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Topic · Mechanics of Materials

Numerical methods in engineering

Numerical methods in engineering is a research topic within Mechanics of Materials. Science Explorer counts 47k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers represents advances in fracture mechanics modeling and simulation, focusing on topics such as fracture, meshless methods, extended finite element method, peridynamics, phase-field modeling, radial basis functions, crack propagation, brittle materials, discontinuities, and structural mechanics.

  • Fracture
  • Meshless Methods
  • Extended Finite Element Method
  • Peridynamics
  • Phase-Field Modeling
  • Radial Basis Functions
  • Crack Propagation
  • Brittle Materials
  • Discontinuities
  • Structural Mechanics
Research works
47k
fractional, since 1950
In the world top 10%
4.6k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-5%
the tick is no change
Largest producer
China
49% of the 10 largest, 2022-now
Numerical methods in engineering

Which countries lead Numerical methods in engineering research?

By volume, China and the United States publish the most (2.7k and 652 works in 2022-now).

By volume, 2022-now

  1. 1 China 2.7k works
  2. 2 United States 652 works
  3. 3 India 600 works
  4. 4 Germany 364 works
  5. 5 Iran 289 works
  6. 6 France 283 works
  7. 7 Italy 248 works
  8. 8 Russia 152 works
  9. 9 Türkiye 152 works
  10. 10 Japan 149 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 48.6%United States: 11.6%India: 10.7%Germany: 6.5%6 others listed: 22.6%49%largest
China2,737 · 48.6%United States652 · 11.6%India600 · 10.7%Germany364 · 6.5%6 others listed1,274 · 22.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Numerical methods in engineering research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Numerical methods in engineering research, followed by Hohai University and Dalian University of Technology.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 114 works
  2. 2 Hohai UniversityChina 83 works
  3. 3 Dalian University of TechnologyChina 80 works
  4. 4 Tongji UniversityChina 78 works
  5. 5 Chinese Academy of SciencesChina 62 works
  6. 6 Russian Academy of SciencesRussia 61 works
  7. 7 Harbin Institute of TechnologyChina 51 works
  8. 8 Shanghai Jiao Tong UniversityChina 48 works
  9. 9 Nanjing University of Aeronautics and AstronauticsChina 47 works
  10. 10 Tsinghua UniversityChina 42 works

Who are the leading researchers in Numerical methods in engineering?

The most-cited researchers publishing on Numerical methods in engineering include Yi Ping Cui, Xiaogang Wang and Donald G. Truhlar.

  1. 1 Yi Ping Cui United States 261k citations
  2. 2 Xiaogang Wang China 260k citations
  3. 3 Donald G. Truhlar United States 230k citations
  4. 4 Takashi Taniguchi Japan 227k citations
  5. 5 A. Meyer France 224k citations
  6. 6 Kai You Wang China 224k citations
  7. 7 Lei Jiang China 214k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

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).

Most cited papers
#PaperReleasedCitations
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 Open access 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 Open access 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
All 100 most cited papers, with filters and sorting

Where is Numerical methods in engineering research done?

The largest centres of Numerical methods in engineering research in 2022-now are Beijing (China), Nanjing (China), Shanghai (China) and Xi'an (China). Among places with at least 20 works in it, it is an unusually large share of all research in Dhanbad.

Largest cities, 2022-now

  1. 1 BeijingChina 385 works
  2. 2 NanjingChina 228 works
  3. 3 ShanghaiChina 215 works
  4. 4 Xi'anChina 144 works
  5. 5 WuhanChina 110 works
  6. 6 TehranIran 107 works
  7. 7 ChengduChina 99 works
  8. 8 DalianChina 95 works
  9. 9 ParisFrance 88 works
  10. 10 HarbinChina 84 works

Where it is the local speciality

  1. DhanbadIN · 27.7 works17×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Numerical methods in engineering than the world average.

See Numerical methods in engineering on the map

Where is the best place to study Numerical methods in engineering?

Among universities, judged by research, Hohai University, Tongji University and Le Quy Don Technical University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%20%40%mean 23.52%fractional works in this field (log) →share of work in the world top 10% →Le Quy Don Technical…Hong Kong Polytechni…Hohai UniversityTongji University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Hohai UniversityChina 67.819.9%21.5×83 +15.4%
2Tongji UniversityChina 63.718.1%7.8×78 +28.4%
3Le Quy Don Technical UniversityVietnam 62.345.0%22.5×8 +108.8%
4Hong Kong Polytechnic UniversityChina 60.926.2%4.9×28 +163.9%
5Dalian University of TechnologyChina 55.916.6%12.9×80 -10.9%
6Bauhaus-Universität WeimarGermany 55.928.8%50.0×14 +6.4%
7Jouf UniversitySaudi Arabia 55.219.1%16.0×14 +151.2%
8Leibniz University HannoverGermany 52.320.3%18.3×35 -5.5%
9Tsinghua UniversityChina 51.820.7%2.8×42 +37.5%
10Southeast UniversityChina 51.120.5%3.2×31 +23.4%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Numerical methods in engineering, country by country

Is Numerical methods in engineering research growing?

Output in 2022-2025 was 5% lower than in 2018-2021, peaking in 2020.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Numerical methods in engineering as a percentage of every work published that year, 0.029% in 2024.

still counting0.025%0.050%0.075%Numerical methods in engineering0.027% in 202519801990200020102020

Fractional works of Numerical methods in engineering over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Numerical methods in engineering9.8% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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