A continuum model for fibre-reinforced plastic materials

Abstract

A simple, general continuum model is proposed for describing the plastic behaviour of a composite material consisting of a metal matrix reinforced by strong fibres. The model is that of an incompressible rigid/plastic continuum which is transversely isotropic—the single preferred direction at any point, and at all times, being the fibre-direction at that point—and which is inextensible in the preferred direction. The principal axes of anisotropy are therefore explicitly determined by the deformation history. The kinematics and general three-dimensional theory for the material are developed and then applied to two cases of plane strain and one of plane stress. The latter is employed in the analysis of previously published experimental data on the yielding of thin fibre-reinforced sheets; good agreement is obtained between the theoretical predictions and the experimental data.