In recent years, significant progress has been made in modeling various additive manufacturing processes such as Fused Deposition Modeling (FDM) for polymers, Directed Energy Deposition (DED) for metals (including and Wire Arc Additive Manufacturing (WAAM) and Wire Laser Additive Manufacturing (WLAM)), or 3D Printed Concrete (3DPC). However, there are few efficient numerical approaches fast enough to compute the influence of process parameters at large scale. For instance within the framework of DED, fast simulation of thermal history and phase transitions have been proposed [1,2]. Nevertheless, for residual stresses most strategies rely on 3D or 2D finite element method (FEM), which requires very fine meshes especially along the print direction to avoid conditioning issues and ensure acceptable convergence [3].

To overcome this difficulty since the aforementioned fabrication processes rely on the deposition of elongated beads, an extended 1D model (immersed in the 3D space) named QuadWire is proposed. It consists in increasing the number of degrees of freedom up to 12 for each material point by considering 4 particles instead of one. This increase is compensated by the reduction to 1D of the the mechanical body’s dimension, which is known to reduce the overall computation time [4,5]. Despite the 1D assumption, such an approach enables us to simulate the fabrication of 3D parts by connecting several beads by applying kinematic conditions between the corresponding QuadWires, while transmitting complex tension, compression and shear stress.

This contribution focuses on the thermodynamic analysis of the proposed theoretical model (based on first and second law of thermodynamics) in order to derive the balance equation that should be verified for any state and for any possible state evolution. On this basis, thermal and fluid diffusion will be presented including not only diffusion along the tangential axis but also from one particle to the other (i.e., cross section of the QuadWire). In addition, examples of a linear thermo-mechanical behavior will be derived from the balance equation. This theoretical framework will enable the development of more complex non-linear thermo-hydro-mechanical behavior adapted for concrete and clay [6, 7].

References

[1] D. Weisz-Patrault; Additive Manufacturing, 2020.

[2] A. Edwards, D. Weisz-Patrault, and E. Charkaluk. Additive Manufacturing, 2023.

[3] D. Weisz-Patrault, P. Margerit, and A. Constantinescu, Additive Manufacturing, 2022.

[4] J. F. Caron, A. Diaz Diaz, R. P. Carreira, A. Chabot, and A. Ehrlacher, Composites Science and Technology, 2006.

[5] A. Ehrlacher, T. Naciri, A. Chabot, and J.F. Caron, Comptes-rendus aux 9ème Journées Nationales sur les Composites (JNC9).

[6] J.F. Caron, L. Demont, N. Ducoulombier, R. Mesnil, Automation in Construction, 2021.

[7] O. Coussy, John Wiley & Sons Ltd, 2004.