A new plastic flow theoretical model and verification for non-dense metals

Abstract

The mechanical behavior and constitutive equations of isotropic non-dense metals, such as metal foams, porous metals, and lattice metals, have been extensively studied, but the subsequent yield surfaces depicted by different theoretical models are somewhat controversial and have not been fully validated in the whole permissible loading space. Based on two accepted assumptions for isotropic non-dense metals, we proposed a new plastic flow theoretical model. In order to verify its rationality, we established two mesoscopic models with different initial relative densities and different meso-structures. Then, the large amount of numerical simulation experimental data was established, which covers enough multiaxial loadings in the permissible principle-strain space. Our model solves some of the controversies in current models and adapts the equivalent stress, equivalent strain, and constitutive equations seamlessly to deformation from non-dense to dense state. Numerical results from two mesoscopic models show the relations between equivalent stress and plastic strain in our theoretical model have better consistency under all multiaxial loadings than those in some known models. We checked the topology of subsequent yield surfaces in the plastic principle-strain space and the results turn out the subsequent yield surfaces are not self-similar. The large amount of numerical test data not only well validates our theoretical model but also will be beneficial to the mechanical study of non-dense metals under multiaxial loadings.