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A multiscale analysis for crack propagation in metallographic structure to realize mechanism of material strength

Research Project

Project/Area Number 17K17627
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Materials/Mechanics of materials
Computational science
Research InstitutionUniversity of Tsukuba

Principal Investigator

Shintaku Yuichi  筑波大学, システム情報系, 助教 (80780064)

Project Period (FY) 2017-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Keywordsマルチスケール解析 / 破壊力学 / 損傷力学 / 結晶塑性 / 異方性損傷モデル / 脆性破壊 / き裂進展 / 計算力学 / 有限要素法 / マルチスケール / 破壊 / 結晶
Outline of Final Research Achievements

In this study, a multiscale analysis for crack propagation in metallographic structure is developed by combination between the proposed anisotropic damage constitutive law and new homogenization method to realize mechanism of material strength. The proposed anisotropic damage constitutive law enables us to represent crystallographic slip and cleavage fracture in brittle fracture. Also, we propose the new homogenization method that does not explicitly assume boundary conditions for microstructures with random or localized inhomogeneities. Specifically, instead of the periodic constraint condition on the fluctuation displacement, a condition is imposed such that the domain integral of the gradient is zero, which preserves the definition of macroscopic strain in the homogenization theory. The capability of our developed multiscale analysis is demonstrated throughout prediction of material strength of the polycrystalline aggregate and its dispersion.

Academic Significance and Societal Importance of the Research Achievements

材料の破壊現象における長年の課題として、同一の材料でも部材ごとに異なる強度を示すバラつきの問題が知られている。しかしながら、既存の理論体系では金属をマクロ的に均一な材料とみなすために材料強度のバラつきの問題を理論的に解決できず、材料組織設計に耐えうるものとはなっていない。そこで本研究では、ミクロ構造におけるき裂進展を微視的メカニズムに基づいてシミュレートし、無用な近似を使うことなく忠実にマクロ構造へ接続する新たなマルチスケール解析手法を構築する。これにより、ミクロ構造の不均一性に起因する脆性破壊における強度発現のメカニズムを再現し、そのバラつきを予測可能とする。

Report

(6 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (63 results)

All 2022 2021 2020 2019 2018 2017

All Journal Article (9 results) (of which Peer Reviewed: 9 results,  Open Access: 9 results) Presentation (54 results) (of which Int'l Joint Research: 13 results,  Invited: 3 results)

  • [Journal Article] An implicit solution for an elastic-plastic model with hardening rule depending on plastic strain range using a primal-dual interior point method2022

    • Author(s)
      新宅 勇一、中村 文俊、堤 成一郎、寺田 賢二郎
    • Journal Title

      Transactions of the Japan Society for Computational Engineering and Science

      Volume: 2022 Issue: 0 Pages: 20220001-20220001

    • DOI

      10.11421/jsces.2022.20220001

    • NAID

      130008145203

    • ISSN
      1344-9443, 1347-8826
    • Year and Date
      2022-01-27
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A CDM-like constitutive law for predicting degradation of strength and ductility of steel subjected to cyclic loading2022

    • Author(s)
      Shintaku Yuichi、Tsutsumi Seiichiro、Terada Kenjiro
    • Journal Title

      International Journal of Plasticity

      Volume: 153 Pages: 103237-103237

    • DOI

      10.1016/j.ijplas.2022.103237

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Numerical material testing based on homogenization method for non-periodic media (Formulation using microscopic fluctuation displacement and macroscopic strain)2022

    • Author(s)
      SHINTAKU Yuichi、IMAI Daiki、TERADA Kenjiro
    • Journal Title

      Transactions of the JSME (in Japanese)

      Volume: 88 Issue: 909 Pages: 22-00049-22-00049

    • DOI

      10.1299/transjsme.22-00049

    • ISSN
      2187-9761
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Cohesive-traction embedded damage-like constitutive law based on non-local approach and its numerical implementation improved by Petrov-Galerkin method2021

    • Author(s)
      金澤 凌平、新宅 勇一、寺田 賢二郎
    • Journal Title

      Transactions of the Japan Society for Computational Engineering and Science

      Volume: 2021 Issue: 0 Pages: 20210008-20210008

    • DOI

      10.11421/jsces.2021.20210008

    • NAID

      130008028635

    • ISSN
      1347-8826
    • Year and Date
      2021-04-22
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An Elastic-plastic Constitutive Law Embedding Cohesive Cracks with Plasticity-induced Damage to Realize Degradation of Strength and Toughness under Cyclic Loading2020

    • Author(s)
      Shintaku Yuichi、Soejima Katsuya、Tsutsumi Seiichiro、Terada Kenjiro
    • Journal Title

      Tetsu-to-Hagane

      Volume: 106 Issue: 9 Pages: 662-671

    • DOI

      10.2355/tetsutohagane.TETSU-2019-121

    • NAID

      130007892964

    • ISSN
      0021-1575, 1883-2954
    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Gurson Model Improved by Cohesive Traction-Separation Law to Realize Transition from Ductile to Brittle Fracture2020

    • Author(s)
      KAGIMURA Takuya、SHINTAKU Yuichi、TSUTSUMI Seiichiro、TERADA Kenjiro
    • Journal Title

      QUARTERLY JOURNAL OF THE JAPAN WELDING SOCIETY

      Volume: 38 Issue: 2 Pages: 126s-130s

    • DOI

      10.2207/qjjws.38.126s

    • NAID

      130007964171

    • ISSN
      0288-4771, 2434-8252
    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Fatigue-damage-induced cohesive zone model derived from Paris law and its parameter identification2019

    • Author(s)
      新宅 勇一、藤原 宇希、高橋 昭如
    • Journal Title

      Transactions of the Japan Society for Computational Engineering and Science

      Volume: 2019 Issue: 0 Pages: 20190013-20190013

    • DOI

      10.11421/jsces.2019.20190013

    • NAID

      130007694932

    • ISSN
      1347-8826
    • Year and Date
      2019-08-23
    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Numerical simulation of fatigue crack propagation with plasticity-induced crack closure under different loading conditions (Development of direct numerical simulation using S-version FEM and simplified method)2019

    • Author(s)
      SHINTAKU Yuichi、SHINOZAKI Yuto、FUJIWARA Takaki、TAKAHASHI Akiyuki、KIKUCHI Masanori
    • Journal Title

      Transactions of the JSME (in Japanese)

      Volume: 85 Issue: 876 Pages: 19-00141-19-00141

    • DOI

      10.1299/transjsme.19-00141

    • NAID

      130007695497

    • ISSN
      2187-9761
    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Anisotropic Damage Constitutive Law for Cleavage Failure in Crystalline Grain by Cohesive Zone Model2017

    • Author(s)
      Shintaku Yuichi、Terada Kenjiro、Tsutsumi Seiichiro
    • Journal Title

      QUARTERLY JOURNAL OF THE JAPAN WELDING SOCIETY

      Volume: 35 Issue: 2 Pages: 165s-168s

    • DOI

      10.2207/qjjws.35.165s

    • NAID

      130006329351

    • ISSN
      0288-4771, 2434-8252
    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 超弾性モデルに基づく結合力埋込型弾塑性損傷構成則によるボイドおよび破壊靭性値に関する不確実性評価2021

    • Author(s)
      稲岡龍彦, 新宅勇一
    • Organizer
      日本機械学会第34回計算力学講演会
    • Related Report
      2021 Annual Research Report
  • [Presentation] き裂面の連続性を考慮した結合力埋込型損傷構成則を 用いた非局所アプローチ2021

    • Author(s)
      榎本亘, 新宅勇一
    • Organizer
      日本機械学会第34回計算力学講演会
    • Related Report
      2021 Annual Research Report
  • [Presentation] A new homogenization scheme based on energy and kinematic preservation: application for predicting dispersion of macroscopic material strength on ferrite-perlite steel2021

    • Author(s)
      D. Imai, Y. Shintaku, K. Terada
    • Organizer
      XVI International Conference on Computational Plasticity
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] rediction of fracture toughness at steel bridge after cyclic loading by a CDM-like constitutive law combined with cohesive zone model and memory surface2021

    • Author(s)
      F. Nakamura, Y. Shintaku, K. Terada
    • Organizer
      XVI International Conference on Computational Plasticity
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 金属材料の脆性破壊に対する強度のばらつき評価に向けた非周期性を許容する均質化法の提案2021

    • Author(s)
      今井大貴, 新宅勇一
    • Organizer
      第29回茨城講演会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 塑性誘起損傷および塑性ひずみ振幅依存性を考慮した 結合力埋込型弾塑性モデルによる地震動を受けた鋼橋の残存耐荷力評価2021

    • Author(s)
      中村文俊, 新宅 勇一
    • Organizer
      第29回茨城講演会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 確率論的選点法を用いた延性脆性遷移領域における破壊靭性値のばらつき評価2021

    • Author(s)
      稲岡龍彦, 新宅勇一
    • Organizer
      第26回計算工学講演会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 塑性解析における計算時間の短縮を目的とした有限要素法の検討2021

    • Author(s)
      榎本亘, 新宅勇一
    • Organizer
      第26回計算工学講演会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Memory surfaceによる硬化の影響を考慮した材料モデルに対する主双対内点法の適用2020

    • Author(s)
      中村文俊、新宅勇一
    • Organizer
      第25回計算工学講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] 数値材料試験を用いたへき開破壊に起因する材料強度のばらつき評価2020

    • Author(s)
      今井大貴、新宅勇一
    • Organizer
      第25回計算工学講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] き裂進展解析に対する損傷の非局所性の影響に関する数値解析的 検討2020

    • Author(s)
      金澤凌平、新宅勇一
    • Organizer
      日本機械学会 2020年茨城講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] フェライト-パーライト鋼における結晶すべりおよびへき開破 壊を考慮した数値材料試験2020

    • Author(s)
      今井大貴、新宅勇一
    • Organizer
      日本機械学会 2020年茨城講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] Memory surface を考慮した弾塑性モデルによる地震時の鋼橋の数 値解析2020

    • Author(s)
      中村文俊、新宅勇一
    • Organizer
      日本機械学会 2020年茨城講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] 主双対内点法を用いた非線形材料モデルのパラメータ同定2020

    • Author(s)
      神田寛明、新宅勇一
    • Organizer
      日本機械学会 2020年茨城講演会
    • Related Report
      2020 Research-status Report
  • [Presentation] Assessment of residual strength and toughness of steel bridge by a cohesive-force embedding constitutive law combined with plasticity-induced damage and memory surface2020

    • Author(s)
      F. Nakamura, Y. Shintaku, S. Tsutsumi and K. Terada
    • Organizer
      COMPSAFE2020
    • Related Report
      2020 Research-status Report
  • [Presentation] Multiscale prediction of macroscopic material strength dispersion on ferrite - pearlite steel by numerical material testing2020

    • Author(s)
      D. Imai, Y. Shintaku, K. Terada
    • Organizer
      COMPSAFE2020
    • Related Report
      2020 Research-status Report
  • [Presentation] A numerical study on discontinuous displacement for crack nucleation and propagation2019

    • Author(s)
      K. Soejima, Y. Shintaku, S. Tsutsumi and K. Terada
    • Organizer
      The 7th Asian-Pacific Congress on Computational Mechanics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] A cohesive-traction embedded model with fatigue-induced damage for prediction of crack nucleation and propagation in a metal2019

    • Author(s)
      R. Kanezawa, Y. Shintaku, and K. Terada
    • Organizer
      The 7th Asian-Pacific Congress on Computational Mechanics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Multiscale simulation of crack propagation due to hydrogen embrittlement with anisotropic behavior of cleavage fracture2019

    • Author(s)
      S. Ishibashi, Y. Shintaku, S. Tsutsumi and K. Terada
    • Organizer
      The 7th Asian-Pacific Congress on Computational Mechanics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Fatigue crack growth simulation system using Paris’ law based cohesive zone model2019

    • Author(s)
      T. Fujiwara, A. Takahashi and Y. Shintaku
    • Organizer
      The 7th Asian-Pacific Congress on Computational Mechanics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 水素濃度に対する破壊靭性値の依存性およびへき開破壊を考慮したき裂進展解析2019

    • Author(s)
      石橋奏, 新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      溶接構造シンポジウム2019
    • Related Report
      2019 Research-status Report
  • [Presentation] An enhanced Gurson model with cohesive traction-separation law to realize transition from ductile to brittle fracture2019

    • Author(s)
      T. Kagimura, Y. Shintaku, K. Terada and S. Tsutsumi
    • Organizer
      The International Symposium on Visualization in Joining & Welding Science through Advanced Measurements and Simulation (Visual-JW 2019)
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 勾配法を用いた弾塑性損傷モデルのパラメータ同定2019

    • Author(s)
      神田寛明, 新宅勇一
    • Organizer
      日本機械学会第32回計算力学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] シームレスき裂進展解析による不連続な変位場の表現に関する数値解析的検討2019

    • Author(s)
      金澤凌平, 新宅勇一, 寺田賢二郎
    • Organizer
      JSCES夏季学生講演会2019
    • Related Report
      2019 Research-status Report
  • [Presentation] 勾配法による丸棒試験片に対する材料パラメータ最適化2019

    • Author(s)
      神田寛明, 新宅勇一
    • Organizer
      JSCES夏季学生講演会2019
    • Related Report
      2019 Research-status Report
  • [Presentation] 延性脆性遷移におけるボイドが破壊靭性値に及ぼす影響評価2019

    • Author(s)
      鍵村拓也, 新宅勇一
    • Organizer
      日本鉄鋼協会 第178回秋季講演大会
    • Related Report
      2019 Research-status Report
  • [Presentation] A seamless transition method from continuity to discontinuity for crack in an elasto-plastic material2019

    • Author(s)
      Y. Shintaku, K. Terada and S. Tsutsumi
    • Organizer
      XV International Conference on Computational Plasticity
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 結合力埋込型複合硬化弾塑性損傷モデルによる繰り返し載荷後の残存耐荷力評2019

    • Author(s)
      副島克哉, 新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      第27回茨城講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] 不連続な変位場に対するシームレスき裂進展解析の優位性2019

    • Author(s)
      金澤凌平, 新宅勇一, 寺田賢二郎
    • Organizer
      第27回茨城講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] へき開破壊の異方性挙動を考慮した水素脆性き裂の進展解析2019

    • Author(s)
      石橋奏, 新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] 結合力埋込型損傷構成則を用いた破壊靭性値に対するボイドの影響評価2019

    • Author(s)
      鍵村拓也, 新宅勇一
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] 疲労損傷を考慮した結合力を埋め込んだ複合硬化弾塑性構成則の提案2019

    • Author(s)
      副島克哉, 新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] 変位の不連続性の近似が異なるき裂進展解析手法の比較検討2019

    • Author(s)
      金澤凌平, 新宅勇一, 寺田賢二郎
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] 非線形材料モデルのパラメータ同定における各種勾配法の適用性に関する検討2019

    • Author(s)
      神田寛明, 新宅勇一
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] Paris則に基づく結合力モデルを用いた疲労き裂進展解析手法の提案2019

    • Author(s)
      藤原宇希, 高橋昭如, 新宅勇一
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Research-status Report
  • [Presentation] 温度依存性を考慮した結合力モデルおよび Gurson モデルによる延性・脆性破壊シミュレーション2018

    • Author(s)
      鍵村拓也, 新宅勇一
    • Organizer
      日本機械学会第31回計算力学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] 移動硬化を考慮した結合力埋込型弾塑性損傷モデルによる構造用鋼材の耐久性評価2018

    • Author(s)
      副島克哉, 新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      日本機械学会第31回計算力学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] 繰り返し応力に伴う弾塑性挙動と疲労き裂発生寿命評価2018

    • Author(s)
      新宅勇一, 寺田賢二郎, 堤成一郎
    • Organizer
      大阪大学接合科学研究所 平成30年度 共同研究成果発表会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 水素の非定常拡散を考慮した水素助長疲労き裂の進展解析2018

    • Author(s)
      石橋奏, 新宅勇一, 寺田賢二郎, 堤成一郎
    • Organizer
      平成30年度 秋季全国大会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Fatigue Crack Growth Simulation Considering Crack Closure Effect2018

    • Author(s)
      Y. Shinozaki, A. Takahashi, Y. Shintaku, M. Kikuchi
    • Organizer
      The 11th International Conference on Fracture and Strength of Solid
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Gursonモデルによる延性き裂進展解析のための非線形計画法の検討2018

    • Author(s)
      鍵村拓也, 新宅勇一
    • Organizer
      第26回茨城講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] A method for seamless transition from degradation of material stiffness to formation of strong discontinuity2018

    • Author(s)
      Y. Shintaku, S. Tsutsumi and K. Terada
    • Organizer
      13th World Congress on Computational Mechanics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 多結晶体金属における水素拡散と水素脆化によるき裂進展の双方向弱連成解析2018

    • Author(s)
      石橋奏, 新宅勇一
    • Organizer
      第23回計算工学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] 複合硬化弾塑性モデルを用いた構造用鋼材の損傷評価と載荷パターン・応力三軸度が及ぼす影響2018

    • Author(s)
      副島克哉, 新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      第23回計算工学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] き裂開閉口挙動を考慮した疲労き裂進展解析システムの構築2018

    • Author(s)
      篠崎勇人, 高橋昭如, 新宅勇一
    • Organizer
      第23回計算工学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] Paris則に基づく結合力モデルを用いた2次元疲労き裂進展解析システムの構築2018

    • Author(s)
      藤原宇希, 高橋昭如, 新宅勇一
    • Organizer
      第23回計算工学講演会
    • Related Report
      2018 Research-status Report
  • [Presentation] 計算材料力学によるマルチフィジックスき裂解析手法の開発2018

    • Author(s)
      新宅勇一
    • Organizer
      第13回産学連携シンポジウム
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 結合力埋込型損傷構成則と有限被覆法を用いた不連続面進展解析の基礎的検討2017

    • Author(s)
      新宅勇一, 寺田賢二郎, 堤成一郎
    • Organizer
      日本機械学会第30回計算力学講演会
    • Related Report
      2017 Research-status Report
  • [Presentation] An adaptive traction approach from weak- to strong-discontinutiy by cohesive traction embedded damage-like constitutive law and finite cover method2017

    • Author(s)
      Y. Shintaku, K. Terada and S. Tsutsumi
    • Organizer
      XIV International Conference on Computational Plasticity
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 結合力埋込型損傷構成則の疲労問題への適用2017

    • Author(s)
      新宅勇一, 堤成一郎, 寺田賢二郎
    • Organizer
      第22回計算工学講演会
    • Related Report
      2017 Research-status Report
  • [Presentation] 繰り返し載荷を経験した鋼構造物の残存耐力評価のための基礎的検討2017

    • Author(s)
      新宅勇一, 番場良平, 渡部慎也, 堤成一郎, 寺田賢二郎
    • Organizer
      第22回計算工学講演会
    • Related Report
      2017 Research-status Report
  • [Presentation] き裂開閉口挙動を考慮した2次元疲労き裂進展解析システムの構築2017

    • Author(s)
      篠崎勇人, 高橋昭如, 新宅勇一, 菊池正紀
    • Organizer
      第22回計算工学講演会
    • Related Report
      2017 Research-status Report
  • [Presentation] Fatigue Crack Growth Simulation with Crack Closure Effect Using S-Version FEM2017

    • Author(s)
      Y. Shinozaki, A. Takahashi, Y. Shintaku
    • Organizer
      14th US National Congress on Computational Mechanics
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Fatigue Crack Growth Simulation with Plasticity Induced Crack Closure Effect Using S-version FEM2017

    • Author(s)
      A. Takahashi, Y. Shinozaki, Y. Shintaku, A. Suzuki, M. Kikuchi
    • Organizer
      The 10th International Conference on Numerical Analysis in Engineering
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research

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Published: 2017-04-28   Modified: 2023-01-30  

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