Papers by Keyword: Homogenization Method

Abstract: Inherent structural stress in a plain weave is induced during the formation process of fabrics, and its evaluation is useful for estimating the mechanical stiffness of weaves. In this study, the effect of inherent stress distributed in a weave fabric was investigated to estimate its mechanical stiffness. Here, a numerical simulation method that imitates the fabrication process of fabrics is proposed to evaluate stiffness. A diagram illustrating the weaving process is defined in this evaluation method. For computational analysis, a unit cell model used in homogenization was developed based on the structural periodicity of the plain weave structure using the finite element method. The weaving state was accomplished by simulating the weaving behavior in this model. The weaving state included the geometric shape and stress/strain data. Subsequently, a model was built to estimate the mechanical stiffness based on the weaving state data. Finally, a uniaxial tensile simulation was conducted using the numerical model. Using this evaluation method, the effect of inherent stress on the mechanical stiffness of weaves was quantified, which indicated that the tensile stiffness improved in a small strain range. The effect gradually decreased as the tension progressed.

Abstract: Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.

Abstract: The water channels inside the Nafion membrane are considered as the elastic particles and the effect of the elastic modulus of the particles on the deformation behavior of the membrane is discussed with a particle-contained composite model, which is constituted based on the homogenization method. The results show that the deformation resistance of the membrane is quite dependent on the elastic modulus of the particles, whereas the strain softening behavior after the yielding of the membrane is almost derived from the onset and the propagation of the localized shear band in the matrix, which also leads to the dramatic disappearance of the entanglement points in the molecular chain network of the matrix.

Abstract: A new numerical method for homogenization of elastic properties of dispersedly-reinforced composites was presented. The method takes into account special model of adhesive contact. Homogenization of properties was performed by averaging the solutions of boundary value problems on representative volume cell (RVC) using the finite element method (FEM). A new approach of calculation of components of effective tensor of elastic moduli was proposed. A heterogeneous finite element model with elements of two types was built: three-dimensional tetrahedron elements for every phases and spring element with zero-length for adhesion layer with zero-thickness. The results of homogenization of elastic properties of dispersedly-reinforced composites with variable stiffness of the adhesive layer between phases were obtained and analyzed. The homogenization results were compared with the available experimental data.

Abstract: This work presents the micro-mechanical models in thermal environment for the vibration behavior of Functionally Graded Materials (FGMs) plate using First-order Shear Deformation Theory (FSDT). In the formulation, the heat transfer effects and the temperature-dependent material properties are considered. Relative estimation of micromechanical behaviors of Mori-Tanaka Method (MTM) is used. And, neutral surface concept is adopted as the reference plane due to the asymmetry in the thickness direction of the model. In the numerical analysis, Finite Element Method is applied for various volume fractions and temperature rising conditions. Also Power-law and Sigmoid FGMs are discussed in thermo-elastic vibration characteristics.

Abstract: Porous polymeric membranes are used for ion exchange membranes, membrane filter and separators of batteries owing to its micro-porous structure. Extension method is one of the inexpensive processes of such membrane. However, any suitable stability condition of the process has not yet been clarified. In this study, SEM (Scanning Electron Microscope) observations in production process are carried out and the simulation technology for production is developed for improvement in productivity. In this simulation model, the evolution equation of microscopic damage, constitutive equation depending on microscopic damage and the homogenization method are used for representation of evolution of micro-porous structure of crystalline polymer. It is indicated that numerical results obtained here are in good agreement with the SEM observations.

Abstract: The equations for layered medium with slippage are obtained using the asymptotic method of homogenization. The terms of second order respectively the small parameter of layer thickness are taken into account. The linear slip condition defines the dependence between the tangential jumps of displacements at the contact boundary and the shear stresses. Such generalized models are needed in the study of static and dynamic deformations of layered rock media. Also these models may be useful for description of composite materials with additional soft sublayers between more rigid layers.

Abstract: Multi-ribbed slab structure (MRSS) is a new structural system developed in recent years, with multi-ribbed slab wall as its main bearing member, which was an orthogonal anisotropic solid constituted by reinforced concrete ribs, frame and embedded solid body. It was suggested to employ asymptotic expansion-based homogenization method to establish the equivalent homogenized model. The method is that it considers the impact of rib relative width and the possion. The research results showed that: the macroscopic constitutive relationship of multi-ribbed wall based by the method has certain accuracy, can provide basis for multi-ribbed slab structure FEM analysis.

Abstract: New finite element homogenization model with nonaffine constitutive equation of rubber is developed to study the deformation behavior of silica-filled rubber under monotonic and cyclic deformation. The obtained results clarified the effect of the volume fraction of the silica coupling agent and the networklike structure connecting the silica particles on essential physical enhancement mechanisms of deformation resistance and hysteresis loss for silica-filled rubber. The finding suggests that the material characteristics of silica-filled rubber are much more controllable than those of carbon-black-filled rubber.

Abstract: This paper combined the homogenization method with finite element method. The equivalent mechanical coefficients of the hexagonal aluminum honeycomb core were computed on ABAQUS platform by developing the user subroutine UEXPAN ( ) and Python script file. The results obtained with homogenization method were compared with those obtained with energy method, and it showed the feasibility of homogenization method. Then the effects of thickness-to-length ratio t/l on equivalent mechanical coefficients were taken into account. The results suggested that the equivalent in-plane mechanical parameters vary non-linearly with respect to t/l, while the equivalent out-of-plane mechanical parameters vary linearly with respect to t/l, which will provide reference for optimizing the design of honeycomb core structure.