A new formulation of the effective elastic–plastic response of two-phase particulate composite materials

• The double-inclusion model is reformulated for plasticity of particulate composites.
• The problem of the plastic deformation of the double-inclusion is solved by the finite element method.
• The predictions of the proposed double-inclusion model agree well with the available exact results.
• The proposed double-inclusion model gives accurate prediction at moderate particle volume fractions.

In this paper the double-inclusion model, originally developed to determine effective linear elastic properties of composite materials, is reformulated and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The resulting problem of elastic–plastic deformation of a double-inclusion embedded in an infinite reference medium subjected to an incrementally applied far-field strain is solved by the finite element method. The proposed double-inclusion model is evaluated by comparison of the model predictions to the available exact results obtained by the direct approach using representative volume elements containing many particles. It is found that the double-inclusion formulation is capable of providing accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions.