Computational homogenization of liquid-phase sintering with seamless transition from macroscopic compressibility to incompressibility

Liquid phase sintering of particle agglomerates is modeled on the mesoscale as the viscous deformation of particle-particle contact, whereby the single driving force is the surface tension on the particle/pore interface. On the macroscale, a quasistatic equilibrium problem allows for the prediction of the shrinkage of the sintering body. The present paper presents a novel FE2 formulation of the two-scale sintering problem allowing for the transition to zero porosity, implying macroscale incompressibility. The seamless transition from compressibility to incompressibility on the macroscale is accomplished by introducing a mixed variational format. This has consequences also for the formulation of the mesoscale problem, that is complemented with an extra constraint equation regarding the prolongation of the volumetric part of the macroscopic rate-of-deformation. The numerical examples shows the sintering of a single representative volume element (RVE) which is sheared beyond the point where the porosity vanishes while subjected to zero macroscopic pressure.