Abstract
In additive manufacturing (AM), stress field drives distortion and warping and promotes delamination and cracking. Fast, accurate stress prediction is therefore essential for AM process planning and control, including real-time adaptive control, AM digital twins, data-driven and physics-driven workflows. However, spot-wise thermo-elasto-plastic finite element method (FEM) are often too slow for design iteration or real time use. Existing semi-analytical thermo-elasto-plastic approaches achieve high speed but are largely limited to 2D. In this paper, a full 3D semi-analytical thermo-elasto-plastic model for AM is built. The method uses a spot-wise analytical thermal field as the load and computes displacements and stresses via Green's function representations in a half space, with plastic flow integrated by an implicit return-mapping algorithm. A surface consistent singular integral regularization at the traction free top surface ensures stable, accurate evaluation of displacements and stresses when sources lie on or near the surface. The proposed model is validated against FEM for transient temperature fields, thermo-elastic responses, thermo-elasto-plastic stress and displacement fields, and residual stresses after cooling. Under temperature-independent material assumptions, the semi-analytical solution closely matches FEM for single-track and multi-track cases. For comparison with an FEM model using temperature-dependent material properties, the semi-analytical thermal solution reproduces the FEM temperature field when constant thermal properties are selected near 650 °C, and stress agreement improves when the temperature-dependent yield strength is updated during return mapping. The residual stress comparison shows that the model captures the dominant longitudinal residual stress and von Mises residual stress after cooling. Runtime comparisons indicate up to 1670 x speedup compared with FEM on consumer-grade hardware. The method's speed enables scalable data generation, adaptive control and optimization-oriented AM process modeling.
Recommended Citation
T. Liu et al., "3D Semi-analytical Thermo-elasto-plastic Model For Additive Manufacturing," Additive Manufacturing, vol. 127, article no. 105308, Elsevier, Jul 2026.
The definitive version is available at https://doi.org/10.1016/j.addma.2026.105308
Department(s)
Mechanical and Aerospace Engineering
Publication Status
Open Access
Keywords and Phrases
Green's function; Physics AI; Residual stress; Semi-analytical model; Stress digital twin; Thermo-elasto-plastic model
International Standard Serial Number (ISSN)
2214-8604
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Publication Date
05 Jul 2026
Comments
Intelligent Systems Center, Grant None