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.

scholarly journals Homogenization of a Continuously Microperiodic Multidimensional Medium

2018 ◽  
Vol 19 (1) ◽  
pp. 15
Author(s):  
Marcos Pinheiro Lima ◽  
Leslie Darien Pérez Fernández ◽  
Julián Bravo Castillero
Keyword(s):  
Asymptotic Solution ◽  
Dirichlet Boundary ◽  
Positive Definiteness ◽  
Homogenization Method ◽  
Dirichlet Boundary Value Problem ◽  
Asymptotic Homogenization ◽  
Asymptotic Homogenization Method ◽  
Mathematical Justification ◽  
Theoretical Results ◽  
Formal Asymptotic Solution

The asymptotic homogenization method is applied to obtain formal asymptotic solution and the homogenized solution of a Dirichlet boundary-value problem for an elliptic equation with rapidly os- cillating coefficients. The proximity of the formal asymptotic solution and the homogenized solution to the exact solution is proved, which provides the mathematical justification of the homogenization pro- cess. Preservation of the symmetry and positive-definiteness of the effective coefficient in the homogenized problem is also proved. An example is presented in order to illustrate the theoretical results.

Modeling of Three-Phase Fibrous Composite Using the Asymptotic Homogenization Method

2003 ◽  
Vol 10 (4) ◽  
pp. 319-333 ◽  
Author(s):  
Raúl Guinovart-Díaz ◽  
Reinaldo Rodríguez-Ramos ◽  
Julián Bravo-Castillero ◽  
Federico J. Sabina
Keyword(s):  
Fibrous Composite ◽  
Homogenization Method ◽  
Asymptotic Homogenization ◽  
Three Phase ◽  
Asymptotic Homogenization Method

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.

Analysis of unbalanced laminate composites with imperfect interphase: Effective properties via asymptotic homogenization method

2021 ◽  
pp. 146442072110600
Author(s):  
Bruno Guilherme Christoff ◽  
Humberto Brito-Santana ◽  
Volnei Tita
Keyword(s):  
Numerical Solutions ◽  
Effective Properties ◽  
Laminated Composite ◽  
Homogenization Method ◽  
Elasticity Tensor ◽  
Asymptotic Homogenization ◽  
Laminate Composites ◽  
Analytical And Numerical Solutions ◽  
Asymptotic Homogenization Method ◽  
The Media

This work addresses the Asymptotic Homogenization Method (AHM) to find all the non-zero independent constants of the fourth-order elasticity tensor of a theoretically infinite periodically laminated composite. The concept of Unit Cell describes the domain, comprised of two orthotropic composite plies separated by an isotropic interphase. A general case with an unbalanced composite is considered. Thus, the coupled components of the tensor are expected. Both analytical and numerical solutions are derived. In addition, an interphase degradation model is proposed to evaluate its effect on the effective properties of the media. Two different stacking sequences are considered with five degrees of interphase imperfection each. The results show good agreement between the analytical and numerical solutions. In addition, it is clear that the more imperfect the interphase is, the more affected the effective properties of the media are, especially those dependent on the stacking direction.

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
Sign in / Sign up

Export Citation Format

Share Document