INFORMATIVO ABCM Nº 025/08 – Mini-Curso “MICROMECHANICS OF COMPOSITE AND SMART MATERIALS: ASYMPTOTIC HOMOGENIZATION”

A Engenharia Mecânica da UFRJ (COPPE/Politécnica) tem o prazer de anunciar o mini-curso “MICROMECHANICS OF COMPOSITE AND SMART MATERIALS: ASYMPTOTIC HOMOGENIZATION” a ser proferido pelo Prof. Alexander Kalamkarov da Dalhousie University, Canada.

Local:
Universidade Federal do Rio de Janeiro, Cidade Universitária.
Centro de Tecnologia Bloco G, sala 205

Horário:
05 de março de 2008, quarta-feira, de 14:00h às 16:30h.

Mais informações: savi@mecanica.ufrj.br

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“MICROMECHANICS OF COMPOSITE AND SMART MATERIALS: ASYMPTOTIC HOMOGENIZATION”

Alexander L. Kalamkarov
Professor of Mechanical Engineering
Director, Smart Materials Centre
Department of Mechanical Engineering
Dalhousie University
Halifax, Nova Scotia
Canada

Advanced composite materials and smart structures are widely used in various areas of modern engineering. Commonly, these materials are highly inhomogeneous with the dimensions of a unit cell much smaller than the overall dimension of the structure. As a result, the coefficients of the differential equations describing mechanical behavior of these composite materials are rapidly varying functions in spatial coordinates. Consequently, the resulting boundary-value problems are very complex. They are so complex that the numerical methods (e.g., Finite Elements) applied directly to the original boundary-value problem for a smart composite structure are inappropriate in their standard form. Therefore, it is very important to develop rigorous analytical methods in order to reduce the complexity of the original boundary-value problems.

An issue of a high significance in micromechanics of advanced composites is determination of the effective properties of highly inhomogeneous composite materials, which will naturally depend on the spatial distribution, geometric characteristics and mechanical properties of the constituent materials of the composite. The micromechanical analysis of composite materials made up of reinforcements embedded in a matrix has been the focus of investigation for many years. At present, different asymptotic methods are developed and applied in micromechanics of composites. Various asymptotic approaches to the analysis of composite materials of a regular structure have apparently reached their conclusion within the framework of the mathematical theory of multi-scale asymptotic homogenization. Indeed, the proof of the possibility of homogenizing the composite material of a regular structure, i.e., of examining a homogeneous material instead of the original highly inhomogeneous composite material, is one of the principal results of this theory. Asymptotic homogenization method has also indicated a method of transition from the original problem (which contains in its formulation a small parameter related to the small dimensions of the unit cell of the composite) to a problem for a homogeneous material described by a set of so-called effective properties. This transition is accomplished through the solution of the local problems formulated on the unit cell of the composite material. The solution of these unit cell problems allows determining the effective properties and distribution of local fields, e.g., displacements and stresses. The indicated results are fundamentals of the asymptotic homogenization, see [1, 2] for details.

Present lectures will cover the basics of the theory of multi-scale asymptotic homogenization. Simple examples will be used to illustrate the method. The general micromechanical asymptotic homogenization models will be further introduced and applied to the analysis of composite materials and smart structures of a practical importance.

References

[1] A.L. Kalamkarov (1992) Composite and Reinforced Elements of Construction, Wiley: Chichester, New-York.

[2] A.L. Kalamkarov and A.G. Kolpakov (1997) Analysis, Design and Optimization of Composite Structures, Wiley: Chichester, New-York.