Vol. 2, No. 4, 2007

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ISSN: 1559-3959
Asymptotic homogenization model for three-dimensional network reinforced composite structures

Krishna S. Challagulla, Anastasis Georgiades and Alexander L. Kalamkarov

Vol. 2 (2007), No. 4, 613–632
Abstract

The method of asymptotic homogenization is used to develop a comprehensive micromechanical model pertaining to three-dimensional composite structures with an embedded periodic network of isotropic reinforcements, the spatial arrangement of which renders the behavior of the given structures macroscopically anisotropic. The model developed in this paper allows the transformation of the original boundary value problem into a simpler one that is characterized by some effective elastic coefficients. These coefficients are calculated from a so-called unit cell or periodicity problem, and are shown to depend solely on the geometric and material characteristics of the unit cell and are completely independent of the global formulation of the boundary-value problem. As such, the effective elastic coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The model is illustrated by means of several examples of a practical importance and it is shown that the effective properties of a given composite structure can be tailored to satisfy the requirements of a particular application by changing certain geometric parameters such as the size or relative orientation of the reinforcements. For the special case in which the reinforcements form only a two-dimensional (in-plane) network, the results converge to those of previous models obtained either by means of asymptotic homogenization or by stress-strain relationships in the reinforcements.

Keywords
asymptotic homogenization, composite structures, 3D spatial network, unit cell, effective elastic coefficients
Milestones
Received: 21 June 2006
Accepted: 1 October 2006
Published: 1 June 2007
Authors
Krishna S. Challagulla
Department of Mechanical Engineering
Dalhousie University
Halifax, Nova Scotia, B3J 2X4
Canada
Anastasis Georgiades
Department of Mechanical Engineering
Dalhousie University
Halifax, Nova Scotia, B3J 2X4
Canada
Alexander L. Kalamkarov
Department of Mechanical Engineering
Dalhousie University
Halifax, Nova Scotia, B3J 2X4
Canada