Takashi Kyoya

Simulation of the multi-scale convergence in computational homogenization approaches

Although the asymptotic homogenization is known to explicitly predict the thermo-mechanical behaviors of an overall structure as well as the microstructures, the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry. In order for the homogenization method for periodic media to apply for general heterogeneous ones, the problems arising from mathematical modeling are examined in the framework of representative volume element (RVE) analyses. Here, the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of RVE is sufficiently large. Then the numerical studies in this paper realize the multi-scale nature of the convergence of overall material properties as the unit cell size is increased. In addition to such dependency of the macroscopic field variables on the selected size of unit cells, the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method. Similar discussions are made for the elastoplastic mechanical responses in both macro- and microscopic levels. In these multi-scale numerical analyses, the specific effects of the microstructural morphology are reflected by using the digital image-based (DIB) finite element (FE) modeling technique which enables the construction of accurate microstructural models.

Global–local analysis of granular media in quasi-static equilibrium

Abstract A method of global–local analysis is developed for quasi-static equilibrium problems for granular media. The two-scale modeling based on mathematical homogenization theory enables us to formulate two separate boundary value problems in terms of macro- and microscales. The macroscale problem governs the equilibrium of a global structure composed of granular assemblies, while the microscale one is posed for the particulate nature of a local structure with the friction-contact mechanism between particles. The local structure is identified with a periodic representative volume element, or equivalently, a unit cell, over which averaging is performed. The mechanical behavior of unit cells is analyzed by a discrete numerical model, in which spring and friction devices connect rigid particles, whereas the continuum-based finite element method is used for the macroscopic one. Representative numerical examples are presented to demonstrate the capability of the proposed two-scale analysis method for granular materials.

Applicability of micro–macro decoupling scheme to two-scale analysis of fiber-reinforced plastics

The numerical study is made to demonstrate the applicability of the method of decoupling multi-scale analysis to the micro–macro evaluation of the mechanical behavior of fiber-reinforced plastics (FRP) that exhibits inelastic deformations and internal damage of the matrix material. During the course of this demonstration, it is confirmed that the reliability of the decoupling method can be guaranteed if the macroscopic constitutive model is introduced so as to inherit the microscopic material behavior. To this end, with reference to the results of the numerical material testing on the periodic microstructures of FRP, we propose an anisotropic elastoplastic-creep-damage combined constitutive model to represent the macroscopic material behavior and illustrate the characteristics of the inelastic deformations that resemble the material behavior assumed for plastics at micro-scale. With the identified macroscopic material parameters, the macroscopic structural analysis, which is followed by the localization analysis consistently, can be an actual proof of the utility value of the decoupling method in practice.

Multi-scale limit load analysis for discontinuous rock mass based on the homogenization method

A new method to evaluate the strength of rock mass structures is proposed and examined. The method is based on the collapse load analysis of elasto-perfectly plastic material along with the homogenization method, which enables the multi-scale analyses for heterogeneous media. The homogenization process replaces a rock mass with cracks by an equivalent continuum medium with macroscopic stiffness while the failure criterion for the rock mass is estimated in the localization process. It is shown that both the averaged stiffness and the macroscopic failure criterion of the discontinuous rock mass are numerically obtained via the finite element analyses. Thus, the failure strength of a rock mass structure is evaluated by the collapse load analysis in the form of Linear Programming with the macroscopic failure criterion. This is the first attempt to apply the homogenization method to the strength analysis of rock mass. Copyright

MULTIPHASE MATERIAL OPTIMIZATION FOR FIBER REINFORCED COMPOSITES CONSIDERING STRAIN SOFTENING

本研究は，繊維強化複合材料，特に繊維補強コンクリート(FRC)を用いた材料最適化手法を提案する．FRCは，通常の鉄筋コンクリートに比べ板厚を極めて薄くできるという優れた長所があるものの，力学的挙動が複雑で一旦損傷が起きると急激に耐荷力が低下するという問題がある．そのため，本研究はFRCの損傷後においても耐荷力を安定的に保持できるような構造に改善することを意図し，それを可能にする構造最適化手法の提案を行う．ここで提案する手法は，単一材料を対象にした一般的なトポロジー最適化の概念を複合材料に応用し，さらに構成材料の材料非線形性を考慮するものである．ここではいくつかの数値解析例を用いて，本手法が繊維複合材料の耐荷力を安定的に保持できる構造に改善することを確認した．