The Finite Element Method for the Thermo-Mechanical Modeling of Additive Manufacturing Processes

This chapter outlines the methodology to numerically solve the equations which describe the thermal and mechanical equations for AM processes. This discussion follows that used by the Netfabb Simulation tool which was used to complete the FE validation studies in the rest of the book. However, the modeling approach is general, and may be applied to any AM code. First the necessity of using the non-linear finite element method is shown then a brief explanation of the non-linear FE process is given. The weakly or decoupled modeling method is described, along with reasons for its usefulness and caveats regarding its limitations. The thermal and mechanical models are described with the relevant boundary conditions. A treatment of the primary methods to model the addition of material is given, along with the advantages and limitations of each method. A brief discussion how temperature dependent material properties are applied in the modeling tool is presented. Meshing concerns and methods are then described. Methods of verifying a model is numerically correct by comparing model results to problems with known answers are discussed at length. Finally validation methods are outlined along with error metrics and a discussion of validation criteria.