Papers by Keyword: Homogenization Theory

Abstract: This paper describes a methodology based on “Bidirectional Evolutionary Structural Optimization” (BESO) for topological design of microstructures of materials with more than two constituent phases. The composite material is made by repeating microstructures known as periodic base cells. The aim is to achieve appropriate topology of microstructure phases that enhances the material’s bulk or thermal conductivity performance in macro-scale. Constituent phases are divided into some groups and by performing finite element analyses on microstructure, sensitivity numbers are calculated with the application of Homogenization theory. Properties of elements are gradually changed in the finite element model based on their sensitivity numbers and controlling volume of each constituent phase in the model. Some sample microstructures are generated and presented to show the capability of the approach. The results indicate that the proposed approach is very cost efficient. Moreover, there are distinctive boundaries between the constituent phases in the generated microstructures; which is an inherent advantage of application of BESO approach.

Abstract: A simulation method of macro-and meso-scales is developed for particle reinforce composite materials. The two-scale modeling based on homogenization theory enables to formulate the macro scale problem with Finite Element Method (FEM), while the meso-scale one with Voronoi Cell Finite Element Method (VCFEM). Dangerous regions are identified in macro scale computing period, which lately be meshed into Voronoi Cells in meso-scale period to get a more accurate solution. Representative numerical examples are presented to demonstrate the capability of the proposed two-scale analysis method of particulate reinforce composite materials.

Abstract: In this paper, an improved model is proposed by combining Mori-Tanaka method with Eshelbys equivalent inclusion concept to derive a closed-form solution of the effective Young's modulus E₁₁ for hybrid composites reinforced with multi-shapes inclusions. When only the fiber-like inclusions are considered in the model, the results are consistent with those from Tandons unidirectional aligned composites based on Mori-Tanaka theory. For composites reinforced with fiber-like and spherical inclusions, the homogenization theory is employed to verify the effects of the proposed model. The influence of volume fraction and Youngs modulus of each phase on effective Youngs modulus E₁₁ is investigated, and the results show that E₁₁ is sensitive to the inclusion shapes, and the model is practicable to predict the effective mechanical properties of composites reinforced by several inclusions with different shapes.

Abstract: On the basis of the theoretical framework of breakage mechanics for geo-material ,the fissured loess can be regarded as a composite material consisting of bonded blocks and weakened bands，therefore a fissured loess binary-medium model is formulated. Then the model will be applied to the study of fissured loess. By the numerical calculation, the relationship of stress-strain can be obtained. A comparative analysis between calculation and triaxial test has been done. The results show that there is a good adaptability to apply the binary medium model to fissured loess.

Abstract: Regular tessellation theory was firstly introduced to deconstruct cells and partition masonry periodically in two dimensions in this paper, the method of regular deconstruction of masonry structures was proposed. In addition, the relationship in mathematical models between the basic cells and RVE was explored, the basic cells and the corresponding RVE boundary and initial conditions was derived.

Abstract: For high temperature applications of laminated composite structures, viscoelastic behavior of laminated composite structures is investigated by multi-scale analysis based on a homogenization theory. Effective viscoelastic properties of the laminas are evaluated by a boundary integral method at a micro-scale level, and viscoelastic analysis for laminated composite structures is performed by a finite element method at a macro-scale level using the effective viscoelastic properties of lamina obtained by the micro-scale analysis. In the multi-scale analysis, the Laplace transformation is adopted and the correspondence principle between elastic and viscoelastic solutions in the Laplace domain is applied. The inverse Laplace transform is formulated by the Duhamel integral, and is calculated numerically. As a numerical example, a laminated composite plate with a hole is treated and the viscoelastic behavior of the laminated composite structure is elucidated.

Abstract: Microscopic stress distributions at an interlaminar area in a CFRP cross-ply laminate are analyzed three-dimensionally using a homogenization theory in order to investigate microscopic interaction between 0°- and 90°-plies. It is first shown that a cross-ply laminate has a point-symmetric internal structure on the assumption that each ply in the laminate has a square array of long fibers. Next, the point-symmetry is utilized to reduce the domain of homogenization analysis by half. Moreover, the substructure method is combined with the homogenization theory for reducing consumption of computational resources. The present method is then employed for analyzing stress distributions at an interlaminar area in a carbon fiber/epoxy cross-ply laminate under in-plane off-axis tensile loading. It is thus shown that microscopic shear stress significantly occurs at the interface between 0°- and 90°-plies. It is also shown that the microscopic interaction between two plies is observed only in the vicinity of the interface.

Abstract: In the present study, a method for reducing the domain of analysis is developed for the homogenization analysis of plain-woven laminates. Moreover, the method is applied to the quantitative prediction of elastic-viscoplastic deformation of plain-woven GFRP laminates. It is first shown that the internal structures of plain-woven laminates satisfy point-symmetry on the assumption that the laminates have the in-phase or out-of-phase laminate configuration of plain fabrics. The point-symmetry is then utilized for the boundary condition of unit cell problems, reducing the domain of analysis to 1/4 and 1/8 for the in-phase and out-of-phase laminate configurations, respectively. Using the present method combined with the nonlinear time-dependent homogenization theory, the elastic-viscoplastic behavior of plain-woven GFRP laminates under in-plane on- and off-axis loading is analyzed. In addition, the tensile tests of a plain-woven GFRP laminate at a constant strain rate are performed at a room temperature. Comparing the results of the present analysis with the experimental ones, it is shown that the analysis successfully predicts the in-plane elastic-viscoplastic behavior of the plain-woven GFRP laminate.