The Effective Properties of Brittle/Ductile Incompressible Composites
A new variational method for estimating the effective properties of nonlinear composites in terms of the corresponding properties of linear composites with the same microstructural distributions of phases is applied to an isotropic, incompressible composite material containing a brittle (linear) and a ductile (nonlinear) phase. More specifically, in this particular work the prescription is used to obtain bounds of the Hashin-Shtrikman type for the effective properties of the nonlinear composite in terms of the well-known linear bounds. It can be shown that in some cases the method leads to optimal bounds.
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