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Proceedings Paper

Bounds on shear moduli for orthotropic elastic composites
Author(s): Robert P. Lipton; James Northrup
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Paper Abstract

Composite and porous materials often appear in nature. Many composites may be considered orthotropic such as wood or bone. The elastic behavior of these composites under shear stresses is characterized by three independent shear moduli. We consider the totality of orthotropic composites made from two isotropic linearly elastic components in fixed proportion. For a prescribed triple of shear stresses we find optimal bounds on the strongest and weakest orthotropic composites. Mathematically this problem is one of constrained optimization. The set of constraints are related to the convex hull of a surface in three dimensions. For given values of the component elasticities the bounds are computed numerically.

Paper Details

Date Published: 22 July 1993
PDF: 11 pages
Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); doi: 10.1117/12.148411
Show Author Affiliations
Robert P. Lipton, Worcester Polytechnic Institute (United States)
James Northrup, Colby College (United States)

Published in SPIE Proceedings Vol. 1919:
Smart Structures and Materials 1993: Mathematics in Smart Structures
H. Thomas Banks, Editor(s)

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