In this study, we develop a material point method (MPM) framework to simulate additive manufacturing processes. The MPM is one of the extensions of the particle-in-cell (PIC) method which has been used in computational fluid dynamics (CFD) applications since 1960s. The main idea behind the material point method is to take advantages of both Eulerian and Lagrangian descriptions which are two different approaches used in the field of mechanics. In material point method, continuum field is represented with a set of particles (material points). All the physical quantities such as mass, stress, deformation gradient, heat flux, and temperature are stored in particles. The particles flow through a fixed background grid and within each time step, and the data stored in particles is mapped into the background grid to solve the governing equations of the problem (e.g. balance of linear momentum, balance of energy) in a similar manner to the finite element method. Then, the particle data is updated remapping the nodal solution from the background grid.

In order to validate our numerical framework, we first considered isothermal droplet impingement problem. The droplet was modeled as an incompressible Newtonian fluid and MPM simulations were validated with COMSOL’s multiphysics solver for two-phase flow modeling with the level set method with different viscosity and surface tension values.