2005 Fiscal Year Final Research Report Summary
Formulation of semi-analytical finite element of composite materials
| Project/Area Number |
15560391
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Civil engineering materials/Construction/Construction management
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| Research Institution | Tohoku University |
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Principal Investigator |
IWAKUMA Tetsuo Tohoku University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (60120812)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Composites / Finite Element / Mori-Tanaka Model / Analytical Homogenization |
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| 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.
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