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Topic · Materials Chemistry

Nonlocal and gradient elasticity in micro/nano structures

Nonlocal and gradient elasticity in micro/nano structures is a research topic within Materials Chemistry. Science Explorer counts 10k research works in it since 1959. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the application of nonlocal continuum mechanics, strain gradient theory, and microstructure-dependent models to analyze the behavior of nanoscale materials. It explores the effects of flexoelectricity, surface tension, and size-dependence on the elasticity, plasticity, and wave propagation in functionally graded beams and other nanoscale structures.

  • Nonlocal Continuum Mechanics
  • Strain Gradient Theory
  • Nanoscale Materials
  • Flexoelectric Effect
  • Surface Effects
  • Functionally Graded Beams
  • Size-dependent Behavior
  • Elasticity and Plasticity
  • Wave Propagation
  • Microstructure-dependent Models
Research works
10k
fractional, since 1959
In the world top 10%
1k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
-6%
the tick is no change
Largest producer
China
39% of the 10 largest, 2022-now
Nonlocal and gradient elasticity in micro/nano structures

Which countries lead Nonlocal and gradient elasticity in micro/nano structures research?

By volume, China and India publish the most (857 and 275 works in 2022-now).

By volume, 2022-now

  1. 1 China 857 works
  2. 2 India 275 works
  3. 3 Iran 226 works
  4. 4 United States 170 works
  5. 5 Türkiye 126 works
  6. 6 Vietnam 124 works
  7. 7 Italy 113 works
  8. 8 Saudi Arabia 100 works
  9. 9 Russia 94 works
  10. 10 Germany 86 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: 39.5%India: 12.7%Iran: 10.4%United States: 7.8%6 others listed: 29.6%39%largest
China857 · 39.5%India275 · 12.7%Iran226 · 10.4%United States170 · 7.8%6 others listed643 · 29.6%

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

Which institutions lead Nonlocal and gradient elasticity in micro/nano structures research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Nonlocal and gradient elasticity in micro/nano structures research, followed by Nanjing University of Aeronautics and Astronautics and Islamic Azad University, Tehran.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 38 works
  2. 2 Nanjing University of Aeronautics and AstronauticsChina 37 works
  3. 3 Islamic Azad University, TehranIran 35 works
  4. 4 Centre National de la Recherche ScientifiqueFrance 34 works
  5. 5 Xi'an Jiaotong UniversityChina 26 works
  6. 6 Chinese Academy of SciencesChina 24 works
  7. 7 Lanzhou University of TechnologyChina 23 works
  8. 8 Jouf UniversitySaudi Arabia 21 works
  9. 9 Le Quy Don Technical UniversityVietnam 19 works
  10. 10 Karabük UniversityTürkiye 19 works

Who are the leading researchers in Nonlocal and gradient elasticity in micro/nano structures?

The most-cited researchers publishing on Nonlocal and gradient elasticity in micro/nano structures include Zhong Lin Wang, Kenji Watanabe and Huan Liu.

  1. 1 Zhong Lin Wang United States 491k citations
  2. 2 Kenji Watanabe Japan 237k citations
  3. 3 Huan Liu Australia 148k citations
  4. 4 Dierk Raabe Germany 125k 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 Nonlocal and gradient elasticity in micro/nano structures?

The most cited paper in Nonlocal and gradient elasticity in micro/nano structures is "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves" (A. Cemal Eringen, 1983), with 4,817 citations. Next come "Micro-structure in linear elasticity" (3,998) and "Strain gradient plasticity: Theory and experiment" (3,767).

Most cited papers
#PaperReleasedCitations
1 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
2 Micro-structure in linear elasticity R. D. Mindlin · Archive for Rational Mechanics and Analysis 1964 3,998
3 Strain gradient plasticity: Theory and experiment Norman Andrew Fleck, Georg M. Müller, Michael Farries Ashby et al. · Acta Metallurgica et Materialia Feb 1994 3,767
4 Couple stress based strain gradient theory for elasticity Fan Yang, Arthur C. M. Chong, DAVID C. C. LAM et al. · International Journal of Solids and Structures May 2002 3,489
5 Experiments and theory in strain gradient elasticity DAVID C. C. LAM, Fujun Yang, Arthur C. M. Chong et al. · Journal of the Mechanics and Physics of Solids 19 May 2003 3,090
All 100 most cited papers, with filters and sorting

Where is Nonlocal and gradient elasticity in micro/nano structures research done?

The largest centres of Nonlocal and gradient elasticity in micro/nano structures research in 2022-now are Beijing (China), Hanoi (Vietnam), Nanjing (China) and Tehran (Iran). Among places with at least 20 works in it, it is an unusually large share of all research in Sakakah.

Largest cities, 2022-now

  1. 1 BeijingChina 114 works
  2. 2 HanoiVietnam 77 works
  3. 3 NanjingChina 76 works
  4. 4 TehranIran 70 works
  5. 5 Xi'anChina 61 works
  6. 6 MoscowRussia 42 works
  7. 7 ShanghaiChina 40 works
  8. 8 WuhanChina 39 works
  9. 9 Ho Chi Minh CityVietnam 35 works
  10. 10 LanzhouChina 32 works

Where it is the local speciality

  1. SakakahSA · 21.2 works56×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Nonlocal and gradient elasticity in micro/nano structures than the world average.

See Nonlocal and gradient elasticity in micro/nano structures on the map

Where is the best place to study Nonlocal and gradient elasticity in micro/nano structures?

Among universities, judged by research, Karabük University, Jouf 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%60%mean 19.14%fractional works in this field (log) →share of work in the world top 10% →Karabük UniversityLe Quy Don Technical…Jouf UniversityNanjing University o…
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
1Karabük UniversityTürkiye 78.254.2%45.9×19 +698.3%
2Jouf UniversitySaudi Arabia 63.520.9%64.5×21 +246.7%
3Le Quy Don Technical UniversityVietnam 58.826.7%136.1×19 +422.9%
4Nanjing University of Aeronautics and AstronauticsChina 56.510.2%16.7×37 +39.5%
5Islamic Azad University, TehranIran 46.911.8%8.5×35 -57.0%
6Bursa Uludağ Üni̇versi̇tesi̇Türkiye 46.415.9%28.7×19 +73.8%
7Huazhong University of Science and TechnologyChina 44.621.0%3.8×17 +12.0%
8Istanbul Technical UniversityTürkiye 42.712.7%18.1×16 +149.1%
9Xi'an Jiaotong UniversityChina 42.614.3%6.0×26 -13.3%
10Lanzhou University of TechnologyChina 42.53.7%28.1×23 +116.9%

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 Nonlocal and gradient elasticity in micro/nano structures, country by country

Is Nonlocal and gradient elasticity in micro/nano structures research growing?

Output in 2022-2025 was 6% lower than in 2018-2021, peaking in 2026.

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 Nonlocal and gradient elasticity in micro/nano structures as a percentage of every work published that year, 0.0083% in 2024.

still counting0.0050%0.010%0.015%Nonlocal and gradient elasticity in micro/nano structures0.011% in 202519801990200020102020

Fractional works of Nonlocal and gradient elasticity in micro/nano structures 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%Nonlocal and gradient elasticity in micro/nano structures9.7% 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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