Effective Properties of Composite Materials, Reinforced Structures and Smart Composites: Asymptotic Homogenization Approach

2013 ◽  
pp. 283-363 ◽  
Author(s):  
Alexander L. Kalamkarov ◽  
Krishna S. Challagulla
Keyword(s):  
Composite Materials ◽  
Effective Properties ◽  
Asymptotic Homogenization ◽  
Smart Composites ◽  
Homogenization Approach

scholarly journals Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach

2019 ◽  
Vol 24 (11) ◽  
pp. 3554-3574 ◽  
Author(s):  
Ariel Ramírez-Torres ◽  
Raimondo Penta ◽  
Reinaldo Rodríguez-Ramos ◽  
Alfio Grillo
Keyword(s):  
Composite Structures ◽  
Effective Properties ◽  
Elastic Solid ◽  
Asymptotic Homogenization ◽  
Linear Elastic ◽  
Homogenization Technique ◽  
Effective Coefficients ◽  
Out Of Plane ◽  
Mineralized Tissues ◽  
Homogenization Approach

The study of the properties of multiscale composites is of great interest in engineering and biology. Particularly, hierarchical composite structures can be found in nature and in engineering. During the past decades, the multiscale asymptotic homogenization technique has shown its potential in the description of such composites by taking advantage of their characteristics at the smaller scales, ciphered in the so-called effective coefficients. Here, we extend previous works by studying the in-plane and out-of-plane effective properties of hierarchical linear elastic solid composites via a three-scale asymptotic homogenization technique. In particular, the approach is adjusted for a multiscale composite with a square-symmetric arrangement of uniaxially aligned cylindrical fibers, and the formulae for computing its effective properties are provided. Finally, we show the potential of the proposed asymptotic homogenization procedure by modeling the effective properties of musculoskeletal mineralized tissues, and we compare the results with theoretical and experimental data for bone and tendon tissues.

Asymptotic Homogenization of Composite Materials and Structures

2009 ◽  
Vol 62 (3) ◽  
Author(s):  
Alexander L. Kalamkarov ◽  
Igor V. Andrianov ◽  
Vladyslav V. Danishevs’kyy
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Composite Shell ◽  
Effective Properties ◽  
Sandwich Composite ◽  
Asymptotic Homogenization ◽  
Random Composites ◽  
Analytical Formulas ◽  
Honeycomb Filler ◽  
Thin Walled

The present paper provides details on the new trends in application of asymptotic homogenization techniques to the analysis of composite materials and thin-walled composite structures and their effective properties. The problems under consideration are important from both fundamental and applied points of view. We review a state-of-the-art in asymptotic homogenization of composites by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications. In addition to the review of existing results, some new original approaches are also introduced. In particular, we analyze a possibility of analytical solution of the unit cell problems obtained as a result of the homogenization procedure. Asymptotic homogenization of 3D thin-walled composite reinforced structures is considered, and the general homogenization model for a composite shell is introduced. In particular, analytical formulas for the effective stiffness moduli of wafer-reinforced shell and sandwich composite shell with a honeycomb filler are presented. We also consider random composites; use of two-point Padé approximants and asymptotically equivalent functions; correlation between conductivity and elastic properties of composites; and strength, damage, and boundary effects in composites. This article is based on a review of 205 references.

Analytical and Numerical Predictions of Thermoelastic Properties of Carbon Single-Walled Nanotubes

Aerospace ◽  
2005 ◽  
Author(s):  
Vinod P. Veedu ◽  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Graphene Sheet ◽  
Effective Properties ◽  
Constitutive Models ◽  
Thermoelastic Properties ◽  
Asymptotic Homogenization ◽  
Element Analysis ◽  
Single Walled Nanotubes ◽  
Numerical Predictions

The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

Consistent Hashin-Shtrikman Bounds on the Effective Properties of Periodic Composite Materials

1999 ◽  
Vol 66 (4) ◽  
pp. 858-866
Author(s):  
P. Bisegna ◽  
R. Luciano
Keyword(s):  
Composite Materials ◽  
Saddle Point ◽  
Variational Principles ◽  
Effective Properties ◽  
The Other ◽  
Constitutive Behavior ◽  
Homogenization Problem ◽  
Numerical Examples ◽  
Periodic Composites ◽  
Periodic Composite

In this paper the four classical Hashin-Shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.

ON AN EXACT DESCRIPTION OF THE SCHOTTKY GROUPS OF SYMMETRIES

2005 ◽  
Vol 9 (2) ◽  
pp. 137-148
Author(s):  
M. V. Dubatovskaya ◽  
S. V. Rogosin
Keyword(s):  
Composite Materials ◽  
Effective Properties ◽  
Schottky Groups ◽  
Multiply Connected ◽  
Schwarz Problem ◽  
Circular Domains ◽  
Exact Description

Exact description of the Schottky groups of symmetries is given for certain special configurations of multiply connected circular domains. It is used in the representation of the solution of the Schwarz problem which is applied at the study of effective properties of composite materials. Santrauka Darbe pateiktas Schottky simetrijos grupiu apibrežimas tam tikros specialios konfiguracijos daugiajungems skritulinems sritims. Jis yra panaudotas gaunant Švarco uždavinio, kuris pritaikomas nagrinejant efektyvias kompoziciju savybes, sprendinio išraiška.

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