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Asymptotic analysis of reinforcement by frictional fibres. (English) Zbl 0913.73058
Summary: We investigate the tensile failure of an infinite brittle matrix reinforced by unidirectionally aligned thin cylindrical fibres, randomly located in the transverse plane. Fibre debonding and pull-out after fibres break, accompanied by frictional sliding, are analysed. The fibres are held in place by Coulomb friction, and elastic properties of the fibre and matrix materials are assumed to be different. We obtain the stress and displacement fields in the composite and the length of the splipping region by solving a model problem for a fibre in an elastic half-space in an ambient stress field generated by all other fibres and the applied loading. The dependence of the solution of the problem on the volume fraction of fibres, material parameters and the value of applied load is examined.

74R99 Fracture and damage
74A40 Random materials and composite materials
74E30 Composite and mixture properties
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