Modified Deshpande–Fleck Model considering a Variable Plasticity Poisson’s Ratio and a Variable Ellipticity

Abstract

It is controversial whether the plastic Poisson’s ratio and ellipticity are invariable in the Deshpande–Fleck model, which describes the constitutive behavior of foam materials. In this paper, the Deshpande–Fleck model is modified by a variable plasticity Poisson’s ratio and a variable ellipticity based on a nonassociated flow rule. The plasticity Poisson’s ratio is measured by in situ digital image correlation (DIC) technology during the uniaxial compression experiment of aluminum foam. The ellipticity is then determined through the experimental data of uniaxial compression and hydrostatic compression. Both the plastic Poisson’s ratio and the ellipticity vary with the strain. The Hanssen model fitted with uniaxial compression experimental data is used to provide the hardening law for the modified Deshpande–Fleck model. The modified Deshpande–Fleck model is realized by the subroutine VUMAT in ABAQUS/Explicit. There is good agreement between the experimental results and the prediction results of the modified Deshpande–Fleck model under multiaxial compression conditions. Furthermore, the influence mechanism of the plastic Poisson’s ratio and ellipticity on the modified Deshpande–Fleck model are investigated. The results prove that it is necessary to consider both the variable plastic Poisson’s ratio and the variable ellipticity in order to improve the prediction accuracy of the modified Deshpande–Fleck model.