|Title||Enriched Analytical Solutions for Additive Manufacturing Modeling and Simulation|
|Publication Type||Journal Article|
|Year of Publication||2019|
|Authors||Steuben J.C, Birnbaum A.J, Michopoulos J.G, Iliopoulos A.P|
Recent developments in additive manufacturing (AM) technologies involving heat and mass deposition have exposed the need for computationally efficient modeling of thermal field histories. This is due to the effect of such histories on resulting morphologies and quantities of interest, such as micro- and meso-structure, residual strains and stresses, as well as on material and structural properties and associated functional performance at the macro-scale. Limiting undesirable manifestations of these phenomena has motivated the development of both feed-forward and feedback loop control methodologies. However, up to now the computational cost of existing methods for predicting thermal fields and associated aspects, have allowed only feed-forward control methods. Consequently, in this paper, analytic solutions are enriched and then used to model the thermal aspects of AM, in a manner that demonstrates both high computational performance and fidelity required to enable "in the loop" use for feedback control of AM processes. It is first shown that the utility of existing analytical solutions is limited due to their underlying assumptions, some of which are their derivation based on a homogeneous semi-infinite domain and temperature independent material properties among others. These solutions must therefore be enriched in order to capture the actual thermal physics associated with the relevant AM processes. Enrichments introduced herein include the handling of strong nonlinear variations in material properties due to their dependence on temperature, finite non-convex solution domains, behavior of heat sources very near domain boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) that implements these enrichments is shown to produce results equivalent to those of numerical methods (such as Finite Elements and Finite Differences) that require six orders of magnitude greater computational cost.