Publications

Elastic Fracture Mechanics (FEM)

• N. Sukumar and M. Kumosa. Finite element analysis of axial splits in composite Iosipescu specimens. 1993. International Journal of Fracture, 62:55–85.
• N. Sukumar and M. Kumosa. Stress singularities at sharp notches: Interpolation formulas. 1992. International Journal of Fracture, 58:R45–R49.
• N. Sukumar and M. Kumosa. Application of the Finite Element Iterative Method to cracks and sharp notches in orthotropic media. 1992. International Journal of Fracture, 58:177–192.

Element-Free Galerkin Method

• N. Sukumar and B. Moran and T. Black and T. Belytschko. An element-free Galerkin method for three-dimensional fracture mechanics. 1997. Computational Mechanics, 20(1/2):170–175.
• N. Sukumar. Patch test in 1D: coupled FE-EFG method. 1996. Unpublished.
• N. Sukumar. Application of the coupled FE-EFG method to material discontinuities in 1D and 2D. 1996. Unpublished.
• N. Sukumar. SIF computations for 2D cracks using enriched basis functions. 1996. Unpublished.

Lattice Models and Multiscale Mechanics

• N. Sukumar and J. E. Bolander. Voronoi-based interpolants for fracture modelling. 2009. in Tessellations in the Sciences:  Virtues, Techniques and Applications of Geometric Tilings. Springer Verlag.
• J. E. Bolander and N. Sukumar. Irregular lattice model for quasistatic crack propagation. 2005. Physical Review B, 71:094106.
• C. B. Hirschberger and S. Ricker and P. Steinmann and N. Sukumar. Computational multiscale modelling of heterogeneous material layers. 2009. Engineering Fracture Mechanics, 76(6):793–812.
• C. B. Hirschberger and N. Sukumar and P. Steinmann. Computational homogenization of material layers with micromorphic mesostructure. 2008. Philosophical Magazine, 88:3603–3631.
• C. B. Hirschberger and S. Ricker and P. Steinmann and N. Sukumar. A computational homogenisation approach for cohesive interfaces. 2007. in Proceedings of the International Conference on Computational Plasticity, Computational Plasticity IX: Fundamentals and Applications, pages 442–445. Barcelona, Spain.

Maximum-Entropy Approximants

• N. Sukumar. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons. 2013. Computer Methods in Applied Mechanics and Engineering. (DOI: 10.1016/j.cma.2013.04.009)
• F. Greco and N. Sukumar. Derivatives of maximum-entropy basis functions on the boundary: Theory and computations. 2013. International Journal for Numerical Methods in Engineering, 94(12):1123–1149.
• G. Quaranta and S. K. Kunnath and N. Sukumar. Maximum-entropy meshfree method for nonlinear static analysis of planar reinforced concrete structures. 2012. Engineering Structures, 42:179–189.
• A. Ortiz and M. A. Puso and N. Sukumar. Maximum-entropy meshfree method for incompressible media problems. 2011. Finite Elements in Analysis and Design, 47(6):572–585.
• A. Ortiz and M. A. Puso and N. Sukumar. Maximum-entropy meshfree method for compressible and near-incompressible elasticity. 2010. Computer Methods in Applied Mechanics and Engineering, 199(25–28):1859–1871.
• L. L. Yaw and N. Sukumar and S. K. Kunnath. Meshfree co-rotational formulation for two-dimensional continua. 2009. International Journal for Numerical Methods in Engineering, 79(8):979–1003.
• K. Hormann and N. Sukumar. Maximum entropy coordinates for arbitrary polytopes. 2008. Comp. Graph. Forum, 27(5):1513–1520. (Proceedings of SGP 2008)
• N. Sukumar and R. J-B Wets. Deriving the continuity of maximum-entropy basis functions via variational analysis. 2007. SIAM Journal of Optimization, 18(3):914–925.
• N. Sukumar and R. W. Wright. Overview and construction of meshfree basis functions: From moving least squares to entropy approximants. 2007. International Journal for Numerical Methods in Engineering, 70(2):181–205.
• N. Sukumar. Where do we stand on meshfree approximation schemes. 2006. Unpublished.
• N. Sukumar. Maximum entropy approximation. 2005. AIP Conference Proceedings, 803(1):337-344.
• N. Sukumar. Construction of polygonal interpolants: A maximum entropy approach. 2004. International Journal for Numerical Methods in Engineering, 61(12):2159–2181.

Natural Element Method (NEM)

• A. Rajagopal and M. Scherer and P. Steinmann and N. Sukumar. Smooth conformal α-NEM for gradient elasticity. 2009. The International Journal of Structural Changes in Solids — Mechanics and Applications, 1(1):83–109.
• E. Cueto and N. Sukumar and B. Calvo and M. A. Martínez and  J. Cegoñino and M. Doblaré. Overview and recent advances in natural neighbour Galerkin methods. 2003. Archives of Computational Methods in Engineering, 10(4):307–384. (proof [M. A. Martinez to be included in the author-list])
• N. Sukumar and J. E. Bolander. Numerical computation of discrete differential operators on non-uniform grids. 2003. CMES: Computer Modeling in Engineering & Sciences, 4(6):691–706.
• N. Sukumar. Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids. 2003. International Journal for Numerical Methods in Engineering, 57(1):1–34.
• N. Sukumar. Sibson and non-Sibsonian interpolants for elliptic partial differential equations. 2001. in Proceedings of the first MIT Conference on Fluid and Solid Mechanics, pages 1665–1667. Elsevier Press, Amsterdam, The Netherlands.
• N. Sukumar and B. Moran and A. Yu. Semenov and V. V. Belikov. Natural neighbor Galerkin methods. 2001. International Journal for Numerical Methods in Engineering, 50(1):1–27.
• D. Bueche and N. Sukumar and B. Moran. Dispersive properties of the natural element method. 2000. Computational Mechanics, 25(2/3):207–219.
• N. Sukumar and B. Moran. C¹ natural neighbor interpolant for partial differential equations. 1999. Numerical Methods for Partial Differential Equations, 15(4):417–447.
• B. Moran and N. Sukumar and T. Belytschko. Application of the natural element method in elastostatics. 1998. in Modeling and Simulation Based Engineering, pages xx. Tech. Science Press.
• N. Sukumar and B. Moran and T. Belytschko. The natural element method in solid mechanics. 1998. International Journal for Numerical Methods in Engineering, 43(5):839–887.
• N. Sukumar. The Natural Element Method in Solid Mechanics. 1998. Ph. D. thesis, Theoretical and Applied Mechanics, Northwestern University, Evanston, IL, U.S.A..
• N. Sukumar. Mixed formulation for the natural element method in linear elasticity. 1998. Unpublished.
• N. Sukumar. A C¹ NEM interpolant for fourth-order PDEs. 1997. Unpublished.
• N. Sukumar. A note on natural neighbor interpolation and the natural element method (NEM). 1997. Unpublished.

Polygonal/Polyhedral FE Methods

• N. Sukumar. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons. 2013. Computer Methods in Applied Mechanics and Engineering. (DOI: 10.1016/j.cma.2013.04.009)
• S. E. Mousavi and N. Sukumar. Numerical integration of polynomials and discontinous functions on irregular convex polygons and polyhedrons. 2011. Computational Mechanics, 47(5):535–554.
• S. E. Mousavi and H. Xiao and N. Sukumar. Generalized Gaussian quadrature rules on arbitrary polygons. 2010. International Journal for Numerical Methods in Engineering, 82(1):99–113.
• N. Sukumar and J. E. Bolander. Voronoi-based interpolants for fracture modelling. 2009. in Tessellations in the Sciences:  Virtues, Techniques and Applications of Geometric Tilings. Springer Verlag.
• K. Hormann and N. Sukumar. Maximum entropy coordinates for arbitrary polytopes. 2008. Comp. Graph. Forum, 27(5):1513–1520. (Proceedings of SGP 2008)
• A. Tabarraei and N. Sukumar. Extended finite element method on polygonal and quadtree meshes. 2008. Computer Methods in Applied Mechanics and Engineering, 197(5):425–438.
• A. Tabarraei and N. Sukumar. Adaptive computations using material forces and residual-based error estimators on quadtree meshes. 2007. Computer Methods in Applied Mechanics and Engineering, 196(25–28):2657–2680.
• A. Tabarraei and N. Sukumar. Application of polygonal finite elements in linear elasticity. 2006. International Journal of Computational Methods, 3(4):503–520.
• N. Sukumar and E. A. Malsch. Recent advances in the construction of polygonal finite element interpolants. 2006. Archives of Computational Methods in Engineering, 13(1):129–163. (proof)
• A. Tabarraei and N. Sukumar. Adaptive computations on conforming quadtree meshes. 2005. Finite Elements in Analysis and Design, 41(7–8):686–702.
• N. Sukumar and A. Tabarraei. Conforming polygonal finite elements. 2004. International Journal for Numerical Methods in Engineering, 61(12):2045–2066.
• N. Sukumar and A. Tabarraei. Polygonal interpolants: Construction and adaptive computations on quadtree meshes. 2004. in Proceedings of the European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2004). Jyvaskyla, Finland.
• N. Sukumar and A. Tabarraei. Numerical formulation and application of polygonal finite elements. 2004. in Proceedings of the Seventh International ESAFORM Conference on Material Forming, pages 73–76. Trondheim, Norway.

PUFEM/X-FEM

• G. Hattori and R. Rojas-Díaz and A. Sáez and N. Sukumar and F. García-Sánchez. New anisotropic crack-tip enrichment functions for the extended finite element method. 2012. Computational Mechanics, 50(5):591–601.
• S. E. Mousavi and J. E. Pask and N. Sukumar. Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds. 2012. International Journal for Numerical Methods in Engineering, 91(4):343–357.
• R. Rojas-Díaz and N. Sukumar A. Sáez and F. García-Sánchez. Fracture in magnetoelectroelastic materials using the extended finite element method. 2011. International Journal for Numerical Methods in Engineering, 88(12):1238–1259.
• G. Hattori and R. Rojas-Díaz and A. Sáez and F. García-Sánchez and N. Sukumar. El Método de los Elementos Finitos Extendidos (X-FEM) para Medios Bidimensionales Fisurados Totalmente Anisótropos. 2011. Anales de Mecánica de la Fractura, 28(2):451-455.
• S. E. Mousavi and N. Sukumar. Numerical integration of polynomials and discontinous functions on irregular convex polygons and polyhedrons. 2011. Computational Mechanics, 47(5):535–554.
• S. E. Mousavi and E. Grinspun and N. Sukumar. Higher-order extended finite element with harmonic enrichment functions for complex crack problems. 2011. International Journal for Numerical Methods in Engineering, 86(4–5):560–574.
• S. E. Mousavi and E. Grinspun and N. Sukumar. Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method. 2011. International Journal for Numerical Methods in Engineering, 85(10):1306–1322.
• J. X. Shi and D. Chopp and J. Lua and N. Sukumar and T. Belytschko. Abaqus implementation of extended finite element using a level set representation for three-dimensional fatigue crack growth and life predictions. 2010. Engineering Fracture Mechanics, 77(14):2840–2863.
• S. E. Mousavi and N. Sukumar. Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method. 2010. Computer Methods in Applied Mechanics and Engineering, 199(49–52):3237–3249.
• S. E. Mousavi and N. Sukumar. Generalized Duffy transformation for integrating vertex singularities. 2010. Computational Mechanics, 45(2–3):127–140.
• R. Rojas-Díaz and N. Sukumar and A. Sáez and F. García-Sánchez. Crack analysis in magnetoelectroelastic media using the extended finite element method. 2009. in Proceedings of the International Conference on Extended Finite Element Methods — Recent Developments and Applications, pages 181–186. Aachen, Germany.
• W. Aquino and J. C. Brigham and C. J. Earls and N. Sukumar. Generalized finite element method using proper orthogonal decomposition. 2009. International Journal for Numerical Methods in Engineering, 79(7):887–906.
• J. Shi and J. Lua and L. Chen and D. Chopp and N. Sukumar. X-FEM for Abaqus (XFA) toolkit for automated crack onset and growth simulation: New development, validation, and demonstration. 2009. in 2009 SIMULIA Customer Conference.
• E. Giner and N. Sukumar and J. E. Tarancón and F. J. Fuenmayor. An Abaqus implementation of the extended finite element method. 2009. Engineering Fracture Mechanics, 76(3):347–368.
• E. Giner and N. Sukumar and F. J. Fuenmayor and A. Vercher. Singularity enrichment for complete sliding contact using the partition of unity finite element method. 2008. Int. J. Num. Meth. Engg, 76(9):1402–1418.
• E. Giner and N. Sukumar and F. D. Denia and F. J. Fuenmayor. Extended finite element method for fretting fatigue crack propagation. 2008. International Journal of Solids and Structures, 45(22–23):5675–5687.
• J. Shi and J. Lua and H. Waisman and P. Liu and T. Belytschko and N. Sukumar and Y. Liang. X-FEM toolkit for automated crack onset and growth prediction. 2008. in 49th AIAA Conference, pages 1–22. Schaumburg, IL.
• N. Sukumar and D. L. Chopp and E. Béchet and N. Moës. Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method. 2008. International Journal for Numerical Methods in Engineering, 76(5):727–748.
• A. Tabarraei and N. Sukumar. Extended finite element method on polygonal and quadtree meshes. 2008. Computer Methods in Applied Mechanics and Engineering, 197(5):425–438.
• N. Sukumar and J. Dolbow and A. Devan and J. Yvonnet and F. Chinesta and D. Ryckelynck and Ph. Lorong and I. Alfaro and M. A. Martínez and E. Cueto and M. Doblaré. Meshless methods and partition of unity finite elements. 2005. International Journal of Forming Processes, 8(4):409–427. (proof)
• Z. Huang and Z. Suo and G. Xu and J. He and J. H. Prévost and N. Sukumar. Initiation and arrest of an interfacial crack in a four-point bend test. 2005. Engineering Fracture Mechanics, 72:2584–2601.
• N. Sukumar and Z. Y. Huang and J.-H. Prévost and Z. Suo. Partition of unity enrichment for bimaterial interface cracks. 2004. International Journal for Numerical Methods in Engineering, 59(8):1075-1102.
• N. Sukumar and D. J. Srolovitz. Finite element-based model for crack propagation in polycrystalline materials. 2004. Computational & Applied Mathematics, 23(2–3):363–380.
• R. Huang and N. Sukumar and J.-H. Prévost. Modeling quasi-static crack growth with the extended finite element method. Part II: Numerical applications. 2003. International Journal of Solids and Structures, 40(26):7539–7552.
• N. Sukumar and J.-H. Prévost. Modeling quasi-static crack growth with the extended finite element method. Part I: Computer implementation. 2003. International Journal of Solids and Structures, 40(26):7513–7537.
• N. Sukumar. Meshless methods and partition of unity finite elements. 2003. in Proceedings of the Sixth International ESAFORM Conference on Material Forming, pages 603–606. Salerno, Italy.
• T. Belytschko and C. Parimi and N. Moës and N. Sukumar and S. Usui. Structured extended finite element methods for solids defined by implicit surfaces. 2003. International Journal for Numerical Methods in Engineering, 56(4):609–635.
• D. L. Chopp and N. Sukumar. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. 2003. International Journal of Engineering Science, 41(8):845–869.
• N. Sukumar and D. J. Srolovitz and T. J. Baker and J.-H. Prévost. Brittle fracture in polycrystalline microstructures with the extended finite element method. 2003. International Journal for Numerical Methods in Engineering, 56(14):2015–2037.
• N. Sukumar and D. L. Chopp and B. Moran. Extended finite element method and fast marching method for three dimensional fatigue crack propagation. 2003. Engineering Fracture Mechanics, 70(1):29–48.
• N. Sukumar. Modeling crack singularities in FEM/X-FEM. 2002. Unpublished.
• N. Sukumar and D. L. Chopp and N. Moës and T. Belytschko. Modeling holes and inclusions by level sets in the extended finite-element method. 2001. Computer Methods in Applied Mechanics and Engineering, 190(46–47):6183–6200.
• N. Moës and N. Sukumar and B. Moran and T. Belytschko. An extended finite element method (X-FEM) for two- and three-dimensional crack modeling. 2000. in Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, pages xx. Barcelona, Spain.
• C. Daux and N. Moës and J. Dolbow and N. Sukumar and T. Belytschko. Arbitrary branched and intersecting cracks with the extended finite element method. 2000. International Journal for Numerical Methods in Engineering, 48(12):1741–1760.
• N. Sukumar and N. Moës and B. Moran and T. Belytschko. Extended finite element method for three-dimensional crack modelling. 2000. International Journal for Numerical Methods in Engineering, 48(11):1549–1570.
• N. Sukumar. PUFEM–Revisited. 1996. Unpublished.
• N. Sukumar. PUFEM in one-dimension. 1996. Unpublished.

Quantum Mechanics

• S. E. Mousavi and J. E. Pask and N. Sukumar. Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds. 2012. International Journal for Numerical Methods in Engineering, 91(4):343–357.
• J. E. Pask and N. Sukumar and S. E. Mousavi. Linear scaling solution of the all-electron Coulomb problem in solids. 2012. International Journal for Multiscale Computational Engineering, 10(1):83–99.
• J. E. Pask and N. Sukumar and M. Guney and W. Hu. Partition-of-unity finite-element method for large scale quantum molecular dynamics on massively parallel computational platforms. 2011. LLNL-TR-470692, Department of Energy LDRD Grant 08-ERD-052.
• N. Sukumar. Finite element methods in quantum mechanics. 2009. Unpublished.
• N. Sukumar and J. E. Pask. Classical and enriched finite element formulations for Bloch-periodic boundary conditions. 2009. International Journal for Numerical Methods in Engineering, 77(8):1121–1138. (Erratum: a = 5.7 bohr for the harmonic oscillator problem in Sec. 4.2.1)

Structural Engineering

• G. Quaranta and S. K. Kunnath and N. Sukumar. Maximum-entropy meshfree method for nonlinear static analysis of planar reinforced concrete structures. 2012. Engineering Structures, 42:179–189.
• L. L. Yaw and N. Sukumar and S. K. Kunnath. Meshfree co-rotational formulation for two-dimensional continua. 2009. International Journal for Numerical Methods in Engineering, 79(8):979–1003.
• L. L. Yaw and S. K. Kunnath and N. Sukumar. Meshfree method for inelastic frame analysis. 2009. ASCE Journal of Structural Engineering, 135(6):676–684.

Uncertainty Quantification

• J. O. Royset and N. Sukumar and R. J-B Wets. Uncertainty quantification using exponential epi-splines. 2013. in Proceedings of the 11th International Conference on Structural Safety and Reliability. New York, NY.