scholarly journals Homogenization Method Based on Cauer Circuit via Unit Cell Approach

2020 ◽  
Vol 56 (2) ◽  
pp. 1-5
Author(s):  
Shingo Hiruma ◽  
Hajime Igarashi
Keyword(s):  
Homogenization Method ◽  
Unit Cell

scholarly journals Manipulate Vibration Propagation by Anisotropic Honeycomb Structure

2018 ◽  
Vol 175 ◽  
pp. 03040
Author(s):  
Xiang Chen ◽  
Xiao-ming Wang ◽  
Yu-lin Mei
Keyword(s):  
Design Method ◽  
Honeycomb Structure ◽  
Homogenization Method ◽  
Unit Cell ◽  
Field Analysis ◽  
Acoustic Wave Propagation ◽  
Asymptotic Homogenization ◽  
Fluid Properties ◽  
Asymptotic Homogenization Method ◽  
New Type

As a new type of acoustic metamaterial, the pentamode material has extensive application prospect in controlling acoustic wave propagation because of its fluid properties. Firstly, a kind of pentamode material unit cell is designed, which is a two-dimensional honeycomb truss structure. Then, the asymptotic homogenization method is used to calculate static parameters of the unit cell, and also the influence of the geometric parameters and material composition of the unit cell on its mechanical properties is studied. Besides, based on transformation acoustics and the design method of the cylindrical cloak proposed by Norris, an acoustic cloak with isotropic density and gradient elastic modulus is constructed by periodically assembling the unit cell to guide the wave to bypass obstacles. Finally, the full displacement field analysis is carried out to prove the stealth effect of the acoustic cloak.

Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure

2016 ◽  
Vol 07 (03) ◽  
pp. 1650006 ◽  
Author(s):  
Alexander L. Kalamkarov ◽  
Igor V. Andrianov ◽  
Pedro M. C. L. Pacheco ◽  
Marcelo A. Savi ◽  
Galina A. Starushenko
Keyword(s):  
Thermal Conductivity ◽  
Composite Materials ◽  
Asymptotic Analysis ◽  
Circular Cross Section ◽  
Homogenization Method ◽  
Hexagonal Structure ◽  
Unit Cell ◽  
Fiber Reinforced ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.

Simple Implementation of Asymptotic Homogenization Method for Periodic Composite Materials

2020 ◽  
Vol 1015 ◽  
pp. 57-63
Author(s):  
S. S. Yang ◽  
T. Gao ◽  
Cheng Shen
Keyword(s):  
Homogenization Method ◽  
Unit Cell ◽  
Small Scale ◽  
Effective Elastic Constant ◽  
Asymptotic Homogenization ◽  
Displacement Boundary ◽  
Periodic Composite ◽  
Asymptotic Homogenization Method ◽  
Simple Implementation ◽  
Implementation Method

In this paper, a simple implementation method of Asymptotic homogenization (AH) method is developed with the aid of commercial FEM software as a tool box. Then, abundant structural elements (like beam, shell and solid elements) in commercial software can be used to model unit cell with various complex substructures of periodic materials, while simultaneously reducing the model to a small scale with less amount of calculation. During the implementation, a set of simple displacement boundary conditions are assumed for unit cell, and final effective elastic constant can be directly calculated after several static analysis. Two representative examples of applications are chosen and discussed to verify the validity and applicability of the new implementation method by comparing with other methods. The proposed method is expected to become an effective benchmark for assessing other homogenization theories and extended to other homogenization problems (such as thermal expansion coefficient) in the future.

Design of Frame-Like Periodic Solids for Isotropic Symmetry by Member Sizing

2016 ◽  
Vol 33 (1) ◽  
pp. 41-54 ◽  
Author(s):  
K. Theerakittayakorn ◽  
P. Suttakul ◽  
P. Sam ◽  
P. Nanakorn
Keyword(s):  
Closed Form ◽  
Elastic Constants ◽  
Strain Energy ◽  
Equivalent Strain ◽  
Homogenization Method ◽  
Unit Cell ◽  
Cubic Symmetry ◽  
Effective Elastic Constants ◽  
Common Unit ◽  
2D And 3D

AbstractIn this study, a methodology to design frame-like periodic solids for isotropic symmetry by appropriate sizing of unit-cell struts is presented. The methodology utilizes the closed-form effective elastic constants of 2D frame-like periodic solids with square symmetry and 3D frame-like periodic solids with cubic symmetry, derived using the homogenization method based on equivalent strain energy. By using the closed-form effective elastic constants, an equation to enforce isotropic symmetry can be analytically constructed. Thereafter, the equation can be used to determine relative unit-cell strut sizes that are required for isotropic symmetry. The methodology is tested with 2D and 3D frame-like periodic solids with some common unit-cell topologies. Satisfactory results are observed.

Mesoscopic Modeling of Deformation Behavior of Semi-Crystalline Polymer

2005 ◽  
Vol 297-300 ◽  
pp. 2915-2921
Author(s):  
M. Uchida ◽  
Yoshihiro Tomita
Keyword(s):  
Deformation Behavior ◽  
Tensile Deformation ◽  
Cell Model ◽  
Computational Simulation ◽  
Crystalline Polymer ◽  
Homogenization Method ◽  
Unit Cell ◽  
Semicrystalline Polymer ◽  
Amorphous Phases ◽  
Tension And Compression

In present study, we clarify the micro- to mesoscopic deformation behavior of semicrystalline polymer unit cell by using large deformation finite element homogenization method. Crystalline plasticity theory with penalty method for enforcing the inextensibility of chain direction and nonaffine molecular chain network theory were applied to the representation of the deformation behavior of crystalline and amorphous phases, respectively, in composite microstructure of semicrystalline polymer. The different directional tension and compression are applied to the 2- dimensional plane strain semi-crystalline unit cell model. A series of computational simulation clarified highly anisotropic deformation behavior of microstructure of semi-crystalline polymer, which is caused by rotation of chain direction and lamella interface, and manifests as a substantial hardening/softening. This anisotropy for tensile deformation is higher than that for compressive deformation.

Study on the Out-Plane Size Effects of Honeycomb Sandwich Panels

2011 ◽  
Vol 66-68 ◽  
pp. 1550-1555
Author(s):  
Shi Ping Sun ◽  
Yu Dong Lai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Size Effects ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Size Variation ◽  
Homogenization Method ◽  
Unit Cell ◽  
Laminated Plate ◽  
Honeycomb Sandwich

A computational model, which can reveal the out-plane size variation of sandwich panel unit cell, is proposed to study the out-plane size effects of honeycomb sandwich panels. In this model, the three dimensional unit cell of sandwich panel, consisting of the upper and the lower skins and the homogenized core, is constructed based on homogenization method. Three methods, i.e., homogenization method, the finite element method and the classical laminated plate theory, are used to study the influences of the out-plane size variation on the bending effect and vibration response of sandwich panel. Numerical results show that the solution of finite element method agrees with that of laminated plate theory when the number of out-plane unit cell is small. However, once the number of out-of-plane unit cell is large enough, the finite element solution is close to the homogenization results.

Optimal design of a multilayered piezoelectric transducer based on a special unit cell homogenization method

2016 ◽  
Vol 227 (7) ◽  
pp. 1837-1847 ◽  
Author(s):  
Houssein Nasser ◽  
Sandra Porn ◽  
Yao Koutsawa ◽  
Gaetano Giunta ◽  
Salim Belouettar
Keyword(s):  
Optimal Design ◽  
Piezoelectric Transducer ◽  
Homogenization Method ◽  
Unit Cell ◽  
Special Unit

Design of periodic unit cell in cellular materials with extreme properties using topology optimization

2016 ◽  
Vol 232 (10) ◽  
pp. 852-869 ◽  
Author(s):  
Wenjiong Chen ◽  
Liyong Tong ◽  
Shutian Liu
Keyword(s):  
Topology Optimization ◽  
Effective Properties ◽  
Optimization Method ◽  
Homogenization Method ◽  
Cellular Materials ◽  
Unit Cell ◽  
Threshold Method ◽  
Penalization Method ◽  
Modulus Maximum ◽  
Periodic Unit Cell

This paper presents a topology optimization method to design periodic unit cell in cellular materials with extreme properties using a moving iso-surface threshold method. The aim is to determine the optimal distribution of material within the periodic unit cell. The effective properties of cellular material are obtained by using a finite element-based homogenization method. The penalty function approach is introduced to construct the objective function for designing material with extreme properties under condition of square or isotropic symmetry. New characteristic response functions of moving iso-surface threshold are proposed for maximum shear or bulk modulus, maximum shear modulus or negative Poisson’s ratio under isotropic symmetry. Several examples are presented and the results are compared to those obtained with the solid isotropic material with penalization method to demonstrate the validity of the method. A series of new and interesting microstructures with extreme properties are found and presented.

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