A micro-mechanical model for statistically unidirectional and randomly distributed fibre-reinforced solids

Abstract

The use of reinforcing fibres in structural materials has been known since ancient time as an effective, simple and economic way to enhance their mechanical characteristics. Among the main mechanical properties that can be improved by such reinforcing techniques the tensile strength, the fracture and fatigue resistance, the wear resistance, the durability etc, can be referred. For the above-mentioned reasons, a tremendous effort in theoretical and experimental research on fibre-reinforced composite (FRC) materials has been made in order to develop suitable models capable of accurately describing the mechanical behaviour of such class of materials, at least at a macroscopic level. In the present paper, an energy-based homogenisation approach to model the mechanical behaviour of fibre-reinforced materials is developed by considering the possibility of fibre debonding and breaking, in order to obtain the macro constitutive equations. Furthermore, the effective spatial distribution of the fibres is accounted for by using its description in terms of probabilistic concepts; the case of randomly spatial-oriented fibres is also considered as a particular case by introducing a uniform probability distribution function. Some peculiarities of the model are outlined by discussing some simple examples in which the effects of different values of the involved parameters are considered.