Limiting solutions are discussed for elastic-plastic deformation around rigid particles of both equiaxed and greatly elongated shapes. It is shown that if the matrix can be characterized as a rigid nonhardening continuum the stress concentration at the particle interface and interior is less than two for either equiaxed or elongated particles. In a rapidly strain hardening matrix, however, while the interfacial stress concentration relative to the distant boundary traction remains at a factor of two for the equiaxed particles, it rises nearly linearly with aspect ratio for slender platelets and rods. Interaction between particles can occur when the local volume fraction of particles is high. Such interactions raise the interface tractions for a given state of shear of the matrix and hasten void formation, and are often discerned as a particle size effect. Another particle size effect based on flawed particles is also discussed.

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