A New Incremental Formulation of Elastic–Plastic Deformation of Two-Phase Particulate Composite Materials

In this study the double-inclusion model, originally developed to determine the effective linear elastic properties of composite materials, is reformulated in incremental form and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The study is limited to composites consisting of purely elastic particles and elastic–plastic matrix of von Mises yield criterion with isotropic strain hardening. The resulting nonlinear problem of elastic–plastic deformation of a double inclusion embedded in an infinite reference medium (that has the elastic–plastic properties of the matrix) subjected to an incrementally applied far-field strain is linearized at each load increment through the use of the matrix tangent moduli. The proposed incremental double-inclusion model is evaluated by comparison of the model predictions to the exact results of the direct approach using representative volume elements containing many particles, and to the available experimental results. It is shown that the incremental double-inclusion formulation gives accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions. In particular, the incremental double-inclusion model is capable of capturing the Bauschinger effect often exhibited by heterogeneous materials. A unique feature of the proposed incremental formulation is that the composite matrix is treated as a two-phase material consisting of both an elastic and a plastic region.