Determination of Aggregate Elastic Properties of Powder-Beds in Additive Manufacturing Using Convolutional Neural Networks

Authors Ardalan R. Sofi, Bahram Ravani

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Ardalan R. Sofi
  • Department of Mechanical and Aerospace Engineering, University of California at Davis, CA, USA
Bahram Ravani
  • Department of Mechanical and Aerospace Engineering, University of California at Davis, CA, USA

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Ardalan R. Sofi and Bahram Ravani. Determination of Aggregate Elastic Properties of Powder-Beds in Additive Manufacturing Using Convolutional Neural Networks. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


The most popular strategy for the estimation of effective elastic properties of powder-beds in Additively Manufactured structures (AM structures) is through either the Finite Element Method (FEM) or the Discrete Element Method (DEM). Both of these techniques, however, are computationally expensive for practical applications. This paper presents a novel Convolutional Neural Network (CNN) regression approach to estimate the effective elastic properties of powder-beds in AM structures. In this approach, the time-consuming DEM is used for CNN training purposes and not at run time. The DEM is used to model the interactions of powder particles and to evaluate the macro-level continuum-mechanical state variables (volume average of stress and strain). For the Neural Network training purposes, the DEM code creates a dataset, including hundreds of AM structures with their corresponding mechanical properties. The approach utilizes methods from deep learning to train a CNN capable of reducing the computational time needed to predict the effective elastic properties of the aggregate. The saving in computational time could reach 99.9995% compared to DEM, and on average, the difference in predicted effective elastic properties between the DEM code and trained CNN is less than 4%. The resulting sub-second level computational time can be considered as a step towards the development of a near real-time process control system capable of predicting the effective elastic properties of the aggregate at any given stage of the manufacturing process.

Subject Classification

ACM Subject Classification
  • Applied computing → Industry and manufacturing
  • Additive Manufacturing
  • Convolutional Neural Network
  • Homogenization
  • Discrete Element Method
  • Powder-Bed


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  1. K. Bagi. Microstructural Stress Tensor of Granular Assemblies With Volume Forces. Journal of Applied Mechanics, 66(4):934-936, December 1999. URL:
  2. Katalin Bagi. Stress and strain in granular assemblies. Mechanics of Materials, 22(3):165-177, March 1996. URL:
  3. H. J. H. Brouwers. Particle-size distribution and packing fraction of geometric random packings. Physical Review E, 74(3):031309, September 2006. URL:
  4. F. Calignano, D. Manfredi, E. P. Ambrosio, L. Iuliano, and P. Fino. Influence of process parameters on surface roughness of aluminum parts produced by DMLS. The International Journal of Advanced Manufacturing Technology, 67(9):2743-2751, 2013. URL:
  5. G. Casalino, S. L. Campanelli, N. Contuzzi, and A. D. Ludovico. Experimental investigation and statistical optimisation of the selective laser melting process of a maraging steel. Optics & Laser Technology, 65:151-158, January 2015. URL:
  6. Wei Gao, Yuanqiang Tan, and Mengyan Zang. A cubic arranged spherical discrete element model. International Journal of Computational Methods, 11(05):1350102, 2014. URL:
  7. Arash Gobal. An Adaptive Discrete Element Method for Physical Modeling of the Selective Laser Sintering Process. PhD thesis, UC Davis, 2017. Google Scholar
  8. Arash Gobal and Bahram Ravani. An Adaptive Discrete Element Method for Physical Modeling of the Selective Laser Sintering Process, 2017. URL:
  9. Arash Gobal and Bahram Ravani. Physical Modeling for Selective Laser Sintering Process. Journal of Computing and Information Science in Engineering, 17(2), June 2017. URL:
  10. Dongdong Gu and Beibei He. Finite element simulation and experimental investigation of residual stresses in selective laser melted Ti–Ni shape memory alloy. Computational Materials Science, 117:221-232, 2016. URL:
  11. S. Haeri, Y. Wang, O. Ghita, and J. Sun. Discrete element simulation and experimental study of powder spreading process in additive manufacturing. Powder Technology, 306:45-54, January 2017. URL:
  12. D. He, N. N. Ekere, and L. Cai. Computer simulation of random packing of unequal particles. Physical Review E, 60(6):7098-7104, December 1999. URL:
  13. George Jefferson, George K. Haritos, and Robert M. McMeeking. The elastic response of a cohesive aggregate—a discrete element model with coupled particle interaction. Journal of the Mechanics and Physics of Solids, 50(12):2539-2575, December 2002. URL:
  14. I. Kouretas and V. Paliouras. Simplified Hardware Implementation of the Softmax Activation Function. In 2019 8th International Conference on Modern Circuits and Systems Technologies (MOCAST), pages 1-4, May 2019. URL:
  15. Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet Classification with Deep Convolutional Neural Networks. In F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger, editors, Advances in Neural Information Processing Systems 25, pages 1097-1105. Curran Associates, Inc., 2012. URL:
  16. Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel. Backpropagation Applied to Handwritten Zip Code Recognition. Neural Computation, 1(4):541-551, December 1989. URL:
  17. Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278-2324, 1998. Conference Name: Proceedings of the IEEE. URL:
  18. Yann LeCun, Patrick Haffner, Léon Bottou, and Yoshua Bengio. Object Recognition with Gradient-Based Learning. In David A. Forsyth, Joseph L. Mundy, Vito di Gesú, and Roberto Cipolla, editors, Shape, Contour and Grouping in Computer Vision, Lecture Notes in Computer Science, pages 319-345. Springer, Berlin, Heidelberg, 1999. URL:
  19. Hyungtae Lee and Heesung Kwon. Going Deeper With Contextual CNN for Hyperspectral Image Classification. IEEE Transactions on Image Processing, 26(10):4843-4855, October 2017. Conference Name: IEEE Transactions on Image Processing. URL:
  20. Yousub Lee. Simulation of Laser Additive Manufacturing and its Applications. PhD thesis, The Ohio State University, 2015. URL:
  21. Xiaoxing Liu, Christophe L. Martin, Gérard Delette, and Didier Bouvard. Elasticity and strength of partially sintered ceramics. Journal of the Mechanics and Physics of Solids, 58(6):829-842, June 2010. URL:
  22. Xingchen Liu and Vadim Shapiro. Homogenization of material properties in additively manufactured structures. Computer-Aided Design, 78:71-82, September 2016. URL:
  23. G. Miranda, S. Faria, F. Bartolomeu, E. Pinto, S. Madeira, A. Mateus, P. Carreira, N. Alves, F. S. Silva, and O. Carvalho. Predictive models for physical and mechanical properties of 316L stainless steel produced by selective laser melting. Materials Science and Engineering: A, 657:43-56, March 2016. URL:
  24. Mojtaba Mozaffar, Arindam Paul, Reda Al-Bahrani, Sarah Wolff, Alok Choudhary, Ankit Agrawal, Kornel Ehmann, and Jian Cao. Data-driven prediction of the high-dimensional thermal history in directed energy deposition processes via recurrent neural networks. Manufacturing Letters, 18:35-39, 2018. URL:
  25. Zhenxing Niu, Mo Zhou, Le Wang, Xinbo Gao, and Gang Hua. Ordinal Regression With Multiple Output CNN for Age Estimation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4920-4928, 2016. URL:
  26. Eric J. R. Parteli and Thorsten Pöschel. Particle-based simulation of powder application in additive manufacturing. Powder Technology, 288:96-102, January 2016. URL:
  27. Arindam Paul, Mojtaba Mozaffar, Zijiang Yang, Wei-keng Liao, Alok Choudhary, Jian Cao, and Ankit Agrawal. A real-time iterative machine learning approach for temperature profile prediction in additive manufacturing processes. arXiv:1907.12953 [cs, stat], August 2019. arXiv: 1907.12953. URL:
  28. Xinbo Qi, Guofeng Chen, Yong Li, Xuan Cheng, and Changpeng Li. Applying Neural-Network-Based Machine Learning to Additive Manufacturing: Current Applications, Challenges, and Future Perspectives. Engineering, 5(4):721-729, August 2019. URL:
  29. Mohammad Rastegari, Vicente Ordonez, Joseph Redmon, and Ali Farhadi. XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks. In Bastian Leibe, Jiri Matas, Nicu Sebe, and Max Welling, editors, Computer Vision – ECCV 2016, Lecture Notes in Computer Science, pages 525-542, Cham, 2016. Springer International Publishing. URL:
  30. Noriko Read, Wei Wang, Khamis Essa, and Moataz M. Attallah. Selective laser melting of AlSi10Mg alloy: Process optimisation and mechanical properties development. Materials & Design (1980-2015), 65:417-424, January 2015. URL:
  31. Luke Scime and Jack Beuth. A multi-scale convolutional neural network for autonomous anomaly detection and classification in a laser powder bed fusion additive manufacturing process. Additive Manufacturing, 24:273-286, December 2018. URL:
  32. Karen Simonyan and Andrew Zisserman. Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv:1409.1556 [cs], 2015. arXiv: 1409.1556. URL:
  33. A.K. Singh and Prakash Regalla Srinivasa. Response surface‐based simulation modeling for selective laser sintering process. Rapid Prototyping Journal, 16(6):441-449, 2010. URL:
  34. Rajwinder Singh, Rahul Rana, and Sunil Kr Singh. Performance Evaluation of VGG models in Detection of Wheat Rust, 2018. Library Catalog: URL:
  35. Bo Song, Shujuan Dong, Baicheng Zhang, Hanlin Liao, and Christian Coddet. Effects of processing parameters on microstructure and mechanical property of selective laser melted Ti6Al4V. Materials & Design, 35:120-125, March 2012. URL:
  36. Ivar Stakgold and Michael J. Holst. Green’s Functions and Boundary Value Problems. John Wiley & Sons, March 2011. Google-Books-ID: 8OeoISCW6qUC. Google Scholar
  37. John C. Steuben, Athanasios P. Iliopoulos, and John G. Michopoulos. On Multiphysics Discrete Element Modeling of Powder-Based Additive Manufacturing Processes. In Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1A: 36th Computers and Information in Engineering Conference. American Society of Mechanical Engineers Digital Collection, 2016. URL:
  38. Tian Wang, Yang Chen, Meina Qiao, and Hichem Snoussi. A fast and robust convolutional neural network-based defect detection model in product quality control. The International Journal of Advanced Manufacturing Technology, 94(9-12):3465-3471, February 2018. URL:
  39. Daniel Weimer, Bernd Scholz-Reiter, and Moshe Shpitalni. Design of deep convolutional neural network architectures for automated feature extraction in industrial inspection. CIRP Annals, 65(1):417-420, January 2016. URL:
  40. Yangzhan Yang, Madie Allen, Tyler London, and Victor Oancea. Residual Strain Predictions for a Powder Bed Fusion Inconel 625 Single Cantilever Part. Integrating Materials and Manufacturing Innovation, 8(3):294-304, 2019. URL:
  41. Bodi Yuan, Brian Giera, Gabe Guss, Ibo Matthews, and Sara Mcmains. Semi-Supervised Convolutional Neural Networks for In-Situ Video Monitoring of Selective Laser Melting. In 2019 IEEE Winter Conference on Applications of Computer Vision (WACV), pages 744-753, January 2019. ISSN: 1550-5790. URL:
  42. Chen-Lin Zhang, Jian-Hao Luo, Xiu-Shen Wei, and Jianxin Wu. In Defense of Fully Connected Layers in Visual Representation Transfer. In Bing Zeng, Qingming Huang, Abdulmotaleb El Saddik, Hongliang Li, Shuqiang Jiang, and Xiaopeng Fan, editors, Advances in Multimedia Information Processing – PCM 2017, Lecture Notes in Computer Science, pages 807-817, Cham, 2018. Springer International Publishing. URL:
  43. Z. Zhang, Z. J. Tan, X. X. Yao, C. P. Hu, P. Ge, Z. Y. Wan, J. Y. Li, and Q. Wu. Numerical methods for microstructural evolutions in laser additive manufacturing. Computers & Mathematics with Applications, 78(7):2296-2307, October 2019. URL:
  44. Anwen Zhu, Xiaohui Li, Zhiyong Mo, and Ruaren Wu. Wind power prediction based on a convolutional neural network. In 2017 International Conference on Circuits, Devices and Systems (ICCDS), pages 131-135, September 2017. URL: