Homogenization modeling of capillary forces in selective laser sintering

We study the initial stage of liquid phase sintering when the particles rearrangement due to densification forces is over. The heterogeneous medium is a mixture of powders, connected by liquid necks. It gives a fluid-structure problem built on a periodic domain, with three phases: an isotropic elastic solid, a newtonian, incompressible, weakly viscous liquid and a barotropic viscous gas. We study this equilibrium under the action of capillary forces on solid–liquid boundary. We penalize the divergence free condition in the liquid and by the energy method, we obtain the homogenized problem satisfied by the macroscopic displacement field in the homogenized medium. The result gets close to a Stokes problem where the capillary forces act as a density of body forces and the viscosity effects vanish.