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Formulation of semi-analytical finite element of composite materials

Research Project

Project/Area Number 15560391
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Civil engineering materials/Construction/Construction management
Research InstitutionTohoku University

Principal Investigator

IWAKUMA Tetsuo  Tohoku University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (60120812)

Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsComposites / Finite Element / Mori-Tanaka Model / Analytical Homogenization
Research Abstract

The Mori-Tanaka averaging scheme is employed to construct a finite element of composite materials. Characteristics of the element are examined in plane strain states. In randomly distributed case, the element shows isotropic property with the average modulus predicted by the Mori-Tanaka theory. The effects of micro structures of inclusions are examined in a beam-bending case to show proper strengthening effect of fiber orientation. Results of a plate with a hole are compared with numerical solutions by the so-called FEM homogenization method, and are in good coincidence. Moreover our model has an advantage in predicting upper and lower bounds of responses, such as stresses of matrix and inclusions.
Since the constitutive equation of micro structures is explicitly formulated, the element can be applied to the stochastic FEM. Such approach can evaluate sensitivity of stiffness and strength due to changes of micro structures. Also in taking advantage of the analytical expression of constitutive equation of micro structures, we apply the element to optimization of structures and materials. A widely-used code is used to construct optimization scheme. Results show positive definiteness of objective functions, and optimum microstructures such as orientation of fibers which can be imagined instinctively.
The model is then generalized into elasto-plastic materials. Furthermore, a model of debonding (no evolution) is included as a simple test of our element. A plate with a hole is examined, and responses are different depending on order of yielding and debonding. Finally rock field with a tunnel is numerically analyzed in order to show where cracks are to open by such excavation. Results are compared with those by another micromechanics-based model and show good coincidence.
Through these numerical calculations, it is shown that the element can be used to design structures made of composite materials, and thus materials themselves can be designed properly.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (13 results)

All 2005 2004 2003 Other

All Journal Article (12 results) Publications (1 results)

  • [Journal Article] 解析的均質化手法を用いた複合材料・構造の簡易解析と最適化2005

    • Author(s)
      王峰
    • Journal Title

      構造工学論文集(土木学会) 51A

      Pages: 1387-1396

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 界面剥離モデルを組み込んだ複合材料有限要素2005

    • Author(s)
      樋口耕平
    • Journal Title

      応用力学論文集(土木学会) 8

      Pages: 367-376

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] 損傷の発展則を含む複合材料の平均化を用いた弾塑性有限要素2005

    • Author(s)
      黒木誠一郎
    • Journal Title

      応用力学論文集(土木学会) 8

      Pages: 377-384

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Simplified analysis and optimization of composite materials and structures using an analytical homogenization method2005

    • Author(s)
      WANG, Feng
    • Journal Title

      J.Str.Eng.JSCE Vol.51A

      Pages: 1387-1396

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Finite element of composite materials with partial debonding along boundary2005

    • Author(s)
      HIGUCHI, Kouhei
    • Journal Title

      J.Appl.Mech.JSCE Vol.8

      Pages: 367-376

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Elasto-plastic averaging finite element of composites with evolution law of micro damages2005

    • Author(s)
      KUROKI, Seiichiro
    • Journal Title

      J.Appl.Mech.JSCE Vol.8

      Pages: 377-384

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 損傷の発展側を含む複合材料の平均化を用いた弾塑性有限要素2005

    • Author(s)
      黒木誠一郎
    • Journal Title

      応用力学論文集(土木学会) 8

      Pages: 377-384

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 解析的均質化手法を用いた複合材料・構造の簡易解析と最適化2005

    • Author(s)
      王峰
    • Journal Title

      構造工学論文集(土木学会) 51A(印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 解析的手法を利用した複合材料有限要素の確率有限要素法への応用と最適化の試行2004

    • Author(s)
      贄川拓
    • Journal Title

      応用力学論文集(土木学会) 7

      Pages: 355-364

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] An application of a semi-analytical finite element of composite materials to the stochastic FEM and to an optimization of microstructures of materials2004

    • Author(s)
      NIEKAWA, Taku
    • Journal Title

      J.Appl.Mech.JSCE Vol.7

      Pages: 355-364

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 解析的平均手法を用いた複合材料の平面ひずみ有限要素2003

    • Author(s)
      樋口耕平
    • Journal Title

      応用力学論文集(土木学会) 6

      Pages: 107-116

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A finite element of composites in plane strain using an analytical averaging method2003

    • Author(s)
      HIGUCHI, Kouhei
    • Journal Title

      J.Appl.Mech.JSCE Vol.6

      Pages: 107-116

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] 樋口耕平, 京谷孝史, 岩熊哲夫, 寺田賢二郎: "解析的平均手法を用いた複合材料の平面ひずみ有限要素"応用力学論文集(土木学会). 6. 107-116 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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