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Topic · Computational Theory and Mathematics

Contact Mechanics and Variational Inequalities

Contact Mechanics and Variational Inequalities is a research topic within Computational Theory and Mathematics. Science Explorer counts 11k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on computational contact mechanics, particularly on the modeling and numerical analysis of contact, friction, and variational inequalities in the context of finite element methods. The research addresses various aspects such as large deformation, viscoelastic materials, nonlinear dynamics, and the development of numerical algorithms for solving contact problems.

  • Contact
  • Friction
  • Variational Inequalities
  • Finite Element
  • Mortar Method
  • Large Deformation
  • Viscoelastic
  • Nonlinear Dynamics
  • Penalty Method
  • Numerical Analysis
Research works
11k
fractional, since 1950
In the world top 10%
1.1k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+15%
the tick is no change
Largest producer
China
35% of the 10 largest, 2022-now
Contact Mechanics and Variational Inequalities

Which countries lead Contact Mechanics and Variational Inequalities research?

By volume, China and the United States publish the most (356 and 114 works in 2022-now).

By volume, 2022-now

  1. 1 China 356 works
  2. 2 United States 114 works
  3. 3 Russia 99 works
  4. 4 India 94 works
  5. 5 France 82 works
  6. 6 Germany 78 works
  7. 7 Italy 59 works
  8. 8 Morocco 51 works
  9. 9 Vietnam 43 works
  10. 10 Saudi Arabia 37 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: 35.1%United States: 11.3%Russia: 9.7%India: 9.3%6 others listed: 34.5%35%largest
China356 · 35.1%United States114 · 11.3%Russia99 · 9.7%India94 · 9.3%6 others listed350 · 34.5%

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

Which institutions lead Contact Mechanics and Variational Inequalities research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Contact Mechanics and Variational Inequalities research, followed by Centre National de la Recherche Scientifique and North-Eastern Federal University.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 38 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 32 works
  3. 3 North-Eastern Federal UniversityRussia 12 works
  4. 4 Université Sultan Moulay SlimaneMorocco 11 works
  5. 5 Université de PerpignanFrance 11 works
  6. 6 National Academy of Sciences of UkraineUkraine 11 works
  7. 7 Vellore Institute of Technology UniversityIndia 11 works
  8. 8 Cadi Ayyad UniversityMorocco 10 works
  9. 9 Jagiellonian UniversityPoland 10 works
  10. 10 University of Electronic Science and Technology of ChinaChina 9 works

Who are the leading researchers in Contact Mechanics and Variational Inequalities?

The most-cited researchers publishing on Contact Mechanics and Variational Inequalities include Lei Jiang, Michael I. Jordan and Hao Chen.

  1. 1 Lei Jiang China 214k citations
  2. 2 Michael I. Jordan United States 182k citations
  3. 3 Hao Chen China 118k citations
  4. 4 Thomas J.R. Hughes United States 106k citations
  5. 5 Jinde Cao China 104k citations
  6. 6 Ted Belytschko United States 89k citations
  7. 7 Dumitru Bǎleanu Türkiye 89k 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 Contact Mechanics and Variational Inequalities?

The most cited paper in Contact Mechanics and Variational Inequalities is "Elastic crack growth in finite elements with minimal remeshing" (Ted Belytschko, T. Howard Black, 1999), with 4,852 citations. Next come "A continuum theory of elastic material surfaces" (3,188) and "Nonlinear Solid Mechanics: A Continuum Approach for Engineering" (2,743).

Most cited papers
#PaperReleasedCitations
1 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
2 A continuum theory of elastic material surfaces Morton E. Gurtin, A. Ian Murdoch · Archive for Rational Mechanics and Analysis Dec 1975 3,188
3 Nonlinear Solid Mechanics: A Continuum Approach for Engineering Gerhard A. Holzapfel 23 Mar 2000 2,743
4 A dual algorithm for the solution of nonlinear variational problems via finite element approximation Daniel Gabay, Bertrand Mercier · Computers & Mathematics with Applications Open access 1976 2,636
5 Convexity conditions and existence theorems in nonlinear elasticity John Macleod Ball · Archive for Rational Mechanics and Analysis Dec 1976 2,451
All 100 most cited papers, with filters and sorting

Where is Contact Mechanics and Variational Inequalities research done?

The largest centres of Contact Mechanics and Variational Inequalities research in 2022-now are Beijing (China), Chengdu (China), Moscow (Russia) and Hanoi (Vietnam).

Largest cities, 2022-now

  1. 1 BeijingChina 50 works
  2. 2 ChengduChina 30 works
  3. 3 MoscowRussia 30 works
  4. 4 HanoiVietnam 24 works
  5. 5 ShanghaiChina 19 works
  6. 6 BucharestRomania 18 works
  7. 7 NanjingChina 18 works
  8. 8 Xi'anChina 18 works
  9. 9 ChongqingChina 18 works
  10. 10 ParisFrance 17 works
See Contact Mechanics and Variational Inequalities on the map

Where is the best place to study Contact Mechanics and Variational Inequalities?

Among universities, judged by research, Vellore Institute of Technology University, University of KwaZulu-Natal and Cadi Ayyad University score highest, combining citation 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%60%mean 23.18%fractional works in this field (log) →share of work in the world top 10% →Vellore Institute of…University of KwaZul…Cadi Ayyad UniversityNorth-Eastern Federa…
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.

Citation 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
1Vellore Institute of Technology UniversityIndia 73.549.7%8.1×11 -
2University of KwaZulu-NatalSouth Africa 57.235.9%17.9×9 +5.5%
3Cadi Ayyad UniversityMorocco 53.718.2%41.4×10 +231.4%
4North-Eastern Federal UniversityRussia 50.07.0%113.5×12 +45.1%
5Université Sultan Moulay SlimaneMorocco 50.011.9%61.6×11 +234.4%
6Université de PerpignanFrance 50.08.1%236.4×11 +12.7%
7Technion – Israel Institute of TechnologyIsrael 47.736.8%15.9×8 +590.6%
8Yulin Normal UniversityChina 45.930.1%231.1×8 +97.8%
9Jagiellonian UniversityPoland 42.121.8%10.7×10 -16.1%
10Universitatea Națională de Știință și Tehnologie Politehnica BucureștiRomania 24.112.3%25.7×8 -13.1%

Universities only. The score blends citation 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 Contact Mechanics and Variational Inequalities, country by country

Is Contact Mechanics and Variational Inequalities research growing?

Output in 2022-2025 was 15% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Contact Mechanics and Variational Inequalities.

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 Contact Mechanics and Variational Inequalities as a percentage of every work published that year, 0.0055% in 2024.

still counting0.010%0.020%Contact Mechanics and Variational Inequalities0.0069% in 202519801990200020102020

Fractional works of Contact Mechanics and Variational Inequalities 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%Contact Mechanics and Variational Inequalities10.5% 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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