OVERALL POTENTIALS AND EXTREMAL SURFACES OF POWER-LAW OR IDEALLY PLASTIC COMPOSITES

A METHOD is proposed for bounding the overall properties of a class of composite materials in terms of the properties of the individual phases and of their arrangement. It applies to power law materials and, as a special case, to rigid ideally plastic materials. A link between the overall potential of a nonlinear composite and the overall energy of a fictitious linear composite is presented with no assumptions on the arrangement of the phases. With this method, any upper bound available for linear materials can easily be transposed to nonlinear materials. A new characterizing of the extremal surface of ideally plastic composites is given. The possible applications of these bounds are illustrated in a study on two-phase isotropic composites and the predictions of the bounds are compared with Finite Element cell calculations.