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Eigentensors and eigenelastic constants for woven composites

L. BEJAN1,* , N. ŢĂRANU2

Affiliation

  1. Technical University “Gh. Asachi” Iasi, Theoretical Mechanics Department, Bdul Prof. D. Mangeron 67, RO-700050 Iasi, Romania
  2. Technical University “Gh. Asachi” Iasi, Civil and Industrial Engineering Department, Bdul Prof. D. Mangeron 43, RO-700050 Iasi, Romania

Abstract

The concept of an eigentensor was introduced by Kelvin and he determined the eigentensors for many elastic symmetries. The eigentensors and eigenelastic constants of particular elastic symmetries are significant because they identify preferred modes of deformation associated with particular anisotropic elastic symmetries and are useful in the design of composite materials. The proportional invariants for each linear anisotropic elastic symmetry have the same properties as the hydrostatic and deviatoric stresses or strains in the case of isotropic elastic symmetry, but the proportional invariants for the linear anisotropic elastic symmetry may depend on the components of elasticity or compliance tensor ( $c or $s ). In the present work, the analysis is focused on an orthogonal unbalanced plain weave fabric lamina. To illustrate the invariant of the eigentensors concept, a woven composite lamina, containing a circular hole of radius 1 mm has been analysed. The analysis carried out the finite element method for orthotropic materials using the software package ALGOR provided information about stress and strain in different points of the finite element grid. The resulting grid enabled the usage of the MATLAB facilities for graphical representation of the surface as well as the mesh or contour plots for the three stress and strain invariants, respectively..

Keywords

Woven composite materials, Anisotropy, Eigentensors, Proportional invariant.

Submitted at: May 30, 2007
Accepted at: Sept. 18, 2007

Citation

L. BEJAN, N. ŢĂRANU, Eigentensors and eigenelastic constants for woven composites, Journal of Optoelectronics and Advanced Materials Vol. 9, Iss. 9, pp. 2902-2909 (2007)