The possibility of using the mesh-free method Smoothed Particle Hydrodynamics (SPH) towards analyzing modern additive manufacturing techniques, extrusion based ones in particular, is investigated in this report. The mathematical foundations and a number of corresponding topics regarding SPH is introduced, ranging from incompressible SPH and implicit timestepping methods to total Lagrangian formulations: displaying its robust capabilities for solving multiphyiscal mechanical problems. Finally, we demonstrate a swarm-intelligence based optimization scheme coupled with our SPH solver to optimize extrusion topologies for DIW (Direct Ink Writing) applications.