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Basic Equations of Solid Mechanics Based on Lattice Dynamics and Molecular Dynamics

Research Project

Project/Area Number 12650094
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Materials/Mechanics of materials
Research InstitutionKeio University

Principal Investigator

TAKAHASHI Kunihiro  Keio University, Faculty of Science and Technology, Professor, 理工学部, 教授 (60095619)

Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2000: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsSolid Mechanics / Constitutive Equation / Higher-Order Stress / Cauchy's Relation / Atomic Configuration / Molecular Dynamics / Thermal Beam Theory / Thermomechanics
Research Abstract

In conventional continuum mechanics, macroscopic state variables such as stress, strain, and temperature are defined at each macroscopic point, and only the macroscale is referenced. On the other hand, since these values are determined from the motions of atoms or molecules, a microscopic scale must be introduced to observe such internal motions from the microscopic standpoint.
The domain in which this mesoscale is used to measure distance is called the mesodomain, i.e., it is sufficiently smaller than the macroscopic domain, yet sufficiently larger than the microscopic volume.
This study proposes a method for expressing stresses from motions of atoms, and for deriving the conservation laws for solids microscopically. Constitutive equations and elastic constants not only for stresses but also for higher-order stresses are also derived microscopically. For the derivation of equations, a concept of a hierarchical Reynolds decomposition is introduced. The hierarchical deviation terms are ex … More pressed by characteristic tensors which can be called P-tensors. The P-tensors are the indexes of atomic configurations and are used effectively for the expression of the elastic constants.
The microscopic expressions described above are useful for obtaining the values of the macroscopic stress, higher-order stresses or constitutive equations from the results of molecular dynamics simulations. A three-dimensional simulation model with 10 x 10 x 10 Al atoms is introduced for calculations. Loads are applied to the atoms on the horizontal surface, changing proportionally with the gradient of 7.06 μN/m. The values of velocities of atoms calculated by molecular dynamics are substituted into the present microscopic expressions of stresses, higher-order stresses and constitutive equations. The numerical values and the theoretical values correspond well.
Based on these results, a notion of one dimensional thermal polar materials are introduced. These materials can be said as thermal beams. A model of the thermal beam is proposed, and thermal cross-sectional constants for the model are obtained by FEM calculations. Less

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Nakane, M., Shizawa, K., Takahashi, K.: "Microscopic Discussions of Macroscopic Balance Equations for Solids Based on Atomic Configuration"Archive of Applied Mechanics. 70. 533-549 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 中根一起, 林謙二, 高橋邦弘: "一般化されたCauchyの関係式の原子運動に基づく導出"日本機械学会論文集A編. 67-654. 259-266 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 村山高志, 高橋邦弘: "熱的なはり理論および断面定数"日本機械学会材料力学部門講演会講演論文集. No.01-16. 591-592 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 今村和彦, 中村仁志, 田口隆敏, 高橋邦弘: "薄肉断面柱における第3の座屈:断面変形座屈"日本機械学会2001年度年次大会講演論文集. I-01-1. 339-340 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Takahashi, K., Ishihara, N., Nakamura, H.: "Analytical and Numerical Solutions for Distortional Instabilities of Thin-Walled Beams under Bending Moment"International Conference on Coupled Instabilities in Metal Structures. CIMS 2000. 73-80 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Takahashi, K.: "Conditions for Desirable Structures Based on a Concept of Load Transfer Courses"International Structural Engineering and Construction Conference. ISEC-1. 699-702 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Takahashi, K., Nakamura, H., Imamura, K.: "Pure Distortional Buckling of Closed Cross-Section Columns"International Conference on Thin-Walled Structures. ICTWS-3. 623-630 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakane, M., Shizawa, K, Takahashi, K.: "Microscopic Discussions of Macroscopic Balance Equations for Solids Based on Atomic Configuration"Archive of Applied Mechanics. 70. 533-549 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakane, M., Hayashi, K., Takahashi, K.: "Derivations of Generalized Cauchy's Relations Based on Atomic Configurations"Transaction of the Japan Society of Mechanical Engineers. 67-654. 259-266 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Murayama, T., Takahashi, K.: "Thermal Beam Theory and Section Moduli"Proceedings of the 2001 Annual Meeting of JSME/MMD. No. 01-16. 591-592 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Imamura, K., Nakamura, H., Taguchi, T., Takahashi, K.: "A New Buckling Mode of Thin-Walled Columns: Distortional Buckling"Mechanical Engineering Congress, 2001 Japan. I-01-1. 339-340 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Takahashi, K., Ishihara, N., Nakamura, H.: "Analytical and Numerical Solutions for Distortional Instabilities of Thin-Walled Beams under Bending Moment"International Conference on Coupled Instabilities in Metal Structures. CIMS 2000. 73-80 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Takahashi, K.: "Conditions for Desirable Structures Based on a Concept of Load Transfer Courses"International Structural Engineering and Construction Conference. ISEC-1. 699-702 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Takahashi, K., Nakamura, H., Imamura, K.: "Pure Distortional Buckling of Closed Cross-Section Columns"International Conference on Thin-Walled Structures. ICTWS-3. 623-630 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakane, M., Shizawa, K., Takahashi, K.: "Microscopic Discussions of Macroscopic Balance Equations for Solids Based on Atomic Configuration"Archive of Applied Mechanics. 70. 533-549 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] 中根一起, 林謙二, 高橋邦弘: "一般化されたCauchyの関係式の原子運動に基づく導出"日本機械学会論文集A編. 67-654. 259-266 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 村山高志, 高橋邦弘: "熱的なはり理論および断面定数"日本機械学会材料力学部門講演会講演論文集. No.01-16. 591-592 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 今村和彦, 中村仁志, 田口隆敏, 高橋邦弘: "薄肉断面柱における第3の座屈:断面変形座屈"日本機械学会2001年度年次大会講演論文集. I-01-1. 339-340 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takahashi, K., Ishihara, N., Nakamura, H.: "Analytical and Numerical Solutions for Distortional Instabilities of Thin-Walled Beams under Bending Moment"International Conference on Coupled Instabilities in Metal Structures. CIMS2000. 73-80 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takahashi, K.: "Conditions for Desirable Structures Based on a Concept of Load Transfer Courses"International Structural Engineering and Construction Conference. ISEC-1. 699-702 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takahashi, K., Nakamura, H., Imamura, K.: "Pure Distortional Buckling of Closed Cross-Section Columns"International Conference on Thin-Walled Structures. ICTWS-3. 623-630 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 中根一起,林謙二,高橋邦弘: "一般化されたCauchyの関係式の原子運動に基づく導出"日本機械学会論文集. 67-654. 259-266 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Takahashi,K.: "Conditions for desirable structures based on a concept of load tarnsfer courses"Proc.first internatinal structural engineering and construction conference. A.A.Balkema. 699-704 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 村山高志,高橋邦弘: "熱的なはり理論および断面定数"日本機械学会M&M2001材料力学部門講演会. 2001-6月(発表予定). (2001)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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