Topic · Numerical methods in engineering
Most cited papers in Numerical methods in engineering
What are the most cited papers in Numerical methods in engineering?
The most cited paper in Numerical methods in engineering is "The Elastic Behaviour of a Crystalline Aggregate" (R. Hill, 1952), with 11,561 citations. Next come "Average stress in matrix and average elastic energy of materials with misfitting inclusions" (8,161) and "A finite element method for crack growth without remeshing" (6,402).
Showing 50 of 100 papers. Every paper with more than 1,190 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | The Elastic Behaviour of a Crystalline Aggregate R. Hill · Proceedings of the Physical Society Section A | May 1952 | 11,561 |
| 2 | Average stress in matrix and average elastic energy of materials with misfitting inclusions T. Mori, Kōichi Tanaka · Acta Metallurgica | May 1973 | 8,161 |
| 3 | A finite element method for crack growth without remeshing Nicolas Mo�s, John E. Dolbow, Ted Belytschko · International Journal for Numerical Methods in Engineering | 10 Sep 1999 | 6,402 |
| 4 | Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Thomas J.R. Hughes, J. Austin Cottrell, Yuri Bazilevs · Computer Methods in Applied Mechanics and Engineering | Feb 2005 | 6,340 |
| 5 | A variational approach to the theory of the elastic behaviour of multiphase materials Zvi Hashin, S. Shtrikman · Journal of the Mechanics and Physics of Solids | Mar 1963 | 5,867 |
| 6 | Element‐free Galerkin methods Ted Belytschko, Ye Lu, Linxia Gu · International Journal for Numerical Methods in Engineering | 30 Jan 1994 | 5,653 |
| 7 | Elastic crack growth in finite elements with minimal remeshing Ted Belytschko, T. Howard Black · International Journal for Numerical Methods in Engineering | 20 Jun 1999 | 4,852 |
| 8 | On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves A. Cemal Eringen · Journal of Applied Physics | Sep 1983 | 4,817 |
| 9 | A proposed modification of the Germano subgrid-scale closure method Douglas K. Lilly · Physics of Fluids A Fluid Dynamics | Mar 1992 | 4,044 |
| 10 | A self-consistent mechanics of composite materials R. Hill · Journal of the Mechanics and Physics of Solids | Aug 1965 | 3,692 |
| 11 | Homotopy perturbation technique Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering | Aug 1999 | 3,485 |
| 12 | A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials Zvi Hashin, S. Shtrikman · Journal of Applied Physics | Oct 1962 | 3,278 |
| 13 | Plane strain deformation near a crack tip in a power-law hardening material JAMES R. RICE, G. F. Rosengren · Journal of the Mechanics and Physics of Solids | 1968 | 3,187 |
| 14 | Meshless methods: An overview and recent developments Ted Belytschko, Y. Krongauz, D. Organ et al. · Computer Methods in Applied Mechanics and Engineering | Dec 1996 | 3,147 |
| 15 | A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits Christian Miehé, Martina Hofacker, Fabian Welschinger · Computer Methods in Applied Mechanics and Engineering | 8 May 2010 | 3,113 |
| 16 | Introduction to the Finite Element Method Sung W. Lee, Peter W. Chung · Cambridge University Press eBooks | 17 Jun 2021 | 2,945 |
| 17 | Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations Christian Miehé, Fabian Welschinger, Martina Hofacker · International Journal for Numerical Methods in Engineering | 22 Mar 2010 | 2,938 |
| 18 | Reproducing kernel particle methods Wing Kam Liu, Sukky Jun, Yi Fei Zhang · International Journal for Numerical Methods in Fluids | 30 Apr 1995 | 2,856 |
| 19 | Smoothed particle hydrodynamics Joseph J. Monaghan · Reports on Progress in Physics | 5 Jul 2005 | 2,753 |
| 20 | A new approach to the application of Mori-Tanaka's theory in composite materials Yakov Benveniste · Mechanics of Materials | Jun 1987 | 2,714 |
| 21 | Nonlocal Continuum Field Theories A. Cental Eringen, JL Wegner · Applied Mechanics Reviews | Mar 2003 | 2,640 |
| 22 | A meshfree method based on the peridynamic model of solid mechanics Stewart A. Silling, Ebrahim Askari · Computers & Structures | 23 Mar 2005 | 2,550 |
| 23 | Peridynamic States and Constitutive Modeling Stewart A. Silling, Michael A. Epton, Olaf Weckner et al. · Journal of Elasticity | 14 Jul 2007 | 2,532 |
| 24 | Mixed and Hybrid Finite Element Methods Franco Brezzi, Michel Fortin · CERN Document Server (European Organization for Nuclear Research) | 23 Nov 2011 | 2,420 |
| 25 | A simple error estimator and adaptive procedure for practical engineerng analysis Olgierd Cecil Zienkiewicz, J.Z. Zhu · International Journal for Numerical Methods in Engineering | Feb 1987 | 2,410 |
| 26 | Numerical simulations of fast crack growth in brittle solids Xiaopeng Xu, Alan Needleman · Journal of the Mechanics and Physics of Solids | Sep 1994 | 2,410 |
| 27 | THE PARTITION OF UNITY METHOD Ivo M. Babuska, Jens Markus Melenk · International Journal for Numerical Methods in Engineering | 28 Feb 1997 | 2,368 |
| 28 | A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics Satya N. Atluri, Tengteng Zhu · Computational Mechanics | 24 Aug 1998 | 2,337 |
| 29 | Strain-energy-density factor applied to mixed mode crack problems G. C. Sih · International Journal of Fracture | Sep 1974 | 2,302 |
| 30 | A finite element calculation of stress intensity factors by a modified crack closure integral E.F. Rybicki, M. F. Kanninen · Engineering Fracture Mechanics | 1977 | 2,282 |
| 31 | A mixed finite element method for 2-nd order elliptic problems Pierre-Arnaud Raviart, J. M. Thomas · Lecture notes in mathematics | 1977 | 2,224 |
| 32 | A posteriori error estimation in finite element analysis Mark Andrew Ainsworth, J. Tinsley Oden · Computer Methods in Applied Mechanics and Engineering | Mar 1997 | 2,193 |
| 33 | A Continuum Model for Void Nucleation by Inclusion Debonding Alan Needleman · Journal of Applied Mechanics | Sep 1987 | 2,150 |
| 34 | Solutions for effective shear properties in three phase sphere and cylinder models Richard M. Christensen, King Him Lo · Journal of the Mechanics and Physics of Solids | Aug 1979 | 2,116 |
| 35 | An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications Esteban P. Samaniego, Cosmin Anitescu, Somdatta Goswami et al. · Computer Methods in Applied Mechanics and Engineering | 16 Jan 2020 | 2,096 |
| 36 | Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations Edward J. Kansa · Computers & Mathematics with Applications | 1990 | 2,064 |
| 37 | Determination of the size of the representative volume element for random composites: statistical and numerical approach Toufik Kanit, Samuel Forest, Isabelle Galliet et al. · International Journal of Solids and Structures | 19 May 2003 | 2,031 |
| 38 | Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid Seiichi Koshizuka, Y. Oka · Nuclear Science and Engineering | Jul 1996 | 2,023 |
| 39 | The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique Olgierd Cecil Zienkiewicz, J.Z. Zhu · International Journal for Numerical Methods in Engineering | 30 May 1992 | 2,020 |
| 40 | Elastic moduli of a cracked solid Bernard Budiansky, Richard J. O’Connell · International Journal of Solids and Structures | 1976 | 2,011 |
| 41 | Generalizing the finite element method: Diffuse approximation and diffuse elements Bernard Nayroles, Gilbert Touzot, Pierre Villon · Computational Mechanics | 1992 | 1,995 |
| 42 | Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates Edward J. Kansa · Computers & Mathematics with Applications | 1990 | 1,965 |
| 43 | Nonlocal Damage Theory Gilles Pijaudier‐Cabot, Zdeněk P. Bažant · Journal of Engineering Mechanics | Oct 1987 | 1,927 |
| 44 | A phase-field description of dynamic brittle fracture Michael J. Borden, Clemens V. Verhoosel, Michael A. Scott et al. · Computer Methods in Applied Mechanics and Engineering | 26 Jan 2012 | 1,914 |
| 45 | The Variational Approach to Fracture Blaise Bourdin, Gilles A. Francfort, Jean‐Jacques Marigo · Journal of Elasticity | 14 Mar 2008 | 1,899 |
| 46 | Slightly curved or kinked cracks Benjamin M. Cotterell, JAMES R. RICE · International Journal of Fracture | Apr 1980 | 1,874 |
| 47 | Radial basis functions theory and implementations Martin Buhmann | 2003 | 1,872 |
| 48 | Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments Moubin Liu, G. R. Liu · Archives of Computational Methods in Engineering | 12 Feb 2010 | 1,856 |
| 49 | Nonlocal theories for bending, buckling and vibration of beams Junuthula Narasimha Reddy · International Journal of Engineering Science | Feb 2007 | 1,802 |
| 50 | Generalized discrete variable approximation in quantum mechanics J. C. Light, Ian P. Hamilton, James Lill · The Journal of Chemical Physics | Feb 1985 | 1,750 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.