Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Mathematical model and analysis of the strength of particle reinforced ideally plastic composites

Author: Guillermo H. Goldsztein
Journal: Quart. Appl. Math. 75 (2017), 769-782
MSC (2010): Primary 74C05, 74Q05, 74Q15, 74Q20
DOI: https://doi.org/10.1090/qam/1469
Published electronically: March 10, 2017
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Abstract: We consider fiber reinforced ideally plastic composites. We analyze a mathematical model valid for microstructures and applied stresses that lead to both microscopic and macroscopic anti-plane shear deformations. We obtain a bound on the yield set of the reinforced material in terms of the shapes of the cross section of the fibers, their volume fraction, and the yield stresses of the matrix. We construct examples showing that our bound is sharp.

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Additional Information

Guillermo H. Goldsztein
Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Steert, Atlanta, Georgia 30332-0160
Email: ggold@math.gatech.edu

DOI: https://doi.org/10.1090/qam/1469
Keywords: Microstructures, yield condition, fiber-reinforced composite material, ideally plastic material, variational calculus
Received by editor(s): August 16, 2016
Received by editor(s) in revised form: February 14, 2017
Published electronically: March 10, 2017
Article copyright: © Copyright 2017 Brown University

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