Lower and upper bound estimates for the macroscopic strength criterion of fiber composite materials

The formulation of a homogenization procedure within the framework of the yield design theory makes it possible to derive a strength criterion for a fiber composite material in a rigorous way, from the only definitions of the strength properties of the constituents (matrix and fibers) and of their geometrical, structural and voluminal arrangement. Making use of both yield design static and kinematic approaches, quite simple analytical lower and upper bounds estimates are obtained for a unidirectional fiber composite. A detailed analysis of those estimates is carried through in the specific case when the composite is subjected to a uniaxial solicitation or to plane strain conditions parallel to the fibers direction.