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Physics Informed Dynamical Modeling of Extrusion Based 3D Printing Processes

Mandana Mohammadi Looey, Marissa Loraine Scalise, Amrita Basak, Satadru Dey

TL;DR

The work tackles the need for real-time, control-oriented modeling of extrusion-based 3D printing by developing a physics-informed reduced-order dynamical model. By partitioning the flow into nozzle interior, nozzle–substrate gap, and deposited layer, and by applying spatio-temporal averaging, the authors derive a lightweight, coupled ODE-like framework with input-dependent parameters identified from CFD data. Validation against CFD across diverse operating conditions demonstrates accurate nozzle dynamics and reasonable fidelity in downstream regions, supporting potential for online monitoring, optimization, and closed-loop control in cementitious direct ink writing. The approach provides a practical foundation for real-time DIW control and paves the way for further integration with automated manufacturing loops.

Abstract

The trade off between model fidelity and computational cost remains a central challenge in the computational modeling of extrusion based 3D printing, particularly for real time optimization and control. Although high fidelity simulations have advanced considerably for offline analysis, dynamical modeling tailored for online, control oriented applications is still significantly underdeveloped. In this study, we propose a reduced order dynamical flow model that captures the transient behavior of extrusion based 3D printing. The model is grounded in physics based principles derived from the Navier Stokes equations and further simplified through spatial averaging and input dependent parameterization. To assess its performance, the model is identified via a nonlinear least squares approach using Computational Fluid Dynamics (CFD) simulation data spanning a range of printing conditions and subsequently validated across multiple combinations of training and testing scenarios. The results demonstrate strong agreement with the CFD data within the nozzle, the nozzle substrate gap, and the deposited layer regions. Overall, the proposed reduced order model successfully captures the dominant flow dynamics of the process while maintaining a level of simplicity compatible with real time control and optimization.

Physics Informed Dynamical Modeling of Extrusion Based 3D Printing Processes

TL;DR

The work tackles the need for real-time, control-oriented modeling of extrusion-based 3D printing by developing a physics-informed reduced-order dynamical model. By partitioning the flow into nozzle interior, nozzle–substrate gap, and deposited layer, and by applying spatio-temporal averaging, the authors derive a lightweight, coupled ODE-like framework with input-dependent parameters identified from CFD data. Validation against CFD across diverse operating conditions demonstrates accurate nozzle dynamics and reasonable fidelity in downstream regions, supporting potential for online monitoring, optimization, and closed-loop control in cementitious direct ink writing. The approach provides a practical foundation for real-time DIW control and paves the way for further integration with automated manufacturing loops.

Abstract

The trade off between model fidelity and computational cost remains a central challenge in the computational modeling of extrusion based 3D printing, particularly for real time optimization and control. Although high fidelity simulations have advanced considerably for offline analysis, dynamical modeling tailored for online, control oriented applications is still significantly underdeveloped. In this study, we propose a reduced order dynamical flow model that captures the transient behavior of extrusion based 3D printing. The model is grounded in physics based principles derived from the Navier Stokes equations and further simplified through spatial averaging and input dependent parameterization. To assess its performance, the model is identified via a nonlinear least squares approach using Computational Fluid Dynamics (CFD) simulation data spanning a range of printing conditions and subsequently validated across multiple combinations of training and testing scenarios. The results demonstrate strong agreement with the CFD data within the nozzle, the nozzle substrate gap, and the deposited layer regions. Overall, the proposed reduced order model successfully captures the dominant flow dynamics of the process while maintaining a level of simplicity compatible with real time control and optimization.

Paper Structure

This paper contains 14 sections, 27 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Dynamical Modeling Framework for Extrusion-based 3D Printing Process
  3. Physical description of the printing process
  4. Architecture of the dynamical model
  5. Input-dependent model parameterization
  6. Data Generation and Reduced-Order Model Fitting
  7. Data generation from high fidelity computational model
  8. Training and testing of the proposed dynamical model
  9. Results and Discussion
  10. High-fidelity data analysis
  11. Model evaluation for different mass flow conditions
  12. Model evaluation under different surface velocity conditions
  13. Model evaluation under randomized train–test partitioning
  14. Conclusions

Figures (12)

  • Figure 1: Schematic of the extrusion-based 3D printing process.
  • Figure 2: Block diagram representation of the input-output dynamics of the 3D printing process.
  • Figure 3: Schematic of sub-system 1.
  • Figure 4: Schematic of sub-systems 2 and 3.
  • Figure 5: (a) High-fidelity computational domain. All dimensions are in mm. (b) A representative DIW strand. The green box indicates the cross-sectional area for (c). (c) Cross-sectional locations of the DIW strand from where the velocity and pressure data are extracted.
  • ...and 7 more figures