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Technical Brief

On the Sufficient Symmetry Conditions for Isotropy of Elastic Moduli

[+] Author and Article Information
Can Ayas

Structural Optimization & Mechanics, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
c.ayas@tudelft.nl

Cihan Tekoglu

Department of Mechanical Engineering, TOBB University of Economics and Technology, Söğütözü, Ankara, 06560, Turkey
c.tekoglu@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4039952 History: Received February 07, 2018; Revised April 06, 2018

Abstract

The structural symmetry of a material can be manifested at a multitude of length scales such as spatial arrangement of atoms in a crystal structure, preferred orientation of grains in a polycrystalline material, alignment of reinforcing particles/ fibres in composites or the micro-architecture of members in cellular solids. This paper proofs, in a simple yet rigorous manner, that six axes of five-fold structural symmetry is necessary and sufficient for isotropy of the elastic moduli tensor in the three-dimensional context.

Copyright (c) 2018 by ASME
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