ON THE DUCTILITY OF LAMINATED MATERIALS

A laminated material is one of the few composite systems for which the effective constitutive behavior can be determined exactly. This is well known for laminated composites with linearly elastic phases in prescribed volume fractions. For these composites, explicit expressions for the effective moduli have been available for at least 30 years. However, it appears that corresponding expressions for the effective energy functions of laminated composites with phases exhibiting nonlinear constitutive behavior are currently unavailable. In this paper, we make straightforward use of a new variational procedure, recently developed by one of the authors, to obtain simple expressions for the effective energy functions of laminated composites with isotropic ductile phases in prescribed volume fractions. The same expressions are given an alternative derivation, starting directly from the classical variational principles. Explicit results are then computed for ductile/brittle systems, such as aluminum/alumina laminates, and also for laminated composites made up of two perfectly plastic phases with different yield stresses. The results-which are representative of other anisotropic geometries, such as fiber-reinforced solids-exhibit a strong coupling between different loading modes that is enhanced by material nonlinearity.