An Eulerian finite element model for the steady state forming of porous materials

This paper is concerned with an Eulerian finite element analysis for the steady state forming of porous materials, such as nano-grained material manufactured via cryogenic milling. The constitutive relation for such porous materials is different from that for a fully dense matrix. The general form of the constitutive equation for a porous material is derived from the yield functions for the plastic deformation of a porous material, as proposed by Shima, Green, Doraivelu, Gurson, Kuhn, Park, and Lee. Then, that general form is utilized in the Eulerian finite element formulation for the strain hardening, dilatant, and viscoplastic deformation. Initial estimation of the porosity distribution in an Eulerian mesh is obtained from the velocity and scaled pressure fields computed by the Consistent Penalty finite element method for the incompressible viscoplastic deformation of the matrix. Applications of the proposed method to rolling and extrusion are given. The change of the porosity is predicted by integrating its evolution equation along a particle path constructed in an Eulerian domain. Comparisons of the predicted distributions of porosity to those by a Lagrangian finite element method and to those by experiments reported in the literature validate the proposed method.