ASCE, and SES Conference (McNU 97), Northwestern University, Evanston, IL (July 1997)

PUBLICATIONS

Refereed Journal & Conference Publications

  1. S. E. Mousavi, J. E. Pask and N. Sukumar (2011), "Efficient Adaptive Integration of Functions with Sharp Gradients and Cusps in n-Dimensional Parallelepipeds," International Journal for Numerical Methods in Engineering, in press. [PDF]
  2. J. E. Pask, N. Sukumar and S. E. Mousavi (2012), "Linear Scaling Solution of the All-Electron Coulomb Problem in Solids," International Journal for Multiscale Computational Engineering, Vol. 10, Number 1, pp. 83–99. Available at arXiv:1004.1765
  3. R. Rojas-Díaz, N. Sukumar, A. Sáez and F. García-Sánchez (2011), "Fracture in Magnetoelectroelastic Materials using the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 88, Number 12, pp. 1238–1259. [PDF]
  4. G. Hattori, R. Rojas-Díaz, A. Sáez, F. García-Sánchez and N. Sukumar (2011), "El Método de los Elementos Finitos Extendidos (X-FEM) para Medios Bidimensionales Fisurados Totalmente Anisótropos," Anales de Mecánica de la Fractura, Vol. 28, Number 2, pp. 451–455. [PDF]
  5. A. Ortiz, M. A. Puso and N. Sukumar (2011), "Maximum-Entropy Meshfree Method for Incompressible Media Problems," Finite Element in Analysis and Design, Vol. 47, Number 6, pp. 572–585. [PDF]
  6. S. E. Mousavi and N. Sukumar (2011), "Numerical Integration of Polynomials and Discontinuous Functions on Irregular Convex Polygons and Polyhedrons," Computational Mechanics, Vol. 47, Number 5, pp. 535–554. [PDF]
  7. S. E. Mousavi, E. Grinspun and N. Sukumar (2011), "Higher-Order Extended Finite Elements with Harmonic Enrichment Functions for Complex Crack Problems," International Journal for Numerical Methods in Engineering, Vol. 86, Number 4–5, pp. 560–574. [PDF]
  8. S. E. Mousavi, E. Grinspun and N. Sukumar (2011), "Harmonic Enrichment Functions: A Unified Treatment of Multiple, Intersecting and Branched Cracks in the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 85, Number 10, pp. 1306–1322. [PDF]
  9. J. X. Shi, D. L. Chopp, J. Lua, N. Sukumar and T. Belytschko (2010) "Abaqus Implementation of Extended Finite Element using a Level Set Representation for Three-Dimensional Fatigue Crack Growth and Life Predictions," Engineering Fracture Mechanics, Vol. 77, Number 14, pp. 2840–2863. [Top 25 Hottest article (July 2010-present)] [PDF]
  10. S. E. Mousavi and N. Sukumar (2010), "Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method," Computer Methods in Applied Mechanics and Engineering, Vol. 199, Number 49–52, pp. 3237–3249. [PDF]
  11. A. Ortiz, M. A. Puso and N. Sukumar (2010), "Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity," Computer Methods in Applied Mechanics and Engineering, Vol. 199, Number 25–28, pp. 1859–1871. [PDF]
  12. S. E. Mousavi and N. Sukumar (2010), "Generalized Duffy Transformation for Integrating Vertex Singularities," Computational Mechanics, 45, Number 2–3, pp. 127–140. [PDF]
  13. S. E. Mousavi, H. Xiao and N. Sukumar (2010), "Generalized Gaussian Quadrature Rules on Arbitrary Polygons," International Journal for Numerical Methods in Engineering, Vol. 82, Number 1, pp. 99–113. [PDF]
  14. R. Rojas-Díaz, N. Sukumar, A. Sáez and F. García-Sánchez (2009), "Crack analysis in magnetoelectroelastic media using the extended finite element method," in Proceedings of the International Conference on Extended Finite Element Methods – Recent Developments and Applications, Eds. T.-P. Fries and A. Zilian, Aachen, Germany, pp. 181–186. [PDF]
  15. A. Rajagopal, M. Scherer, P. Steinmann and N. Sukumar (2009), "Smooth Conformal α-NEM for Gradient Elasticity," The International Journal of Structural Changes in Solids – Mechanics and Applications, 1, Number 1, pp. 83–109. [PDF]
  16. W. Aquino, J. C. Brigham, C. J. Earls and N. Sukumar (2009), "Generalized Finite Element Method using Proper Orthogonal Decomposition," International Journal for Numerical Methods in Engineering, Vol. 79, Number 7, pp. 887–906. [PDF]
  17. L. L. Yaw, N. Sukumar and S. K. Kunnath (2009), "Meshfree Co-Rotational Formulation for Two-Dimensional Continua," International Journal for Numerical Methods in Engineering, Vol. 79, Number 8, pp. 979–1003. [PDF]
  18. L. L. Yaw, S. K. Kunnath and N. Sukumar (2009), "Meshfree Method for Inelastic Frame Analysis," ASCE Journal of Structural Engineering, Vol. 135, Number 6, pp. 676–684. [PDF]
  19. N. Sukumar and J. E. Pask (2009), "Classical and Enriched Finite Element Formulations for Bloch-Periodic Boundary Conditions,", International Journal for Numerical Methods in Engineering, Vol. 77, Number 8, pp. 1121–1138. [Erratum: a = 5.7 bohr for the harmonic oscillator problem in Sec. 4.2.1] [PDF]
  20. E. Giner, N. Sukumar, J. E. Tarancón and F. J. Fuenmayor (2009), "An Abaqus Implementation of the Extended Finite Element Method," Engineering Fracture Mechanics, Vol. 76, Number 3, pp. 347–368. [Top 25 Hottest article (January 2009-present)] [PDF]
  21. E. Giner, N. Sukumar, F. J. Fuenmayor and A. Vercher (2008), "Singularity Enrichment for Complete Sliding Contact using the Partition of Unity Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 76, Number 9, pp. 1402–1418. [PDF]
  22. E. Giner, N. Sukumar, F. D. Denia and F. J. Fuenmayor (2008), "Extended Finite Element Method for Fretting Fatigue Crack Propagation," International Journal of Solids and Structures, Vol. 45, Number 22–23, pp. 5675–5687. [PDF]
  23. K. Hormann and N. Sukumar (2008), "Maximum Entropy Coordinates for Arbitrary Polytopes," Computer Graphics Forum, Vol. 27, Number 5, pp. 1513–1520. Proceedings of SGP 2008. [PDF]
  24. N. Sukumar, D. L. Chopp, E. Béchet and N. Moës (2008), "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method," International Journal for Numerical Methods in Engineering, Vol. 76, Number 5, pp. 727–748. [PDF]
  25. N. Sukumar and J. E. Bolander (2009), "Voronoi-based Interpolants for Fracture Modelling," in Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, Springer Verlag, pp. xxx–xxx. [PDF]
  26. C. B. Hirschberger, S. Ricker, P. Steinmann and N. Sukumar (2009),"Computational multiscale modelling of heterogeneous material layers," Engineering Fracture Mechanics, Vol. 76, Number 6, pp. 793–812. [PDF]
  27. J. Shi, J. Lua, H. Waisman, P. Liu, T. Belytschko, N. Sukumar and Y. Liang (2008), "X-FEM Toolkit for Automated Crack Onset and Growth Prediction," 49th AIAA Conference, Schaumburg, IL, April 2008, pp. 1–22. [PDF]
  28. A. Tabarraei and N. Sukumar (2008), "Extended Finite Element Method on Polygonal and Quadtree Meshes," Computer Methods in Applied Mechanics and Engineering, Vol. 197, Number 5, pp. 425–438. [PDF]
  29. C. B. Hirschberger, N. Sukumar and P. Steinmann (2008),"Computational homogenization of material layers with micromorphic mesostructure," Philosophical Magazine, Vol. 88, pp. 3603–3631. [PDF]
  30. C. B. Hirschberger S. Ricker, P. Steinmann and N. Sukumar (2007),"A computational homogenisation approach for cohesive interfaces," in Proceedings of the International Conference on Computational Plasticity, Computational Plasticity IX: Fundamentals and Applications, Eds. D. R. J. Owen and E. Onate, Barcelona, Spain, pp. 442–445.
  31. N. Sukumar and R. J-B Wets (2007), "Deriving the Continuity of Maximum-Entropy Basis Functions via Variational Analysis," SIAM Journal of Optimization, Vol. 18, Number 3, pp. 914–925. [PDF] or Journal
  32. A. Tabarraei and N. Sukumar (2007), "Adaptive Computations Using Material Forces and Residual-Based Error Estimators on Quadtree Meshes," (2007) Computer Methods in Applied Mechanics and Engineering, Vol. 196, Number 25–28, pp. 2657–2680. [PDF]
  33. N. Sukumar and R. W. Wright (2007), "Overview and Construction of Meshfree Basis Functions: From Moving Least Squares to Entropy Approximants," International Journal for Numerical Methods in Engineering, Vol. 70, Number 2, pp. 181–205. [PDF]
  34. A. Tabarraei and N. Sukumar (2006), "Application of Polygonal Finite Elements in Linear Elasticity" International Journal of Computational Methods, Vol. 3, Number 4, pp. 503–520. [PDF]
  35. N. Sukumar and E. A. Malsch (2006), "Recent Advances in the Construction of Polygonal Finite Element Interpolants," Archives of Computational Methods in Engineering, Vol. 13, Number 1, pp. 129–163. [PDF] (proof)
  36. N. Sukumar, "Maximum Entropy Approximation," in Proceedings of the 25th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Eds. K. H. Knuth, A. E. Abbas, R. D. Morris and J. P. Castle, AIP Conference Proceedings, 803(1), 2005, pp. 337–344. [HTML]
  37. N. Sukumar, J. Dolbow, A. Devan, J. Yvonnet, F. Chinesta, D. Ryckelynck, Ph. Lorong, I. Alfaro, M. A. Martínez, E. Cueto, and M. Doblaré, "Meshless Methods and Partition of Unity Finite Elements," International Journal of Forming Processes, 8(4), 2005, pp. 409–427. [PDF]
  38. Z. Huang, Z. Suo, G. Xu, J. He, J. H. Prévost and N. Sukumar, "Initiation and Arrest of an Interfacial Crack in a Four-Point Bend Test," Engineering Fracture Mechanics, 72(17), 2005, pp. 2584–2601. 2005. [PDF]
  39. J. E. Bolander and N. Sukumar, "Irregular Lattice Model for Quasistatic Crack Propagation," Physical Review B, 71, 2005, 094106 [PDF]
  40. A. Tabarraei and N. Sukumar, "Adaptive Computations on Conforming Quadtree Meshes," Finite Elements in Analysis and Design 41(7–8), 2005, pp. 686–702. [PDF] or UC repository postprints
  41. N. Sukumar, "Construction of Polygonal Interpolants: A Maximum Entropy Approach," International Journal for Numerical Methods in Engineering, 61(12), 2004, pp. 2159–2181. [PDF]
  42. N. Sukumar and A. Tabarraei, "Conforming Polygonal Finite Elements," International Journal for Numerical Methods in Engineering, 61(12), 2004, pp. 2045–2066. [PDF]
  43. N. Sukumar and A. Tabarraei, "Polygonal Interpolants: Construction and Adaptive Computations on Quadtree Meshes," in European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Eds. P. Neittaanmäki, T. Rossi, S. Korotov, E. Onate, J. Periaux and D. Knörzer, Jyväskylä, Finland, 2004 [PDF]
  44. N. Sukumar and A. Tabarraei, "Numerical Formulation and Application of Polygonal Finite Elements," in Proceedings of the Seventh ESAFORM Conference on Metal Forming, Ed. S. Stören, Trondheim, Norway, pp. 73–76, 2004 [PDF]
  45. N. Sukumar, Z. Y. Huang, J.-H. Prévost and Z. Suo "Partition of Unity Enrichment for Bimaterial Interface Cracks," International Journal for Numerical Methods in Engineering, 59(8), 2004, pp. 1075–1102. [Abstract] [PDF] [PS]
  46. N. Sukumar and D. J. Srolovitz, "Finite Element-Based Model for Crack Propagation in Polycrystalline Materials," Computational & Applied Mathematics , 23(2–3), 2004, pp. 363–380 [PDF]
  47. E. Cueto, N. Sukumar, B. Calvo, M. A. Martínez, J. Cegoñino and M. Doblaré (2003), "Overview and Recent Advances in Natural Neighbour Galerkin Methods," Archives of Computational Methods in Engineering, 10(4), 2003, pp. 307–384. [PDF] (proof [M. A. Martínez is missing in the author-list])
  48. N. Sukumar and J. E. Bolander "Numerical Computation of Discrete Differential Operators on Non-Uniform Grids," Computer Modeling in Engineering & Sciences, 4(6), 2003, pp. 691–706. [PDF]
  49. N. Sukumar and J.-H. Prévost "Modeling Quasi-Static Crack Growth with the Extended Finite Element Method. Part I: Computer Implementation," International Journal of Solids and Structures, 40(26), 2003, pp. 7513–7537. [Abstract] [PDF] [PS]
  50. R. Huang, N. Sukumar and J.-H. Prévost "Modeling Quasi-Static Crack Growth with the Extended Finite Element Method. Part II: Numerical Applications," International Journal of Solids and Structures, 40(26), 2003, pp. 7539–7552. [Abstract] [PDF] [PS]
  51. N. Sukumar, "Meshless Methods and Partition of Unity Finite Elements," in Proceedings of the Sixth International ESAFORM Conference on Material Forming, Salerno, Italy, Ed. V. Brucato, April 2003, pp. 603–606. [PDF] [PS]
  52. T. Belytschko, C. Parimi, N. Moës, N. Sukumar and S. Usui, "Structured Extended Finite Element Methods for Solids Defined by Implicit Surfaces," International Journal for Numerical Methods in Engineering, 56(4), 2003, pp. 609–635. [PDF]
  53. N. Sukumar, "Voronoi Cell Finite Difference Method for the Diffusion Operator on Arbitrary Unstructured Grids," International Journal for Numerical Methods in Engineering, 57(1), 2003, pp. 1–34. [Abstract] [PDF]
  54. D. L. Chopp and N. Sukumar, "Fatigue Crack Propagation of Multiple Coplanar Cracks with the Coupled Extended Finite Element/Fast Marching Method," International Journal of Engineering Science, 41(8), 2003, pp. 845–869. [PDF]
  55. N. Sukumar, D. L. Chopp and B. Moran, "Extended Finite Element Method and Fast Marching Method for Three-Dimensional Fatigue Crack Propagation," Engineering Fracture Mechanics, 70(1), 2003, pp. 29–48. [PDF] [PS]
  56. N. Sukumar, D. J. Srolovitz, T. J. Baker and J.-H. Prévost, "Brittle Fracture in Polycrystalline Materials with the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, 56(14), 2003, pp. 2015–2037. [PDF]
  57. N. Sukumar, "Sibson and Non-Sibsonian Interpolants for Elliptic Partial Differential Equations," in Proceedings of the First MIT Conference on Fluid and Solid Mechanics, Volume 2, Ed. K. J. Bathe, Elsevier Press, 2001, pp. 1665–1667. [PDF]
  58. N. Sukumar, D. L. Chopp, N. Moës and T. Belytschko, "Modeling Holes and Inclusions by Level Sets in the Extended Finite–Element Method," Computer Methods in Applied Mechanics and Engineering, 190(46–47), 2001, pp. 6183–6200. [PDF] [PS]
  59. N. Sukumar, B. Moran, A. Yu Semenov and V. V. Belikov, "Natural Neighbour Galerkin Methods," International Journal for Numerical Methods in Engineering, 50(1), 2001, pp. 1–27. [PDF] [PS]
  60. C. Daux, N. Moës, J. Dolbow, N. Sukumar and T. Belytschko, "Arbitrary Branched and Intersecting Cracks with the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, 48(12), 2000, pp. 1741–1760. [PDF] [PS]
  61. N. Sukumar, N. Moës, B. Moran and T. Belytschko, "Extended Finite Element Method for Three-Dimensional Crack Modelling," International Journal for Numerical Methods in Engineering, 48(11), 2000, pp. 1549–1570. [PDF] [PS]
  62. N. Moës, N. Sukumar, B. Moran and T. Belytschko, "An Extended Finite Element Method (X-FEM) for Two- and Three-Dimensional Crack Modeling," in Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, Spain, September 2000. [PDF] [PS]
  63. D. Bueche, N. Sukumar and B. Moran, "Dispersive Properties of the Natural Element Method," Computational Mechanics, 25(2/3), 2000, pp. 209–217. [PDF] [PS]
  64. N. Sukumar and B. Moran "C1 Natural Neighbor Interpolant for Partial Differential Equations," Numerical Methods for Partial Differential Equations, 15(4), 1999, pp. 417–447. [PDF] [PS]
  65. B. Moran, N. Sukumar and T. Belytschko, "Application of the Natural Element Method in Elastostatics," in Modeling and Simulation Based Engineering, Volume 1, Eds. S. Atluri and P. O'Donoghue, Tech. Science Press, 1998.

  66. N. Sukumar, B. Moran and T. Belytschko, "The Natural Element Method in Solid Mechanics," International Journal for Numerical Methods in Engineering, 43(5), 1998, pp. 839–887. [PDF] [PS]
  67. N. Sukumar, B. Moran, T. Belytschko and T. Black, "An Element-Free Galerkin Method for Three-Dimensional Fracture Mechanics," Computational Mechanics, 20, 1997, pp. 170–175. [PDF] [PS]
  68. N. Sukumar and M. Kumosa, "Finite Element Analysis of Axial Splits in Iosipescu Specimens," International Journal of Fracture, 62, 1993, pp. 55–85.

  69. N. Sukumar and M. Kumosa, "Stress Singularities at Sharp Notches: Interpolation Formulas," International Journal of Fracture, 58, 1992, pp. R45–R49.

  70. N. Sukumar and M. Kumosa, "Application of the Finite Element Iterative Method to Cracks and Sharp Notches in Orthotropic Media," International Journal of Fracture, 58, 1992, pp. 177–192.

Thesis

Technical Reports

  1. B. Moran, T. Belytschko and N. Sukumar, " On the Element Free Galerkin Method for 3D Fracture Mechanics" FAA Technical Report, 1998.
  2. B. Moran, A. Zulfiqar and N. Sukumar, " On the Direct Integration Method for Fatigue Reliability Calculations" Technical Report to Center for Integrated Diagnostics, Georgia Tech., July 1996
  3. B. Moran, T. Belytschko and N. Sukumar, " NU-FORM, Program Documentation and Listing" FAA Technical Report, July 1994.

Unpublished/Web Documents

  1. N. Sukumar, "Where Do We Stand on Meshfree Approximation Schemes?" in Online Blog on Meshfree Methods, September 2006 [HTML] or [HTML]
  2. N. Sukumar, " A C1 NEM Interpolant for Fourth-Order PDEs," Internal Report, Theoretical and Applied Mechanics, Northwestern University, December 1997 [LaTeX2HTML document]

  3. N. Sukumar, " A Note on Natural Neighbor Interpolation and the Natural Element Method," Internal Report, Theoretical and Applied Mechanics, Northwestern University, May 1997 [LaTeX2HTML document]

  4. N. Sukumar, " Patch test in 1D using FE-EFG coupling," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  5. N. Sukumar, " Application of the coupled FE-EFG method to material discontinuities in 1D and 2D," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  6. N. Sukumar, " SIF computations for 2D cracks using enriched basis functions," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  7. N. Sukumar, " PUFEM in one-dimension," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  8. N. Sukumar, " PUFEM--revisited," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]

EXTERNAL REVIEWER
  • Journals: Over twenty journals in solid mechanics, computational mechanics, fracture, computer graphics, and physics
  • Research Proposals: NSF, DOE, AFOSR, ARO, Minnesota Supercomputing Institute, Israeli and Czech Science Foundations

SOFTWARE

Last update: July 22, 2010
N. Sukumar [E-mail]