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/fibers in composites or the micro-architecture of members in cellular solids. This paper proofs, in a simple yet rigorous manner, that six axes of fivefold structural symmetry is necessary and sufficient for isotropy of the elastic moduli tensor in the three-dimensional (3D) context.
On the Sufficient Symmetry Conditions for Isotropy of Elastic Moduli
TOBB University of Economics and Technology,
Ankara 06560, Turkey
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 7, 2018; final manuscript received April 6, 2018; published online May 8, 2018. Assoc. Editor: Shaoxing Qu.
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Ayas, C., and Tekog̃lu, C. (May 8, 2018). "On the Sufficient Symmetry Conditions for Isotropy of Elastic Moduli." ASME. J. Appl. Mech. July 2018; 85(7): 074502. https://doi.org/10.1115/1.4039952
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