Structural Mechanics

Associate Professor SAIKI, Isao Assistant Professor YAMAMOTO, Tateki

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Our research activities

Homogenized model of composits and polycrystals

モデル Even in civil engineering field, composites are the most useful materials, because they can be properly and effectively designed for a particular purpose. In such a designing process of materials, it is needed that the characteristics of the overall properties of composite materials and/or polycrystalline materials can be estimated by a simple tool but with some degrees of accuracy. Numerical simulations may predict more or less good estimate of such average behavior, but to that end one must use a large number of finite elements, and it may not be easy to use in designing process. From this viewpoint, an analytical model such as the classical Voigt model may be much more useful than complicated numerical analyses.

モデルの結果     Although there exists may such models, but we have proposed that a two-phase material is modeled by an artifical material with three materials, but one of which will be set to be zero as a limit. A typical result of the Young modulus and the Poisson ratio is shown in the right-hand figure. Our predictions are drawn by solid curves, while dashed curves indicate the pre-existing results. Our estimate lies between a pair of the pre-existing predictions which are considered to be one of the upper and lower bounds. Furthermore, our results are very close to those by Hill's self-consistent method indicated by `SC' in the figure. A figure below shows comparison with the experimental data of Young's modulus and Poisson's ratio of a composite.
実験との比較
    The folloing figures show elasto-plastic predictions by our method.
実験との比較弾塑性

Material model with two inelastic mechanisms

The figure below shows several patterns of development of the localized deformation in the ground beneath a direct footing.
押し込み
It is true that the foundation materials such as sands and clays are not continua, but continuum models are frequently used in predicting the global behavior of such geo-materials. However, if one uses a modified model with a simple plasticity based on the metal plasticity, the localized deformation patterns shown above are not properly predicted in numerical simulations. We here add a non-coaxial flow rule to a non-associate plasticity in order to take some properties of non-continuum into account. Furthermore, in order to stabilize material responses with such a non-coaxiality, another inelastic mechanism of micro slips is added. Such a model can yield the results in the figure above, where the materials have different internal friction angles (the one to the right has bigger angles than that in the left). As can be seen in this figure, patterns quite similar to those observed in the small-scall and large-scale experiments are obtained by numerical simulations with this material model.
     animation (symmetric loading)      animation (unsymmetric loading)
Figures below show the development of such a localized deformation in the sedimentary layer above an active fault.

断層A
断層B

Simplified FEM of compsite materials

確率有限要素法 It is nice to have an analytical averaging scheme of composites explained above, but more precise simulation may be needed at some stages of material design process. There is a very powerful tool called a `Homogenization Method' based on the singular perturbation method and possibly with an FEM for the actual calculations. We here imitate the method without any mathematical proofs between their micro and macro analyses, and have proposed a method where an analytically averaged constitutive model is employed at an integration point of one finite element. A figure at the left shows probabilistic perturbations of stress components due to a variation of the volume fractions of inhomogeneity obtained by the stochastic FEM. Two curves correspond to two different composites with inhomogeneities of different aspect ratios.

確率有限要素法     Such estimates become possible because the stiffness matrix, for example, is given explicitly in terms of micro-structures such as volume fraction and aspect ratio of inclusions of composites. The figure at the right shows a result of optimization with respect to the volume fractions of reinforcing fibers in a simple beam composed of composite materials. The objective function is specified by
     
namely, by the maximization of stiffness K with a given force F in terms of the volume fractions of fibers. The resulting objective function is a convex function as is shown in the right figure, and convergence of optimization is achieved at the fourth step. Starting from initial value as 3% for the volume fractions, we obtained their optimum values as f1=1.1%, and f2=3.9%.


Graduation Theses (last 3 years)

2013
Generalization and Improvement of Predictive Method of Biphase Composite Material Average Elasticity (SUZUKI, Takahiro)
A Consideration on Performance of Panel Points based on Redundancy (TAKIMOTO, Koudai)
2014
An approximate self-consistent estimate of anisotropic elasticity of composites (ARAI, Akitomo)
Quantitative evaluation of redundancy multigirder bridges based on nonlinear finite element analysis (KUMAGAI, Hiroyuki)
Fundamental Consideration on Semianalytic Approach for Shear Lag using Periodic Boundary Condition (NISHII, Daiki)
2015
Choice of stress rate for hypoelasticity from the viewpoint of shear resistance characteristics (FUJIMOTO, Masaaki)

Master Theses (last 3 years)

2013
Characteristics of objective stress rates used in incremental elastoplastic constitutive law with hypoelasticity and Localization of deformation (ARAKAWA, Junpei)
Numerical Evaluation of the Nonlinear Shear Properties of Composite Member (SETOGAWA, Atsushi)
2014
Numerical study of interaction between extended floor deck for non-jointification of a bridge and backfill soil (AKIBA, Shota)
Fundamental consideration on the redundancy of steel Langer bridges based on nonlinear finite element analysis (KAWAMURA, Kota)
Evaluation of Shear Properties of Composite Members with Considering Friction and Bond of Material Interface (KUROSAWA, Akifumi)
Numerical Evaluation of Load Capacity of a Steel Truss Bridge with Considering Dynamic Effect of Member Failure (TSUKADA, Kenichi)
2015
Approximate self-consistent prediction of average elastoplastic behavior of composite with stress-induced anisotropy (SUZUKI, Takahiro)
Quantitative evaluation of dynamic effect of member failure of the steel truss bridges on nonlinear redundancy analysis (TAKIMOTO, Koudai)

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