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2019 年度 実績報告書

Mesoscale modeling for disclinations toward a theory for kink and material strengthening

公募研究

研究領域ミルフィーユ構造の材料科学-新強化原理に基づく次世代構造材料の創製-
研究課題/領域番号 19H05131
研究機関九州大学

研究代表者

Cesana Pierluigi  九州大学, マス・フォア・インダストリ研究所, 准教授 (60771532)

研究期間 (年度) 2019-04-01 – 2021-03-31
キーワードDisclinations / Kink formation / Calculus of Variations / Solid Mechanics
研究実績の概要

Developed an analytical theory to describe self-similar microstructures in elastic crystals as the solutions to differential inclusion problems in non-linear elasticity (1 paper). As an application, performed exact constructions of disclinations observed in lead-orthovanadate and provided energy estimates. Computed numerical solutions to compression experiments of columnar structures modelling various lattice symmetries. Showed that kinks emerge due to interplay of structural vs. material instabilities. Preliminary results complement existing literature on the kinematics of disclinations and kinks by providing a setting in the framework of minimization problems for non-convex energies (1 paper in preparation).
Computed exact solutions to a fourth order model for surface diffusion (1 paper).

現在までの達成度 (区分)
現在までの達成度 (区分)

2: おおむね順調に進展している

理由

A first paper on the modeling of disclinations has been accepted for publication on ARMA. This paves the way to modeling of disclinations and other mismatches in single-slip plasticity models. Another paper describing surface-diffusion in metals has been published on Physica D. A paper is being prepared on the modeling of disclinations caused by angular mismatches in the crystallographic lattice by means of an atomistic nearest-neighbor-type model in planar domains. Submission expected soon. A paper describing numerical computation of kink formation in columnar structures based on a continuum model capable of describing micro-plasticity is currently in progress.

今後の研究の推進方策

To continue the analysis of a continuum, non-convex model in non-linear elasticity capable of detecting plasticity at the lattice level. To compute solutions to compression and extension experiments in simple geometries. To compute stress-strain curves and phase-diagrams depending on geometrical and material parameters and show the effect of parameters on various morphologies of kinks. To elucidate the effects of kinks and disclinations on the overall physical properties of the material.
To continue the variational analysis of atomistic models for planar disclinations.
To initiate the modeling and analysis of disclinations with a semi-discrete (diffuse-core) approach by means of Gamma-convergence.

  • 研究成果

    (11件)

すべて 2020 2019 その他

すべて 国際共同研究 (2件) 雑誌論文 (2件) (うち国際共著 2件、 査読あり 2件、 オープンアクセス 2件) 学会発表 (6件) (うち招待講演 6件) 学会・シンポジウム開催 (1件)

  • [国際共同研究] Max-Planck-Institute for Math. in Sc./Technische Universitat Berlin(ドイツ)

    • 国名
      ドイツ
    • 外国機関名
      Max-Planck-Institute for Math. in Sc./Technische Universitat Berlin
  • [国際共同研究] La Trobe University(オーストラリア)

    • 国名
      オーストラリア
    • 外国機関名
      La Trobe University
  • [雑誌論文] Solution for 4th-order nonlinear axisymmetric surface diffusion by inverse method2020

    • 著者名/発表者名
      Gallage Dilruk、Triadis Dimetre、Broadbridge Philip、Cesana Pierluigi
    • 雑誌名

      Physica D: Nonlinear Phenomena

      巻: 405 ページ: 132288~132288

    • DOI

      10.1016/j.physd.2019.132288

    • 査読あり / オープンアクセス / 国際共著
  • [雑誌論文] Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers2020

    • 著者名/発表者名
      Pierluigi Cesana, Francesco Della Porta, Angkana Rueland, Christian Zillinger, Barbara Zwicknagl
    • 雑誌名

      Archive for Rational Mechanics and Analysis

      巻: - ページ: -

    • 査読あり / オープンアクセス / 国際共著
  • [学会発表] Mesoscale modeling for disclinations toward a theory for kink and material strengthening2020

    • 著者名/発表者名
      Pierluigi Cesana
    • 学会等名
      University of Osaka
    • 招待講演
  • [学会発表] Mathematical models and ideas for disclinations and avalanches in elastic crystals2020

    • 著者名/発表者名
      Pierluigi Cesana
    • 学会等名
      State Key Lab for Mechanical Behavior of Materials, Xi’an Jiaodong University, PRC
    • 招待講演
  • [学会発表] Mathematical models and ideas for disclinations2019

    • 著者名/発表者名
      Pierluigi Cesana
    • 学会等名
      JP-ITA Mini-symposium on Elastic Structures and Defects, Kyushu University, JP
    • 招待講演
  • [学会発表] Mathematical models and ideas for disclinations2019

    • 著者名/発表者名
      Pierluigi Cesana
    • 学会等名
      EU-JP MFS Conference Prague, CZ
    • 招待講演
  • [学会発表] Mathematical models and ideas for disclinations2019

    • 著者名/発表者名
      Pierluigi Cesana
    • 学会等名
      Pattern formation and defects, RIMS Gasshuku, Kyoto
    • 招待講演
  • [学会発表] Variational and stochastic models for martensite2019

    • 著者名/発表者名
      Pierluigi Cesana
    • 学会等名
      Gradient flows workshop, Kanazawa, JP
    • 招待講演
  • [学会・シンポジウム開催] JP-ITA Mini-symposium on Elastic Structures and Defects, Kyushu University, JP2019

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公開日: 2021-01-27  

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