Numerical assessment of an anisotropic porous metal plasticity model

• We compute rigorous upper bound yield loci for orthotropic porous plastic materials.
• The loci are obtained by numerical solution of a variational optimization problem.
• The numerical loci are compared against an approximate analytical yield criterion.
• Evolution of the microstructure during plasticity is computed using finite elements.
• Good quantitative agreement is observed between the analytical and numerical results.

The objective of this paper is to perform numerical assessment of a micromechanical model of porous metal plasticity developed previously by the authors. First, upper bound estimates for the yield loci are computed using homogenization and limit analysis of a spheroidal representative volume element containing a confocal spheroidal void, neglecting elasticity. Unlike in the development of the analytical model, the computational limit analysis is performed without recourse to approximations so that the obtained yield loci are rigorous upper bounds for the true criterion. Next, the model’s macroscopic dilatancy at incipient plastic flow is compared against that of the numerical limit analysis approach. Finally, finite-element calculations, with elasticity included, are presented for transversely isotropic porous unit-cells loaded axisymmetrically. The effective stress–strain response as well as evolution of the unit-cell porosity and void aspect ratio are compared with theoretical predictions.