A unified fluid–solid formulation for thermo-mechanical problems using the Particle Finite Element Method: Application to metal additive manufacturing

Metal Additive Manufacturing (MAM) processes are characterized by highly localized heat inputs, steep thermal gradients, rapid phase transitions, and evolving interfaces. Numerical simulation of MAM processes is particularly challenging due to the multiphysics nature of these phenomena. Our original contribution lies in the development of a single robust numerical framework based on the Particle Finite Element Method (PFEM) capable of simulating laser–fluid–solid interaction in MAM processes. Our PFEM formulation is unified and monolithic since the same conservation equations (momentum balance, mass conservation and heat equations) and nodal unknowns (velocity, pressure and temperature) are used in a single global system of equations to solve the fluid and solid parts. Fluids are represented using a general non-Newtonian fluid model while solids are represented using a thermo-elasto-visco-plastic model (hypoelastic formulation). A phase transformation model allowing a smooth transition in material properties is presented. To properly model the thermo-mechanical couplings, an expression of the thermal expansion coefficient including a pressure-dependent term, which is usually not taken into account, is derived. The problem is solved using the finite element method within the Lagrangian framework and large deformations of fluids and solids are addressed using a remeshing procedure, which is the underlying principle of the PFEM. First, the proposed formulation is extensively verified using simple benchmarks from the literature. Then, more complex problems where a bare metal substrate is melted using a laser beam are studied in 2D and 3D to show the capabilities of the method.