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.

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.

Two applications of the asymptotic homogenization method

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Sergey Sheshenin ◽  
Nina Artamonova ◽  
Petr Klementyev
Keyword(s):  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Asymptotic Homogenization Method

scholarly journals Assessment of models and methods for pressurized spherical composites

2016 ◽  
Vol 23 (2) ◽  
pp. 136-147
Author(s):  
David Guinovart-Sanjuán ◽  
Raffaella Rizzoni ◽  
Reinaldo Rodríguez-Ramos ◽  
Raúl Guinovart-Díaz ◽  
Julián Bravo-Castillero ◽  
...  
Keyword(s):  
Transversely Isotropic ◽  
Homogenization Method ◽  
Heterogeneous Structure ◽  
Asymptotic Homogenization ◽  
Contact Conditions ◽  
Effective Coefficients ◽  
Asymptotic Homogenization Method ◽  
Perfect Contact ◽  
Periodic Components ◽  
Radial Axis

The elastic properties of a spherical heterogeneous structure with isotropic periodic components is analyzed and a methodology is developed using the two-scale asymptotic homogenization method (AHM) and spherical assemblage model (SAM). The effective coefficients are obtained via AHM for two different composites: (a) composite with perfect contact between two layers distributed periodically along the radial axis; and (b) considering a thin elastic interphase between the layers (intermediate layer) distributed periodically along the radial axis under perfect contact. As a result, the derived overall properties via AHM for homogeneous spherical structure have transversely isotropic behavior. Consequently, the homogenized problem is solved. Using SAM, the analytical exact solutions for appropriate boundary value problems are provided for different number of layers for the cases (a) and (b) in the spherical composite. The numerical results for the displacements, radial and circumferential stresses for both methods are compared considering a spherical composite material loaded by an inside pressure with the two cases of contact conditions between the layers (a) and (b).

The Asymptotic Homogenization Method of the Settlement Calculation of the Cement-Soil Pile Composite Foundation

2011 ◽  
Vol 217-218 ◽  
pp. 390-395
Author(s):  
Ming Qin Guo ◽  
Jie Li ◽  
Shi Cheng Ma ◽  
Zhi Lin Liu
Keyword(s):  
Elastic Foundation ◽  
Three Dimensional ◽  
Elastic Parameter ◽  
Homogenization Method ◽  
Calculation Model ◽  
Composite Foundation ◽  
Homogenization Theory ◽  
Asymptotic Homogenization ◽  
Asymptotic Homogenization Method ◽  
Cement Soil

The finite element calculation model of the cement-soil pile composite foundation based on asymptotic homogenization theory has been built, under the state of three-dimensional stress, the equivalent elastic parameter of the composite elastic foundation model has been calculated, and depending on which, the settlement quantity has been calculated. Analysis through comparison with the testing result shows that it is feasible to use the homogenization method for calculating the settlement quantity of the composite elastic foundation, which sets up a theoretical basis for further analysis of homogenization method about composite foundation.

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