Lower and upper numerical bounds to the off-axis strength of unidirectional fiber-reinforced composites by limit analysis methods

The aim of this paper is to determine the strength domain of highly heterogeneous ductile materials such as Metal Matrix Composites (MMC). By using the homogenization method of periodic media, the macroscopic plasticity domain can be found from the resolution of a limit analysis problem on a unit cell. For the kinematic and static methods, we use specific periodic boundary conditions when displacement, velocity and stress fields are discontinuous. Static and kinematic finite element programs, have been developed which allow linear optimization problems to be solved on a personal computer or unix workstation. The programs are used to determine the off-axis strength of unidirectional long fiber composites. In this case plane finite element mesh can be employed. The static and kinematic finite element programs allow the yield domain to be constructed for any loading. Determination of the macroscopic strength of an MMC is thus derived from a knowledge of the strength properties of its constituents and of their structural arrangement. It is shown that, taking into account a decohesion criterion at the fiber/matrix interface, the numerical predictions and available experimental data are in good agreement.