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

Cihan Tekoglu

Department of Mechanical Engineering, TOBB University of Economics and Technology, Söğütözü, Ankara, 06560, Turkey

1Corresponding author.

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


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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