Bounds on shear moduli for orthotropic elastic composites

Robert P. Lipton; James Northrup

doi:10.1117/12.148411

22 July 1993 Bounds on shear moduli for orthotropic elastic composites

Robert P. Lipton, James Northrup

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148411
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

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.

Citation Download Citation

Robert P. Lipton and James Northrup "Bounds on shear moduli for orthotropic elastic composites", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148411

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