A homogenization scheme for elastoplastic composites using concept of Mori-Tanaka method and average deformation power rate density

Abstract

The conventional mean-field homogenization (MFH) schemes are mainly based on the volume averages of stress and strain (or their rates), which do not seem sufficiently universal. In this paper, we proposed a new scheme for estimating the mechanical properties of elastoplastic composites, which makes use of the concepts the Mori-Tanaka (M-T) scheme and average deformation power rate density that can be expressed as a second-order moment of stress/strain rate. In the proposed scheme, the equality between the average deformation power rate density of a composite and those of its constituents is used as one of the mandatory conditions for the determination of the overall tangent stiffness of the composite, which was found to have Voigt symmetry. For a composite consisting of elastic constituents, the equality between the average deformation power rate density of the composite and those of its constituents are reduced to the equality between the average strain energy density of the composite and those of its constituents, and the resulting overall stiffness of the composites has the same expression as that of elastoplastic composites. To verify the proposed scheme, the elastoplastic behaviors of some particulate composites were predicted and compared with that obtained respectively using the finite element approach, the conventional M-T scheme, and the Hill's self-consistent (S–C) scheme. It showed that the proposed scheme could satisfactorily replicate the elastoplastic responses of composites reinforced with spheroidal particle inclusions of moderate volume fraction and aspect ratios, and in many cases it could give better predictions compared with that obtained using the conventional M-T and S–C schemes.