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Mathematical model and analysis of the strength of particle reinforced ideally plastic composites. (English) Zbl 1368.74016

Summary: 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 fiber cross sections, their volume fraction, and the yield stresses of the matrix. We construct examples showing that our bound is sharp.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74Q05 Homogenization in equilibrium problems of solid mechanics
74Q15 Effective constitutive equations in solid mechanics
74Q20 Bounds on effective properties in solid mechanics
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