scholarly journals Effective Behavior of Nonlinear Microperiodic Composites with Imperfect Contact Via the Asymptotic Homogenization Method.

2021 ◽  
Vol 22 (1) ◽  
pp. 79-90
Author(s):  
R. Décio Jr ◽  
L. D. Pérez-Fernández ◽  
J. Bravo-Castillero
Keyword(s):  
Nonlinear Differential Equations ◽  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Imperfect Contact ◽  
Piecewise Constant ◽  
Important Approach ◽  
Asymptotic Homogenization Method ◽  
Dimensional Boundary ◽  
Constant Coefficients ◽  
Effective Behavior

The asymptotic homogenization method is applied here to one-dimensional boundary-value problems for nonlinear differential equations with rapidly oscillating piecewise-constant coefficients which model the behavior of nonlinear microperiodic composites, in order to assess the influence of interfacial imperfect contact on the effective behavior. In particular, a nonlinear power-law flux on the gradient of the unknown was considered. Several calculations were performed and are discussed at the end of this work, including a comparison of some results with variational ounds, which is also an important approach of this work.

Micro-Macro Characterization of Effective Properties for Fibrous Composites With Parallelogram Cells and Imperfect Contact Condition

2011 ◽  
Author(s):  
Reinaldo Rodriguez-Ramos ◽  
Juan Carlos Lo´pez-Realpozo ◽  
Rau´l Guinovart-Di´az ◽  
Julia´n Bravo-Castillero ◽  
J. A. Otero ◽  
...  
Keyword(s):  
Effective Properties ◽  
Transverse Isotropy ◽  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Two Phase ◽  
Imperfect Contact ◽  
Three Phase ◽  
Asymptotic Homogenization Method ◽  
Theoretical Results

In this work, two-phase parallel fiber-reinforced periodic piezoelectric composites are considered wherein the constituents exhibit transverse isotropy and the cells have different configurations. Two types of imperfect contact at the interface of the composites are studied: a) imperfect contact via spring model, b) three phase model. Simple closed-form formulae are obtained for the effective properties of the composites with both types of contact and different parallelogram cells by means of the asymptotic homogenization method (AHM). Some numerical examples and comparisons with other theoretical results illustrate that the model is efficient for the analysis of composites with presence of parallelogram cells and imperfect contacts.

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).

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.

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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