Carlos J. G. Rojas

Carlos J. G. Rojas, Md. Tusher Mollah, C. A. Gómez-Pérez et al.

Accurate numerical simulation of material extrusion additive manufacturing requires reliable tracking of evolving material interfaces while preserving mass conservation. Inaccurate mass conservation can lead to significant discrepancies between simulated and deposited strand geometries, undermining the predictive capability of the model. In this work, we investigate the mass conservation performance of the conservative level-set (CLS) method in extrusion-based 3D printing simulations. A systematic parametric study is conducted to quantify the influence of the interface thickness and reinitialization parameters on mass conservation, using the steady-state cross-sectional area of deposited strands as a quantitative metric. Simulated cross-sections are compared against reference values obtained from analytical mass balance relations. The results show that reducing both the interface thickness and the reinitialization parameter improves mass conservation accuracy, although diminishing returns and increased computational cost are observed beyond certain thresholds. In addition, appropriate tuning of the interface thickness can relax mesh refinement requirements while maintaining acceptable accuracy. The proposed parameter selection strategy is validated across a range of printing conditions, materials, and nozzle geometries, including multilayer deposition of viscoplastic fluids. The simulations show reasonable agreement with experimentally validated data from the literature, confirming that careful CLS parameter tuning enables accurate and computationally efficient prediction of strand geometry in extrusion-based 3D printing.

Carlos J. G. Rojas, Esteban Lage Cano, Leyla Özkan

This paper presents two explicit Model Predictive Control formulations for linear systems parameterized in terms of design variables. Such parameter dependent behavior commonly arises from operating point dependent linearization of nonlinear systems as well as from variations in mechanical, electrical, or thermal properties associated with material selection in the design of the process or system components. In contrast to explicit MPC approaches that treat design parameter variations and dependencies as disturbances, the proposed methods incorporate the parameters directly into the system matrices in an affine manner. However, explicitly incorporating these dependencies significantly increases the complexity of explicit MPC formulations due to resulting nonlinear terms involving decision variables and parameters. We address this complexity by proposing two approximation methods. Both methods are applied to two examples, and their performances are compared with respect to the exact eMPC implementation.